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highbush cranberry (Viburnum edule)
Posted by Delena Rose in forage, tea, wild berries
berry picking, harvest, highbush cranberry, mooseberry, swampberry, wild berries, wild cranberry
Today I spent the afternoon picking highbush cranberries up the road near the cabin. I hunted for them last October when I first moved in and was only able to harvest a handful of the last berries of the season. The leaves had already fallen and some of the shrubs still had a few of the red berries, hanging like little shining jewels. Having never picked them before, I had to approach an elderly neighbor walking down the road and ask him to peer into my basket and confirm whether or not these were indeed highbush cranberries. He ended up bringing me home to his wife who confirmed the identity of the berries and told me where to find more. This time around, almost a year later, I knew just where to look and was not disappointed!
Highbush cranberries are also known as crampbark, squashberry and mooseberry. The name ‘cranberry’ is deceiving as they are not true members of the heath family, but instead belong to the honeysuckle family.
This deciduous shrub can be found across Canada and in the northern United States growing in the woods or along riverbanks and streams. Ideally they prefer moist, acidic soil in partial shade. The shrub may grow up to 8 feet tall and has smooth reddish bark and opposite three-lobed leaves. In spring, small white flowers grow in clusters. By late summer, the small red globular berries, each containing a single flat seed, can be harvested.
When the berries are still unripe, they are hard, very sour and may give off an unpleasant musty odor, described by a few of my neighbors as ‘stinky socks’. After the first frost, they become soft, juicy and more palatable. You can use the bark, inner bark and berries.
The bark contains calcium, chromium, cobalt, iron, magnesium, manganese, phosphorus, potassium, selenium, tin and zinc. The berries are high in vitamin C and K.
Pick the berries late in the summer or in early fall, after the first frost, when they are soft and juicy. The bark should be harvested before, or after the plant has gone into berry.
Medicinal Uses:
Antispamodic (due to a bitter compound called viburnine)- the bark helps stop stomach, muscle and menstrual cramps. Also relieves cramping of the uterus after childbirth. To prepare, whittle off some of the bark and simmer it into a tea or poultice.
Sedative
To treat bronchial irritation and spasmodic coughing
As a gargle for sore throats and as a rinse for gingivitis
Culinary Uses:
Mainly in syrups and jelly (where straining removes the seed)
Make tea: crush 1/2 cup berries, add 2 cups boiling water. Steep, strain. Sweeten with honey.
Use the jelly on toast or on thumbprint cookies or as a condiment served with wild game
Bennett, J. (1991). Berries. Camden House: Camden East, ON.
Gladstar, R. (2001). Rosemary Gladstar’s Herbal Recipes for Vibrant Health: 175 teas, tonics, oils, salves, tinctures, and other Natural Remedies for the Entire Family. Storey Publishing, North Adams, MA.
Gray, B. (2011). The boreal herbal: wild food and medicine plants of the north; a guide to harvesting, preserving, and preparing. Aroma Borealis Press: Whitehorse, Yukon.
6 thoughts on “highbush cranberry (Viburnum edule)”
Frieda said:
I never heard of high-bush cranberries before.
The island where we came from had wild low bush cranberries that my parents picked and they made jelly, juice etc. Very nutritious!
The history of that was that a ship had stranded and a barrel of cranberries was opened on the beach and the birds took the seeds to the dunes and now there are enormous patches of cranberry bushes. Terschelling ( the island) is famous for them.
cabinorganic said:
I love that story! Does anyone on Terschelling make cranberry products for export, I wonder? Oh, Frieda, did you get your jam? I sent some home with Cheryl for you… Lots of love in there!
Pingback: wild highbush cranberry compote (Viburnum edule) « cabinorganic
Yes, There is big business of cranberry products on the island. They make tea, wine, jam, syrop and more different products that go to different stores on the main land.
There is also a cranberry museum, with the history and video’s how they make the products and you can taste them there too. Lots of tourists gather there in the summer.
No, I have not talked to Cheryl yet, but that’s so sweet of you to send some homemade jam along. I’m looking forward to that, made with love, it sounds wonderful.
Pingback: highbush cranberry jelly & thumbprint cookies « cabinorganic
tina peterson said:
Here in Fairbanks we have “high bush cranberries” which are related to honey suckles. What we call “low bush cranberries” are vaccinium vitis idaea, and are called Lingonberries in Europe. I refer to them as red blueberries, because they are most closely related to blueberries, also vaccinium. Then there are the “bog cranberries” which have a long stem and tiny leaves, about the size of a nail clipping from a newborn baby. Usually you just see the berry sitting alone on a bed of sphagnum moss. Those are oxycoccus microcarpus, which are the only real cranberries (oxycoccus) we have in Alaska.
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Home > New Jersey > Spectrum Columbia, NJ
Guide to Buying Spectrum in Columbia, NJ!
If you’re wondering how to get the very best Internet, TV and Voice services in Columbia, New Jersey, look no further than Spectrum. Spectrum in Columbia, NJ offers the fastest Internet speeds, the most comprehensive selection of programming (both live and recorded) and the widest array of digital voice services. It’s simply an unparalleled combination of features and functionality, all offered at very affordable prices. Many consider Spectrum in Columbia, NJ to be the best in the business.
Here are just 11 of the reasons why you should buy Spectrum Packages in Columbia:
If you’re like most people, you want the fastest possible Internet connections – and that’s exactly what Spectrum Internet Plans in Columbia, NJ delivers. Internet speeds start at 60 Mbps, which is incredibly fast. That’s 20 times faster than traditional DSL, and it’s plenty fast for all of your browsing, streaming, downloading and video game playing needs.
With 60 Mbps speeds, your household can enjoy everything high speed Internet has to offer. You also don’t have to worry about several people using the Internet at once, since there’s more than enough bandwidth to go around. Anyone using Spectrum Internet in Columbia gets those super-fast 60 Mbps speeds.
You’ve probably heard horror stories about Internet hackers stealing personal identities, or breaking into computers to steal sensitive financial information. Well, you don’t have to worry about that when you use the best-in-class security software offerings from Spectrum Internet in Columbia, New Jersey.
Spectrum TV in Columbia, NJ offers an incredible variety of sports, news, kids’ programming and entertainment shows. There are three different tiers of Spectrum TV – Select, Silver and Gold. With Select, you get over 125 channels, including many in HD. With Silver, you get over 175 channels, and with Gold, you get over 200 channels.
You can immediately see why Spectrum TV in Columbia divides up these channels the way they do – it makes it easier for households to pick just the right package. For example, if you’re a major “Game of Thrones” fan or you enjoy watching fast-hitting NFL action on Sundays, then the Silver package is a must-have. And if you’re a real movie enthusiast, or if you’re a hard-core football fan, you’ll almost certainly want to upgrade to the Gold plan.
And there’s one more very interesting option with Spectrum TV in Columbia, New Jersey, and that’s the unbridled access to Pay Per View (PPV) offerings. Usually, these are events like wrestling matches, UFC matches and boxing matches. In the old days, you might have needed to fly into Las Vegas to watch these premium events.
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When you sign up for a Time Warner Cable package, you are in good hands. That’s because Spectrum in Columbia, NJ always puts the customer first. Here’s just one basic example: Spectrum is now offering a 30-day money-back guarantee.
Yes, each of the offerings from Spectrum in Columbia, NJ – TV, Internet and Voice – is quite impressive, as you can see above. However, the true power and functionality comes from bundling them all together. By combining TV and Internet, you get access to on-the-go TV content.
See? You can think of the bundle as not only bundling different services (e.g. Internet and Voice), but also bundling TV channels for you. Your goal is to get the biggest bundle possible (who wants one of those “skinny” bundles?), and that’s what Time Warner Cable in Columbia, NJ makes possible.
In short, Spectrum in Columbia offers best-in-class Internet, TV and Voice offerings for households across the nation. And, best of all, by bundling them together, you can get the best prices available that are affordable for every budget! Spectrum is one of the best in business.
So what are you waiting for? Spectrum in Columbia, New Jersey now offers a 30-day money-back guarantee. And the company is also willing to cover up to $500 in early termination fees, so it’s easy to switch from your current service provider.
FAQ Spectrum Columbia, NJ
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You can order Spectrum TV and Internet services in Columbia, NJ by calling 1-855-345-0205.
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Anomaly [sound recording] / Lecrae.
Lecrae (Musician) (Performer). Mineo, Andy. (Performer). Crystal Nicole. (Performer). Jobe, Kari. (Performer). Bowie, Dustin. (Performer). Prielozny, Joseph. (Performer). Davidson, David (Violinist) (Performer, Arranger). Catchings, John. (Performer). Wilkinson, Kristen. (Performer). Angell, David (Violinist) (Performer). S1 (Musician) (Performer). Lettieri, Mark. (Performer). Epikh Pro (Musician) (Performer). Chizari, Sal. (Performer). McDowell, Dimitri. (Performer). Sims, Natalie. (Performer). Hawkins, Danika. (Performer). Rice, Dirty. (Performer). Lawrence, Demonterious. (Performer). Ghosh, Robin. (Performer). N'Dambi. (Performer). Speer, Mark. (Performer). Jones, Melvin (Horn player) (Performer). Burton, Mike (Horn player) (Performer). Williams, Wilbert, trombonist. (Performer). Swoope (Allen Swoope) (Performer). Sean, Caleb. (Performer). J. Paul (Musician) (Performer). Catour, Tasha. (Performer). Crawford, Sean (Guitarist) (Performer). Rashel, Kasey. (Performer). Robinson, Nate. (Performer). For King & County (Musical group) (Performer).
Physical Description: 1 sound disc (58 min.) : digital ; 4 3/4 in.
Publisher: [S.l.] : Reach Records, [2014]
Credits (2 booklets) inserted in container.
Outsiders -- Welcome to America -- Say I won't (feat. Andy Mineo) -- Nuthin -- Fear -- Anomaly -- Timepiece -- Dirty water -- Wish -- Runners -- All I need is you -- Give in (feat. Crystal Nicole) -- Good, bad, ugly -- Broken (feat. Kari Jobe) -- Messengers (feat. For King & Country).
Lecrae, rap vocals ; with featured performers.
Subject: Christian rap (Music)
Contemporary Christian music.
Popular music > 2011-2020.
Outsiders / Dustin "Dab" Bowie, Torrance Esmond, Kenneth Chris Mackey, Lecrae Moore, Joseph Prielozny.
Welcome to America / Lecrae Moore, J. Rhodes.
Say I won't / Gabriel Azucena, Matt Massaro, Andy Mineo, Lecrae Moore, Tyshane Thompson.
Nuthin / Gabriel Azucena, Michael Marshall, Dimitri McDowell, Andy Mineo, Lecrae Moore.
Fear / Kenneth Chris Mackey, Lecrae Moore, Joseph Prielozny, Natalie Sims.
Anomaly / Lecrae Moore, N'Dambi, Nate Robinson.
Timepiece / Serge Gustave, Mashell Leroy, Lecrae Moore.
Dirty water / Lecrae Moore.
Wish / J. Griffin, Lecrae Moore, Joseph Prielozny.
Runners / Gabriel Azucena, Lasanna Harris, Lecrae Moore.
All I need is you / Dustin "Dab" Bowie, Kenneth Chris Mackey, Lecrae Moore, Joseph Prielozny, Latasha Williams.
Give in / Gabriel Azucena, Crystal Johnson, Alex Medina, Lecrae Moore.
Good, bad, ugly / Jhaun Downer, Lecrae Moore, Kasey Sims.
Broken / Cody Carnes, Kari Jobe, Kenneth Chris Mackey, Lecrae Moore, Joseph Prielozny, Latasha Williams.
Messengers / Torrance Esmond, Ran Jackson, Ricky Jackson, Kenneth Chris Mackey, Lecrae Moore, Joseph Prielozny, Joel Smallbone, Luke Smallbone.
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Comment Opinion & Features
The moral theory that failed – but is now back in fashion
Fr Thomas Berg
Vatican II (CNS)
You don’t have to be a Catholic theologian, journalist or even that much of a Church-watcher to understand that there has been a battle afoot during the Francis pontificate. It is a struggle for hegemony between two competing accounts of morality. That conflict has been notably more pronounced in the past three years with often very public manifestations.
From the promulgation of the apostolic exhortation Amoris Laetitia and the ensuing firestorm over what exactly it implied about Holy Communion, divorce and remarriage; to the reconstitution of Rome’s John Paul II Institute, the unprecedented firing of two tenured faculty members and the hiring of two moral theologians known to challenge the Church’s teaching on contraception and homosexuality; and to the German bishops, led by Cardinal Reinhard Marx, embarking upon a “synodal process” apparently contrary to Pope Francis’s wishes, and unmistakably aimed at rethinking priestly celibacy and certain of the Church’s teachings on sexual morality. It’s all connected.
It’s a final push by a bloc of grey and ageing moral theologians and like-minded bishops to attain hegemony for their brand of moral theology, namely, Proportionalism.
Proportionalism is an umbrella term that groups together several approaches to moral theology that broadly share certain beliefs about human nature and the moral life.
Each is a version of an “ends justify the means” approach to moral problem solving. Proportionalism offers the possibility of engaging in a moral calculus of values which, presupposing a good intention or sufficiently weighty reason in the moral actor, could potentially validate any action – even those which Sacred Scripture and the Church’s perennial moral teaching have held to be intrinsically evil.
Proportionalism flourished in the three decades spanning the 1960s through the 1980s and dominated Catholic seminaries and moral theology departments on both sides of the Atlantic, particularly in Germany and then notably in the United States. It was the theoretical vehicle justifying theological dissent from St Paul VI’s teaching on contraception in Humanae Vitae. And it quickly became clear that Proportionalism could justify much more.
Many of the world’s bishops today were schooled as seminarians in Proportionalism. Not all embraced it, but many undoubtedly did, and their own understanding of Christian moral life was deeply affected by their exposure to it.
In addition to its radically autonomous concept of moral conscience (I – and only I – decide what’s right and wrong), Proportionalism follows many of the other contours of the modern moral zeitgeist: the subjective trumps the objective, conscience trumps the norm, a good intention trumps intrinsic malice. The theory presumes that virtually all human moral experience is so irreducibly complex that no one moral norm could possibly be generated over time to respond to each situation, and no behaviour in itself could be understood as always immoral in all circumstances.
Pope St John Paul II felt the urgency of responding to the fundamental tenets of Proportionalism, tackling them 26 years ago in the encyclical Veritatis Splendor. In paragraphs 54-64, he rejected the notion of conscience as autonomous decision, and in paragraphs 74-83, he refuted Proportionalism’s denial of intrinsically evil acts.
For his part, Pope Emeritus Benedict XVI has been unrelenting in his critique of Proportionalism, describing it as a moral theory detached from metaphysical moorings, “deaf and blind to the divine word in being” and a moral theory “that contradicts the very foundations of the Christian vision” He’s even gone so far – on more than one occasion – as to suggest that Proportionalist ideas are at least partly to blame for the clerical abuse crisis.
That notwithstanding, Proportionalism has had a broad appeal among progressive Catholics. Its veneer of eminent reasonableness, resulting primarily from its submissiveness to the secular moral zeitgeist, is also enhanced by the circumstances of history.
Proportionalism was a theological reaction to an older method of doing and teaching moral theology which had held sway in Catholic seminaries from the late 16th to the mid 20th centuries. That method – casuistry, sometimes referred to as manualism – while providing the Church with plenty of sound moral theology, also engendered a legalistic approach to the moral life which sapped moral truth of its richness and Christ-centered vitality.
With good reason Vatican II called for a renewal in the teaching of moral theology: a robust rooting of moral teaching in Sacred Scripture and a new emphasis on virtue, on the Beatitudes and on Christ-centred discipleship.
And there were some good steps taken in that direction. Yet, by and large, much of mainstream Catholic moral theology caved in to the cultural onslaught of the 1960s. And in that milieu, the first Proportionalist theories proliferated.
We can only be grateful that many among a new generation of theology students in the early-to-mid 1990s began to take a pass on the Proportionalism they continued to be taught in their moral theology courses. If the theory continues to exercise an influence today, it does so principally through an older generation of priests and bishops who stubbornly cling to it, while rejecting the teaching of Veritatis Splendor.
It’s not surprising then that over the decades a certain narrative has arisen around Proportionalism, contrasting its adherents with a caricature of its opponents. Adherents are reasonable and balanced; opponents are rigid and extreme. Proponents employ sound moral “discernment” in order to understand the specific situation of the individual; opponents do not. Proponents are pastorally realistic and sensitive; opponents not so much.
Pope Francis, for his part, has shown sympathy for that narrative. One can only assume that this is because he has been exposed to Proportionalism for much of his life. When Pope Francis speaks of priests who turn the confessional into a “torture chamber,” or who pharisaically “indoctrinate the Gospel”, converting its life-giving message into “dead stones to be hurled at others”, he might simply be referring to the older manualist approach to the moral life. But it also serves to reinforce the Proportionalist narrative.
The latest twist to the narrative holds that a cabal of American conservative Catholics is threatening schism with Francis or at least trying to undermine his pontificate. If Proportionalist loyalists have chosen to weaponise the notion of schism, maybe it’s because they are getting desperate.
Nonetheless, the German Church’s “synodal process”, along with the Amazon synod in Rome, present a cadre of progressive bishops, theologians and journalists with fresh opportunities to continue to press the Pope for an unambiguous endorsement of Proportionalism-inspired reworking of Catholic moral teaching – beyond the tacit endorsement some would speculate he has already granted.
Fr Thomas Berg is vice rector and professor of moral theology at St Joseph’s Seminary (Dunwoodie) in Yonkers, New York. He is author of Hurting in the Church: A Way Forward for Wounded Catholics (Our Sunday Visitor, 2017)
Why exorcism went out of fashion – and why it’s back
Matthew Schmitz
After years as the ‘Hotel Inspector’, I’m going back into the business myself
Alex Polizzi
Cranmer’s accidental gift to Catholics
Why you should read St Augustine’s Confessions this year
Benedict and Sarah back Francis’s position on priestly celibacy. Media storm ensues
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Little Women: much more than a feminist screed
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Planned Parenthood is worried. And it should be
What the ‘State of the World’ address reveals about the state of the Church
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Archbishop speaks to Jewish community at Hanukkah
Archbishop Chaput’s 2019 Christmas message
Irony and Catholic memory
DACA and our future
Safe injection sites: A dose of despair
Domestic violence and our respect for life
Archbishop Chaput's column
The epidemic and its cure
Archbishop Charles Chaput, O.F.M. Cap.
I’ve always loved the movies, and one of the scariest films in recent memory is 28 Days Later, released in 2002. The plot is simple. Animal-rights activists break into an experimental disease lab in Britain. They free a group of innocent test monkeys from their cages. That’s the good news.
The bad news is that the monkeys are infected with a weaponized, fiercely communicable rage virus. The monkeys attack their liberators. The humans immediately catch the virus. They then attack each other and anyone else they can grab. The virus spreads geometrically. It burns through the population like a gasoline fire. A month later, civilization in the United Kingdom has collapsed. The few remaining healthy humans struggle to survive while eluding the infected.
If that story line sounds vaguely similar to the tone of our national discourse over the past 10 months, it should. We’re not yet tearing at each other with our teeth. But the irrational fury on our campuses, in the streets, in our news media, and in our larger political and cultural debates leads inevitably in that direction. When ESPN feels compelled to pull an Asian-American commentator named Robert Lee from covering a University of Virginia football game for his own safety and to avoid offending others, we’re well beyond the realm of the strange and into the surreal.
It’s easy, and warranted, to blame the White House for our current toxic national atmosphere. President Trump, with his baffling manner and lack of self-control, has earned a healthy portion of the blame. But there’s more than enough blame – a lot more than enough – to go around. “Hate has no home here” is an admirable theme for one of today’s most popular lawn sign campaigns. But its message simply isn’t true. Hate does have a home here. It’s welcome and very well-fed in a lot of our hearts, regardless of our political allegiances. And our refusal to admit that is part of the problem.
When an organization like the Southern Poverty Law Center labels a mainstream religious liberty advocate like the Alliance Defending Freedom (ADF) as a “hate group” it’s simply betraying its own bitter contempt for the people and convictions the ADF defends. So yes, hate has a home here alright: not just among white nationalists, immigrant-haters and neo-Nazis, as loathsome as their ideas are, but also among the “progressive” and educated elites who have the power to insulate themselves from the consequences of their own delusions and bigotries.
The reason the Church names anger as one of the seven “deadly” sins is because it’s simultaneously so poisonous, so delicious, and so addictive. Anger congeals quite comfortably into hatred. In C.S. Lewis’s novel The Great Divorce, the damned cling jealously to their anger (among other sins) because it’s so reassuring; so satisfying and self-justifying. The point is, people easily begin to like being angry. Wrath feels good, especially when the ugliness of the habit can be dressed in a struggle against real or perceived evils.
Christians aren’t the first to notice this terrible truth. The great Roman Stoic philosopher Seneca, writing in the First Century A.D., put it this way:
“[Anger] is the most hideous and frenzied of all the emotions. The others have something quiet and placid in them, whereas anger is all excitement and impulse. Raving with a desire that is utterly inhuman for instruments of pain and reparations in blood, careless of itself so long as it harms the other, it rushes onto the very spear points, greedy for vengeance that draws down the avenger with it.”
Anger “is greedy for punishment” and a kind of “brief insanity” as Seneca says elsewhere. It first deforms and then destroys the person and the culture that cultivate it. If that’s true – and it clearly is – America 2017 is urgently in need of a healing. We’re a culture addicted to anger. And we’re relentlessly reinforced in it by mass media that compulsively feed our emotions and starve our reason.
Here’s a final thought from Seneca:
“Human life rests upon kindness and concord; bound together, not by terror but by love reciprocated, it becomes a bond of mutual assistance.”
Those are beautiful words, and true. They’re not far from the deeper truths of the Gospel. But they’re also empty words unless we live them. That will demand from us a holy skepticism about the bad things we hear and see and assume about our perceived enemies. Our “enemies” are people like us, whatever their ideas and identities. And they have a right to our patience, restraint and respect, whatever the cost – just as we have a right to demand the same from them.
It’s not easy work, but it needs to start somewhere. It should start with us.
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Dr. Don says:
Virginia Smith is wrong. Mrs. Clinton is a terrible candidate. Abortion is the worse of the 2 evils. We are very generous , as a country. Our churches give massive amounts of time, treasure and talent to the poor.
Donna Jorgenson Farrell says:
If we continue this pattern of — pardon the expression — whitewashing our history, we will doom ourselves to repeat the mistakes of the past. Archbishop Chaput is just the kind of leader we need to begin the process of getting out of this mess. He is so correct that we begin by loving and respecting one another. We need to recognize that God gave us this world, and the only way we can express our gratitude is by working together to make it a harmonious place for all. Thanks, Archbishop, it does indeed begin with each of us in our individual lives. Little things with great love, as St. Mother Teresa of Calcutta told us. We can build a better environment for all.
Michelle McDermott says:
Thank you Archbishop Chaput for your wisdom.
I am concerned about our whitewashing history and rewriting it, because that’s the best way to guaranty that we will repeat the same mistakes again. Anger is usually a result of hurt. We need to stop hurting each other and love instead. I pray that we will wake up before we destroy our beautiful God-given world. I appreciate you, Archbishop Chaput, for reminding us that we must make changes in our attitudes and actions.
Gerhard Leipzig says:
“.. bitter contempt for the people and convictions the ADF defends.”
Bishop, once James Dobson finishes up with the Homosexual Menace, he’s coming for the Catholics. But I’m sure you’ll have a security detail to separate you from the hate.
Virginia smith says:
The only thing I’m angry and feel betrayed about is that the Catholic Church, my church, supported an incompetent ego maniac in this last election. How could you put aside all our moral compass to vote for an immoral and unethical man only because of one issue. Abortion. I am pro life but I will not sell my soul and my country for it at the cost of everything else I hold dear. There are other ways to counteract abortion. And the truth is he is only pro life as it is convenient and effective to be pander to the religious vote. How many women has he suduced? How many abortions has he bought? Read his history. We can work on this issue in many other ways. And really, what has changed? Nothing now, nothing later and we have a disaster waiting to happen
You mention anger. This president encourages anger, uses it and wants to divide us in ways that are useful to him. He brings out the WORST in us for his advancement. True leaders will bring out our best. So what do we do now?
I respect this essay but it seems to me too weak to be effective. Only when one accepts responsibility, and in case the Catholic Church, for contributing greatly to the situation, only then can change begin. Good people have to clearly state they were wrong and work for change. Believing any organization can control someone to further their goals is always a mistake. There are ethical and moral ways to effect change. Congress thought they could manage trump for their own aims: budget, etc and this church thought the same thing for abortion. How foolish is that.
I had a professor who used to say the fish stinks from the head. Our country is definitely smelling worse right from the top. I am outraged and disappointed in my church for supporting this travesty. When we meet Jesus one day, he isn’t going to ask us how we voted and how many times we marched against abortion. He will ask us how we treated the least of our brothers and each other’s. He’s going to ask us about compassion and our goodness. How did we help combat the sadness in this world? God bless us all❤️
Gerard J. St. John says:
The writer does not like those of us who elected Donald Trump President of the United States. But the author does not consider the persons or the issues that brought about that result. For example, what was the alternative to a vote for Trump? Hillary Clinton? The “response” does not even mention Hillary Clinton. Nor does the response mention the significant efforts of the previous presidential administration to narrow the scope of the First Amendment to the Constitution with respect to freedom of religion. It is not hard to imagine that a “Clinton Presidency” would likely nominate Supreme Court justices who would continue to narrow the rights of religious-minded citizens. And by the way, I am not about to apologize for riding down to Washington, D.C. on several occasions to protest the Supreme Court’s terrible decision in Roe v Wade.
I have been a registered Democrat for sixty years, and have been active in many elections. The Democratic Party walked away from me. I do not take these issues lightly.
Robin Fisher-Terry says:
I couldn’t have said it better myself. All of your points are valid and need to be taken into account as we deal with the bigotry this president supports and foments. Thank you for writing this, a Methodist sister-in Christ.
For starters, the Church in this country didn’t unanimously support Donald Trump. Secondly, there’s a false dichotomy you’re presenting between marching against abortion and caring for the least of our brothers and sisters. The unborn children in danger of being aborted ARE the least of our brothers and sisters. Without the right to be be born, all other rights are worthless, including the right to food, clothing, shelter, medical care and the rest of it. Stop putting all the blame for what’s wrong with the world on the president of the US and recognize that conversion begins by looking in the mirror and asking yourself: What can I do to more closely imitate Jesus Christ? That’s where the real change starts, by comparing ourselves to Christ instead of to one another.
Bill Sweeney says:
Thank you for your wisdom and your willingness to articulate it. Nice to see a quote from Seneca as well.
R L Oerman says:
I was directed to this site interested in what I knew to be the cure but curious to find what is being stated here.
The cure to the question is not SELF and our efforts, but is CHRIST and trust and faith in him. Our efforts are feeble at best without His direction and His strength guiding them.
This answer is weak … our power comes from Him, it’s not of an internal origin.
Ted Bochanski says:
Great observation of a long simmering delima which has since boiled over and become as you say “surreal”.
The irony of the “no hate signs”, is the very erection of them is the manifestation of anger and hate which ignores the insult to homeowner’s closest neighbors. But sadly the owners of these signs are blinded by their anger.
If researched, I believe you would find an inverse proportion over the last 5 decades between weekly participation in religious services and anger and violence in our world. Many people will say, “I don’t need to go to church to speak to God”, while this certainly is true, gathering in Christ’s Name gives us the physical connection with our neighbors we so desperately need.
My next-door neighbor, a fellow Catholic, has an anti-hate sign in his front yard. He and his wife are strongly pro-choice and opposed Trump (and all pro-life Republicans) because they hope for some medical-breakthrough coming from fetal research. Good Catholics, they do attend Sunday Mass, and love the sermons. In our discussions, they don’t see the disconnect between the killing of millions of children, and their Catholic faith. They voted for Ms Clinton, knowing her strident, pro-abortion views. The Church must do a better job.
Gregory Sadler says:
I’d agree that anger is involved in many ways in our current political environment, and it has been worsening for several decades.
I’d also point out that anger, when well understood and properly directed, can play a useful role in political life (as well as in many other areas). Not all anger is vicious, for thinkers like Aristotle, Augustine, and Thomas Aquinas (while for Stoics, like Seneca, and some Christian thinkers like John Cassian, all anger is vicious).
Here’s a talk series on classic views on anger that some of your readers may be interested in viewing – starting with Greek drama and epic and ending with Thomas Aquinas – https://www.youtube.com/playlist?list=PL4gvlOxpKKIgDHsCEZq4gk2R8TGTMJajH
Sister Pamela Smith, SSCM says:
Archbishop Chaput, thank you for your words of reason and challenge
Christopher Mottes says:
Thank you, Archbishop Chaput. It is helpful indeed in the midst of such conflict, to find a path of love and peace.
Anger at what the progressive and educated elite have done to our society is justified. Not hate, but righteous anger. That’s why the 2016 Election turned out the way it did. The majority of Bishops I would place in that progressive and educated elite camp. Archbishop Chaput at least being an honest broker. The headlines on this website are a daily diatribe against President Trump. Thank goodness for his election as the alternative would have been unthinkable for the traditional values that made this country a success.
Jean Pierre says:
Excellent reflection. Anyway we can get this to the mass media? Probably nott because it doesn’t fit there narrative.
Beth Wright says:
Thank you for this message. It is frightening how people would rather rant and rave rather than discuss and dialogue
A Ramos says:
I wish you could put this on the mass media. No one is listening to reason. I have experienced this anger/hatred with people very close to me and find it so hard to not respond in a similar way. I just keep praying for sanity.
Theresa Haggerty says:
Powerful statement, thank you! You are correct, we are addicted to anger (and angst, and fear-mongering).
John Hughes says:
Refreshing common Sense on social media
We definitely need more common sense in our lives. We must also practice common sense
Violence and Hatred lead us down a very very dangerous path where you will find no peace and tolerance just more violence and Hatred
Surly we can use our own intelligence and find a way to peace and yes Forgiveness too
Mason Yost says:
“Of the Seven Deadly Sins, anger is possibly the most fun. To lick your wounds, to smack your lips over grievances long past, to roll over your tongue the prospect of bitter confrontations still to come, to savor to the last toothsome morsel both the pain you are given and the pain you are giving back–in many ways it is a feast fit for a king. The chief drawback is that what you are wolfing down is yourself. The skeleton at the feast is you.” Frederick Buechner
Excellent message! May God Bless our Archbishop!
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Clutch Authority Store
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Cavs promote Mike Gerrity to director of player development
Virgil Villanueva
Mike Gerrity, who started out part of the Cleveland Cavaliers’ video staff, has been promoted to the Cavs’ Director of Player Development and assistant coach.
As reported by Dave McMenamin of ESPN:
Mike Gerrity, who I've seen give the business to more than a few Cavs over the years in 3-on-3 games, has been promoted to director of player development/assistant coach in Cleveland, sources tell ESPN. The former USC Trojan/D-League player worked his way up thru the video staff
— Dave McMenamin (@mcten) July 17, 2018
Gerrity has been with the Cavaliers organization since 2014, starting out as an assistant video coordinator. The following year, he was then promoted to assistant coach. Come 2016, Gerrity became the player Development Assistant. In the same year, he was promoted to Director of Player Development of the Cavaliers’ G League Affiliate, the Canton Charge.
Before starting out his career as part of a team’s coaching staff, Gerrity was starred at USC on the hardwood. His high school coach complimented his work ethic, per Arash Markazi of ESPN:
“Few people have the drive he has,” said Mater Dei High School basketball coach Gary McKnight, who started Gerrity all four years, making him only the second player to do so at the perennial prep powerhouse in Santa Ana. “Some people talk about shooting 500 times a day, Mike’s the kind of guy who doesn’t leave until he makes 500.”
NBA legend and former USC coach Paul Westphal noted Gerrity’s skills as a point guard and his overall passion:
“Mike has always been a true point guard. His teams won and he got the ball to the players who needed to get the ball. He penetrated defenses and broke presses easily. He’s one of the most driven players I’ve ever coached.”
Indeed, Gerrity has come a long way. A look back at this past reveals that he deserves his recent promotion.
JUST IN: Collin Sexton’s ‘Super Saiyan defense’ draws attention from Jaren Jackson Jr.
Related TopicsCavaliersMike Gerrity
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Copyright © Cavs Nation. Partner of iOne Digital / Cassius Network.
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McDonald’s launches popular breakfast across restaurants in North and East India
McDonald’s breakfast will also be available through McDelivery...
ETBrandEquity
McDonald’s has launched its popular breakfast across restaurants in North and East of India. The menu offers a choice of breakfast options such as Veg McMuffin, Egg & Cheese McMuffin, Sausage McMuffin, Egg & Sausage McMuffin, Hot cakes, Hash brown along with coffee and available beverages.
Ajita Saxena, director – marketing, McDonald’s, North and East India, said, “Our customers are at the core of everything that we do at McDonald’s. We have been receiving continuous customer feedback to bring the breakfast menu back in North and East of India. We are excited to launch breakfast with a variety of menu items. We look forward to their continuous patronage."
According to the company, currently, select restaurants across North and East of India will serve breakfast between 8am to 11am with extended timings in highway Drive-thru restaurants. McDonald’s breakfast will also be available through McDelivery. Adding delight to the mornings, McDonald’s is offering the choice of a complimentary beverage with Veg McMuffin or Egg & Cheese McMuffin (offer until 31 Jan 2020). Additionally, dine-in customers can enjoy unlimited coffee refills during breakfast hours, the company added.
Connaught Plaza Restaurants
Ajita Saxena
Marketing / 2 hours ago
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Camila Morrone shuts down cruel comments about relationship with Leonardo DiCaprio
By Britt Middleton| 6 months ago
Camila Morrone isn't letting the haters get her down.
The 22-year-old actress spoke out after trolls left hurtful comments on an Instagram post she shared on Friday, which depicted several black-and-white photos of late Hollywood icons Lauren Bacall and Humphrey Bogart. Bacall and Bogart notably had a 20-year age gap, which is the same as she and DiCaprio, 44.
A love like this
A post shared by Camila Morrone (@camilamorrone) on Jul 25, 2019 at 7:37pm PDT
Morrone captioned the photos, "A love like this," leading some of her followers to believe that she was comparing her relationship with DiCaprio to Bacall and Bogart's.
"I feel sorry for her," one person wrote.
"You only have a couple more years before he dumps you girl!" wrote another.
Added another follower: "What he has with you is not love."
Camila Morrone shut down cruel comments on her Instagram Story. (Instagram)
On her Instagram Story, the Mickey and the Bear actress clapped back at those naysayers.
"I just read some of the comments on my Instagram and… my God, people are so mean and full of anger with people that they know nothing about," she said. She expressed that she hoped "people learn to live with a little less hatred and place their time and interests elsewhere, because living without hatred feels pretty good."
Leonardo DiCaprio unveils 'Once Upon a Time in Hollywood' poster
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Russell Crowe got drunk and bought a dinosaur head from Leonardo DiCaprio
This week, Morrone accompanied DiCaprio to the red carpet premiere of his new film, Once Upon a Time in Hollywood in Los Angeles. To commemorate the night, she shared a photo of herself wearing a strapless, satin white gown to Instagram, which she captioned simply, "Tonight."
tonight 💎
The pair have been romantically linked for the past year, and according to an E! News source, it's getting "serious."
Leonardo DiCaprio and his girlfriend Camila Morrone, below DJ Snake attend the UEFA Champions League Group C match between Paris Saint-Germain (PSG) and Liverpool FC at Parc des Princes stadium on November 28, 2018 in Paris, France. (Getty)
"They've been inseparable for the last year and are crazy about one another," the source said. "They've gotten to know each other's families and they love being together."
Celebrity couples who have huge age gaps but are more loved up than ever
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COVER REVEAL: Only a Breath Apart by Katie McGarry
June 21, 2018 June 20, 2018 ~ celiamoontown ~ Leave a comment
Would you dare to defy destiny? Are our destinies written in stone? Do we become nothing more than the self-fulfilling prophesies of other people’s opinions? Or can we dare to become who we believe we were born to be?
“A gorgeous, heartfelt journey of redemption and love” (Wendy Higgins), ONLY A BREATH APART is a young adult contemporary novelfrom critically acclaimed Katie McGarry. “Haunting, authentic, and ultimately hopeful” (Tammara Webber), ONLY A BREATH APART will be available on all retailers on January 22, 2019!
About ONLY A BREATH APART:
Jesse dreams of working the land that’s been in his family forever. But he’s cursed to lose everything he loves most.
Scarlett is desperate to escape her “charmed” life. But leaving a small town is easier said than done.
Despite their history of heartbreak, when Jesse sees a way they can work together to each get what they want, Scarlett can’t say no.Each midnight meeting between Jesse and Scarlett will push them to confront their secrets and their feelings for each other.
Amazon: https://amzn.to/2K4poUy
Kobo:http://bit.ly/2M7Sn7f
Google Play: http://bit.ly/2M6S24K
B-A-M: http://bit.ly/2M2na5h
Barnes & Noble: http://bit.ly/2tnkyXZ
iBooks: https://apple.co/2K0iAE4
“Gritty and real, Only a Breath Apart is a story of hope conjured from pain, strength drawn from innocence, and love earned from self-respect. Beautiful, poignant, and fierce.”
―Kristen Simmons, critically acclaimed author of the Article 5 series
Add it to your Goodreads today!
Katie McGarry Bio:
Katie McGarry was a teenager during the age of grunge and boy bands and remembers those years as the best and worst of her life. She is a lover of music, happy endings, reality television, and is a secret University of Kentucky basketball fan.
Katie is the author of full length YA novels, PUSHING THE LIMITS, DARE YOU TO, CRASH INTO YOU, TAKE ME ON, BREAKING THE RULES, and NOWHERE BUT HERE and the e-novellas, CROSSING THE LINE and RED AT NIGHT. Her debut YA novel, PUSHING THE LIMITS was a 2012 Goodreads Choice Finalist for YA Fiction, a RT Magazine’s 2012 Reviewer’s Choice Awards Nominee for Young Adult Contemporary Novel, a double Rita Finalist, and a 2013 YALSA Top Ten Teen Pick. DARE YOU TO was also a Goodreads Choice Finalist for YA Fiction and won RT Magazine’s Reviewer’s Choice Best Book Award for Young Adult Contemporary fiction in 2013.
Website: www.katielmcgarry.com
Twitter: @katiemcgarry
Facebook: https://www.facebook.com/katielmcgarry
Goodreads: http://www.goodreads.com/author/show/4575371.Katie_McGarry
Pinterest: http://www.pinterest.com/katielmcgarry/
Tumbler: https://katiemcgarryauthor.tumblr.com/
Instagram: http://instagram.com/katielmcgarry
BLOG TOUR: The Sapphire Widow by Dinah Jefferies
April 1, 2018 April 1, 2018 ~ celiamoontown ~ Leave a comment
To be published on 5th April 2018, Viking Penguin, 400 pages, £5.75
Courage. Grief. Passion. It always amazes me how Dinah Jefferies can create characters with such immense inner strength and intense vulnerability. Every year I wait to get lost in the sensory and emotional explosion of her writing. The Sapphire Widow is set in Ceylon during the 1930s. Louisa is a young wife besotted with her charming, handsome and charismatic husband Elliot. She is convinced they have the perfect marriage, but still struggles with their inability to have children and Elliot’s reckless behaviour. After the shock of his sudden death, strange mysteries and terrible secrets are revealed, exposing a side of her husband she had never known or truly acknowledged.
This novel was a real journey. Amongst the utterly gorgeous descriptions of the everyday scenes, sights and smells of Ceylon, Jefferies unravels a compelling tale of heart-break and betrayal. The reader slips effortlessly into Louisa’s routine, her inner thoughts, needs and anxieties. We are gently eased into a story about marital issues, which at first appear typical, but are soon revealed to be tiny cracks towards a dark mesh of secrets. After news of Elliot’s sudden death, Louisa discovers each of these with thrilling fast-paced succession. Whilst she struggles to process the consequences of Elliot’s behaviour, the reader tries to catch up with the baffling and dangerous turn of events. We then follow Louisa’s attempts to pick up the pieces, find some sort of resolve and move on with admirable composure. Jefferies writes about grief with tenderness and delicacy.
There is a small but stable set of secondary characters lending both uplifting support and grating antagonism. Louisa’s path runs into Leo, an owner to a Cinnamon plantation where Elliot spent much of his time. Silent, steely and sensitive, Leo is blatantly Elliot’s opposite. Her attraction to him is immediate but troubling. Is it her vulnerable need for companionship or the start of a bond stronger than her whole marriage? As she tries to negotiate her feelings, there is no doubt that she depends on Leo, who is the only link to one of Elliot’s mysterious legacies. A really absorbing read.
Many thanks to Penguin for my review. Can’t wait for another story soon…
Read review of other books by Dinah Jefferies
Say You’ll Remember Me by Katie McGarry
March 11, 2018 ~ celiamoontown ~ Leave a comment
Published HQ YA, 30th Jan 2018, 464 pages, £3.99
A great read, but unfortunately not the most powerful of Katie McGarry stories. Walk The Edge still remains for me the most intense and romantic. Say You’ll… is about a privileged but stifled governor’s daughter and an alleged convict on a government rehab scheme. Drix was convicted of a crime he didn’t commit. The time he spent away was still a reality check for the reckless lifestyle he led and when he was chosen to take part in the governor’s ‘Second Chance’ program, it seemed like an opportunity to get his act together concerning school and family. The program aims to keep young offenders from returning to crime and reintegrate back into society, as well as providing publicity for the governor’s campaign trail. His daughter, Elle faces constant pressure to be the perfect politician’s daughter, in the way she acts, looks and creepily who she might be dating. Everything is planned, cultivated and controlled. This leaves little room for exploring her identity and interests, especially if she has been raised to do what she is best at rather than what makes her happy.
The whiff of Drix and Elle’s instant attraction is caught immediately by Elle’s parents, who make it clear that Drix is completely off the radar; especially if it indicates her father’s program being tainted with bias. Likewise, Drix is fully aware that getting involved with the governor’s daughter, a man who has given him the only lifeline he has had in many years, is the worst first step he can make.
I really wanted to be swept up in this story. There is plenty of feisty flirting, but the dialogue carried on longer than it needed. There was a lot of sentimental and motivational talk, but repeated and continued rather than amounting to action. This novel taps into many interesting topics such as controlled and abusive relationships, double standards in politics and rehabilitation programs. There is also the mystery of who actually committed the crime, resulting in an action packed struggle at the end. However, I just didn’t latch on as I normally would for a McGarry instalment, maybe just needed more punch and heat rather than emotion. I will of course keep reading and I can’t wait for the story, be it in this series or a Thunder Road (please!) one.
Begin Again by Mona Kasten
February 18, 2018 February 18, 2018 ~ celiamoontown ~ Leave a comment
Published Nov 2017, Bastei Entertainment, 278 pages, £4.31
A sizzling new adult novel that got sparks flying between the MCs pretty much from the first page. I kindly received a copy from the publishers after the cover caught my eye on twitter. I wasn’t expecting anything unique, just a familiar plot of love-in-denial and dramatic spins. It mostly delivered and made a nice transitional read between more serious texts. If you are experiencing an endless winter season, it is an ideal book to crawl away with and escape under the sheets.
I think there is something seductive about new experiences in plot, following a character who moves to a new town and meets new people. Allie runs away from her domineering parents to start college and begin a new life. The only available apartment left, however, is owned by the most intolerable, arrogant and insensitive (but of course incredibly attractive) guy. Determined to suck it up, she agrees to move in with Kaden and grudgingly accepts his outrageous ‘rules’, one being never to talk about her ‘girl problems’. But of course, with each day the beast reveals snippets of his vulnerability and painful memories. Just as they begin to connect, their past lives seep back in causing mayhem and destruction.
There is some clumsy narration where the story lacks subtlety, and certain scenes were a little crass for me, which is the case for many contemporary NA, especially college based ones. The characters are not the most memorable, but the pacing and build-up of heat between them is well done. Their friends add a comedic touch to the story. A tiny bit of lag during the bonding moments, but this picks up towards the second half of the book. Simple, direct and satisfying.
Many thanks Bastei for my copy.
For more live-in romances I would recommend Japanese high school drama ‘Good Morning Call’ on Netflix. And For new starts, Nicholas Spark’s Safe Haven.
Blog Tour: Wilde in Love by Eloisa James
November 9, 2017 ~ celiamoontown ~ 1 Comment
Published by Piatkus, 31st October 2017, 416 pages, £8.99
Eloisa James returns with another heart-hugging and racy romp perfect for this season. As days darken and leaf strewn streets beckon us into the sanctuary of a warm reading nook, this book is ideal for curling up and warming the soul, with of course some pulse quickening moments.
It’s the first in a new series (although it never really matters which part of a romance series you begin with), set in the Georgian period and is an idol story. Lord Alaric Wilde returns to England from years of exploring and writing to find out he has become something of a sensation, with leagues of women devouring his books and plastering their bedroom walls with his handsome face. Confused by all the attention he retreats to his father’s castle to reunite with his family only to find a host of their guests fawning over his every movement. The one who isn’t the least bit interested (of course) is a young woman called Willa Ffynche. Spirited and witty, Willa is unfazed by his reputation and is frankly indifferent to him.
The fact that it’s a simple plot set in one location with a small circle of characters, is a testament to the author, who kept me reading into the night. The obstacles keep on piling. Alaric has to convince Willa that his interest in her, whilst other women are throwing themselves at him, is not because she is another unmarked territory to conquer. Willa, composed and sensible, finds it increasingly difficult to ignore the mere heat of his presence. James is skilled at creating tension without dialogue, just with the characters being in the same space. Even if Willa does succumb to her attraction, marriage with Alaric, who is followed eagerly by every newspaper, is the last thing that she wants if she is to have a peaceful life. James expertly drops moments of recognition and satisfaction, building towards a blissful ending with a note of suspense. She also throws in memorable quirks such as a delusional missionary and an intelligent skunk that helps save the day.
Many thanks to Piatkus for my review copy xxx
Dare You To by Katie McGarry (Pushing The Limits #2)
October 17, 2017 ~ celiamoontown ~ Leave a comment
Published by May 2013, Harlequin Teen, 456 pages, £3.49
I thoroughly enjoyed this. Before embarking on an 11 hour flight across the world, I knew I needed a Katie McGarry. Everything she writes somehow both soothes and excites me. Pushing the Limits, the first in this series was great, full of crackling chemistry and drama. I would recommend reading this book first as it contains the characters’ history, which isn’t completely essential, but boosts the engagement.
This story follows Beth, another girl from the wrong side of town (Check out Red At Night). All she has known since she was a child was to protect her mother from everything.. drugs, a violent boyfriend and prison. Growing up with unsavoury characters, she has learnt to be tough as nails and sharp as a whip in order to survive. Her character jumped out at me with her dialogue ringing out loud and clear. Her vulnerability and strength also felt raw.
As problems spiral out of control, Beth is forced to move away with her uncle who makes it his mission to reform her. Scared for her mother, separated from her best friends and attending the local ‘hick’ high school, she experiences her worst nightmare. Despite this, she finds herself drawn to the most stereo-typical guy she should avoid, golden boy jock Ryan. He is your average High School Musical star, but with baseball and a bit more muscle. On track to play pro, the cracks in his perfect life start to inch further into the book; a domineering father, a depressed mother and an estranged brother. What starts off as a dare to ask out scary skater girl, leads to deep attraction and mutual understanding. This romance started off quite slow with a lot of back tracking, which made the book longer than necessary. I was impressed with the shift in Ryan’s character, who started off as an macho airhead.
Beth and Ryan have to face a lot of courage to make their relationship a reality. They have to face abilities that have been suppressed or forgotten. For Beth it’s trust, while for Ryan it’s rebellion.
Happy to continue my journey through the series..
The Hate U Give by Angie Thomas
September 17, 2017 February 18, 2018 ~ celiamoontown ~ Leave a comment
Published by Walker, April 2017, 436 pages, £2.00
This is an outstanding debut novel, young adult story and a contemporary peep hole into the thorny topic of race in America. I loved every word of it and slowed down my reading pace to stall its ending. It’s also a very ‘now’ book, like Melissa de la Cruz’s Something in Between which is about immigration and identity in the eyes of a high schooler, published just before Trump’s rise to power. I was half way through ‘The Hate…’ when I heard news of the Charlottesville rally. However, that doesn’t mean it should be read just because of its current-ness. What strikes the reader is the stubborn timelessness of prejudice and corrupted politics. There is however, a sense of hope that change is still possible, even if it’s slow and painful.
Sixteen-year-old Starr witnesses her childhood friend being shot by a police officer for no real reason. And just like that her life is turned upside down. Raised in a rundown community, known for crime and gang warfare, she attends a private school on the privileged side of town. After the incident, Starr is exposed to the harsh division of her two worlds. As the case builds up and goes public, injustices and ugliness are dragged to the fore. Attitudes remain infuriatingly fixed, refusing to budge. As the sole witness, the pressure and responsibility rests upon Starr’s young shoulder to set the score.
‘The Hate U Give’ also stands for THUG, which is taken from the rapper Tupac’s lyrics: ‘Thug life: the hate you give to infants f*** everybody’, a nod to the author’s musical past. The seed of hate fosters fear and even more hate, like an endless circle with no progress for anyone. Starr is made to realise how she had succumbed to acting and talking different at her school. The fear of being stereo-typed as ‘ghetto’ or ‘angry black girl’, caused her to iron out her identity. This is something I understood as an ‘ethnic minority’- the desire to down play your race and to blend in.
Despite the seriousness of the topics, Thomas manages to keep the novel strictly teen with talk about fashion and sports, as well as a cute romance. Most of the plot is centred around an exciting build-up as the readers wait to see whether Starr will speak out. However, there were some slow parts which I believe is intended as relief from the heavy subjects.
We need more books like this.
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450 431-0000 info@centredentairedunord.com
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He is committed to continuous education; as well as furthering his skills in order to keep up to date with the latest techniques and technologies.
Our hygienists, assistants and dental secretaries
Our team of hygienists, assistants and dental secretaries, warmly welcome you to our clinics. We are passionate and work with the best equipment to promote, restore and maintain excellent oral health. Our mission: Your family’s smile! We wish to thank you for your continued support and trust which greatly motivates us to remain leaders in our field.
Contact our dental center today to make an appointment with a dentist in Saint-Jérôme.
Crowns, bridges & prosthodontics
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Peter Neufeld
Founder, The Innocence Project; Author; Attorney
LawAir Date 02/17/2000
A conversation about the use of DNA testing to free wrongly convicted inmates.
The Innocence Project; Dave Eggers
Books, LawAir Date 02/17/2000
A conversation about The Innocence Project; Dave Eggers talks about his book, "A Heartbreaking Work of Staggering Genius."
Law, Science, TechAir Date 11/01/1996
Co-founders of the Innocence Project, Barry Scheck and Peter Neufeld, discuss the exoneration of criminals using new DNA tests.
Barry Scheck and Peter Neufeld, Innocence Project co-founders, discuss the exoneration of criminals using new DNA tests. Founder of Oracle Corp.
Related Guests 5
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Neuroscientist Simon LeVay presents his new book exploring sexuality and the brain, "The Sexual Brain." 09:46
Arnold Rampersad
Books, Sports, Health
Arnold Rampersad of Princeton on the book "Days of Grace," which he wrote with the late tennis player Arthur Ashe. 14:39
Tim Russert; Michael Eric Dyson; Sam Neill
On politics and President Clinton. Baptist minister and author of "Between God and Gangsta Rap." On his role as King Charles II in "Restoration." 53:59
Guest host Paul Nurse and Drs. Robert Basner and Charles Czeisler discuss the topic of sleep and sleep disorders. 25:27
'Whiskey Tango Foxtrot'; Joe Nocera; Tim...
Entertainment, Business, Books, Sports, Tech
"Whiskey Tango Foxtrot" with Tina Fey et al. Joe Nocera exposes the NCAA. Apple C.E.O Tim Cook on the future. 53:54
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Michael Korda, editor in chief of Simon & Schuster, discusses his work as both an editor and an author.
Books Media
October 2017 October 2017 November 2007 November 2007 January 2002 January 2002 April 2001 April 2001 August 1999 May 1999
Primaries 1992; Joan Collins; Michael Korda
Journalists analyzes the primaries that set up the '92 general election; Joan Collins on her return to the stage; editor Michael Korda. 56:26
Author George Saunders explains why he writes fiction and short stories. 29:49
Politics, Books, History
Robert Caro talks about writing the fourth volume in his series on the life and career of LBJ. 35:25
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Editor Ellen Datlow and authors Thomas Disch, Ben Bova, and Samuel Delany on contemporary science fiction. 10:11
Michael Korda; Stephen King
In a remix of earlier segments, Michael Korda on his publishin-business memoir and Stephen King on his new novel, "Bag of Bones." 53:40
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Artist Career Research Methods
A comparative analysis of research methods for understanding artists’ career paths, work conditions, and incomes
The objectives of the study were to:
Obtain a synthesis and analysis of the different approaches and methodologies in research focused on artists’ careers, practices and livelihoods undertaken in jurisdictions across Canada and internationally.
Gain an understanding of the underlying reasons and motivations behind the common and varied findings.
Identify best practices and lessons learned in methodologies and approaches.
Many artists have atypical work patterns, characterized by:
high self-employment rates
multiple job-holding
the predominance of short-term employment opportunities
relatively low incomes
low unionization rates
challenges regarding professional development and career advancement
unusual work flows
In addition, there are differences in how artists work between arts disciplines and regions of the country. These specificities make artists a challenging labour group to study.
The funding agencies wanted to understand the opportunities for future Canadian research related to the situation of artists and any potential challenges.
The report synthesizes information about methods used in the studies that were found in the literature search and interviews. This includes an analysis of:
the studies’ goals
their definitions of “artist,”
their novel methods (i.e., methods that have gone beyond traditional statistical sources in exploring the situation of artists)
the variables they analyzed
their analysis (or lack thereof) of sub-national statistics
methodological notes related to Indigenous and equity-seeking groups in the arts
their presentation and distribution of findings
other methodological considerations
This report summarizes an in-depth Canadian and international literature review into methods used to understand artists’ work conditions, incomes, and career paths.
The research team also conducted 12 semi-structured interviews with arts researchers, research commissioning organizations, and representatives of Indigenous and equity-seeking groups.
Overview / Key Findings
Outside of census data, there have been no systematic efforts in Canada aimed at understanding the situation of all the country's artists. Many Canadian studies have covered certain types of artists only.
In terms of the methodologies, given the limitations of official national statistics, researchers have conducted special studies of artists, including three main methods:
compilation of lists of artists, and then survey sampling
respondent-driven sampling
analysis of big data
There are other research methods that have rarely been used to examine the situation of artists. A study using one or more of these rarely-used methods—longitudinal research, quasi-experimental methods, intensive qualitative research, and arts-based research—could fill a gap in the research literature.
In Canada, the vast majority of custom surveys into the situation of artists have used “convenience samples,” i.e., non-random samples with the largest possible number of responses, given the size of the group being studied.
The research identified some key studies that delved much further than conventional national statistics into two important issues: time use and incomes. However, it is worth noting that, all of the studies focusing on artists’ personal incomes, none reported on household income levels.
Some studies asked about receipt of grants and supports from other sources, such as spouses, while other studies contained questions related to other facets of artists’ working lives, such as:
supplementary health benefits
recognition within the arts community
self-assessment of their career achievements
international artistic engagements
the use of creative skills in non-arts work
This report on Artist Career Research Methods was prepared for a consortium of Canadian public arts funders:
the British Columbia Arts Council
the Calgary Arts Development Authority
It was prepared in partnership with:
the Toronto Arts Foundation
the Conseil des arts et des lettres du Québec
Artist Career Research Methods - Executive summary (PDF 1.2 MB)
Artist Career Research Methods - Full report (PDF 1.6 MB)
Artist Career Research Methods - Annotated bibliography (PDF 1.4 MB)
Authors: Kelly Hill and Alix MacLean, with the collaboration of Sherri Helwig
Publisher : Canada Council for the Arts
Tagged As Cultural Human Resources
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Home> News and events> CNES at the 2011 Paris Air Show
CNES at the 2011 Paris Air Show
The 49th Paris Air Show at Le Bourget from 20-26 June will be showcasing the latest technological innovations in aerospace. CNES will be there with an original pavilion spotlighting three themes: daily applications, innovation and Europe.
Innovation as communication
The last Paris Air Show in 2009 pulled in the crowds. Credits: CNES.
The 49th Paris Air Show opens its doors this year at Le Bourget from 20-26 June.
As a key player in the space community, CNES will once again be present at this must-attend event on the aerospace calendar with a new pavilion for professionals and the public.
And to celebrate its 50th anniversary, France’s space agency intends to leave its mark on this year’s show.
CNES pavilion at the 2009 Paris Air Show. Credits: CNES.
Three thematic areas in the pavilion—focusing on daily applications, innovation and Europe—will be showcasing practical applications and new technologies, and will also have some sensory surprises in store for visitors.
A giant screen in the shape of the CNES logo on the front of the pavilion, life-size holographic and interactive characters and spectacular 3D films will be putting the emphasis on the use of novel means of communication.
An audiovisual Pandora’s box
Sneak preview of the Pandora production showing changing landscapes and an Earth that turns into the Moon. Credits: UTRAM/CNES.
Among these will be Pandora, a truly unique experience in the Innovation area of the pavilion
Pandora will project pictures, sound and light onto 3D shapes, putting the visitor in the middle of an eye-catchingly staged show.
This 2-minute audiovisual production will trace the rich heritage of modern space innovations.
CNES will also be sharing its exhibition space for the first time with DLR, the German space agency, thus affirming its commitment to pursuing the successful bilateral cooperation between the two agencies.
A series of conferences will also be taking place throughout the week in the meeting area of the pavilion.
A wide range of topics will be discussed from telehealth, space ethics and parabolic flights to planetology.
Paris Air Show website (FR)
CNES at the 48th Paris Air Show
[PRESS] [#SPACEBOURGET17] 52nd International Paris Air Show. An exceptional week for CNES
[PRESS] [#SPACEBOURGET17] Valerian masterclass invites public to meet cartoonist Mézières and concept artist Sylvain Despretz
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The truth about the obesity paradox
By Sam Downing| 2 years ago
Do overweight people really live longer?
The "obesity paradox" arises from data that appears to suggest overweight people live longer and healthier than those of a normal weight — which, to put it bluntly, is pretty confusing.
"I get a lot of patients who ask, 'Why do I need to lose weight, if research says I'm going to live longer?''' said Dr Sadiya Khan, a Northwestern University cardiologist. "The obesity paradox caused a lot of confusion and potential damage."
But the paradox isn't what it seems.
Khan is the lead author of a new study that debunks the paradox, demonstrating exactly what you'd expect: heavier people don't live as long, and are more likely to suffer from cardiovascular disease (think stroke, heart attack, heart failure and even death).
"Our data show you will live longer and healthier at a normal weight," Khan said in a statement.
Published in JAMA Cardiology, the study pored over health data taken from almost 200,000 people over a 50-year period up to 2015, stacking their weight (as measured by body mass index) against their longevity and risk of cardiovascular disease.
Men of a normal weight lived two years longer than obese men and six years longer than mordibly obese men. Normal-weight women lived almost a year and a half longer than to overweight women, three years than obese women, and six years than morbidly obese women.
While normal-weight men and overweight men lived about the same length, the latter's likelihood of cardiovascular death or disease was 21 percent higher, and for obese men, it was almost 70 percent higher.
That also held true for overweight and obese women, who were 32 percent and 85 percent more likely to fall victim to cardiovascular disease than normal-weight women.
"A healthy weight promotes healthy longevity or longer healthspan in addition to lifespan, so that greater years lived are also healthier years lived," Khan said. "It's about having a much better quality of life."
RELATED: There is no obesity paradox: The higher your weight, the higher your chances of early death
Got 15 minutes? Tone up your legs and butt with this body-weight workout for your lower body:
Obesity Paradox
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Bruichladdich Distillery – Stepping Back in Time and Into the Future
In early 2016, Mrs. Wonk and I trekked across Islay and Speyside in Scotland, visiting as many single malt Scotch whisky distilleries as time allowed during our all too brief ten-day stay. In a series of posts, I’m documenting our experiences, one distillery at a time with tons of photos. If you’re not familiar with how single malt Scotch whisky is made, I highly suggest first reading my prologue post, Essential Highlights of a Scotch Whisky Distillery Visit. What follows is our visit to the Bruichladdich distillery on the island of Islay.
While on Islay, you’d be hard-pressed to skip visiting or at least not drive through scenic Port Charlotte, home of one of the nicest hotels on the island. Heading southwest on the A847 toward town, you have to work to keep your eyes on the road rather than gawk at the roving bands of sheep and splendorous views over Loch Indall to your left, just a few dozen yards away. Passing a cluster of white painted houses perched on the right side of the road, you might think you’re on the outskirts of Port Charlotte. Except that, blink once, you’ve passed by a white, two-story stone-walled compound. This is your first encounter with Bruichladdich– an Islay distillery vastly different than Laphroaig and Lagavulin, who get the lion’s share of this small island’s attention.
Sheep near Bruichladdich
Our arrival at Bruichladdich coincides with a slight break in Storm Gertrude, which hammered Scotland with high winds exceeding 100 miles perhour at times—thankfully not while we were crossing open water in our car ferry two evenings before. During a short lunch break between our morning Bowmore tour and Bruichladdich, we stopped at infamous Bowmore round church for a quick peek at the grounds and found ourselves—hardly wee people, we sturdy Americans–barely able to stay upright as wind gusts hurled us around. So it was with great relief that we pulled into the protected courtyard of Bruichladdich, sheltering walls on all four sides.
The story of modern day Bruichladdich is straight out of a movie montage, linking together facilities and equipment of the Victorian past with very modern, non-traditional approaches to making and marketing single malt whisky. Established in 1881, the distillery experienced many rough patches in its history and apparently never went through any sort of comprehensive modernization. In 2000 it was purchased by a group of investors led by Mark Reynier of Murray McDavid, an independent bottler of Scotch whisky. Interestingly, the primary reason for the purchase was Bruichladdich’s maturing whisky stocks, rather than the antiquated distillery itself, which had been shuttered in 1994.
Sensing an opportunity, Mark’s team restarted the distillery on a shoestring budget, keeping much of the original equipment, including its grain mill, mash tuns, and most of the stills. Additional stills were scavenged from another distillery about to be demolished. In short order, the Bruichladdich brand established a reputation for being highly experimental, creating dozens of small, one-time releases based on a particular local grain, a special occasion (such as a local festival), or some other unique twist. Their motto: Progressive Hebridean Distillers.
In addition to the namesake Bruichladdich non-peated single malt, the distillery also makes the peated Port Charlotte brands, the nuclear peat-bomb Octomore series, and Botanist gin — more on the gin later. In a controversial 2012 decision, enough other investors voted against Reynier, forcing Bruichladdich’s sale to the French spirit giant Remy Cointreau for a hefty sum around $95m, U.S. Don’t feel too sorry for Mark though. He’s already off in his next venture–Waterford, a very newish Irish whiskey distillery purchased from Diageo.
Although Mark no longer wanders the Bruichladdich facility, a bit of that short, glorious era still remains with Carl Reavey, Bruichladdich’s head of public relations, who greets us shortly after we step into the warm and cozy visitor center, away from the gale force winds.
Before diving into our private tour, we share a few wee drams — practically a legal requirement upon arrival at a Scotch whisky distillery. Carl tells of the early days of bootstrapping the once-dormant distillery – he was there for much of it. Carl came to the Bruichladdich via an interesting path. After an early start in writing and audio electronics, Carl and his wife took over renovating and then running the Port Charlotte Hotel in 1995, during which he became acquainted with the Bruichladdich investors, eventually becoming part of the team himself. These days, Carl’s duties include content creation for Bruichladdich and regaling visiting whisky wonks like me with stories about the distillery.
Bruichladdich distillery, Islay
Properly fortified with whisky (or gin, in Mrs. Wonk’s case, since she has an on-again, off-again relationship with peat smoke), we braved the buffeting winds to travel across the courtyard to our first stop. Along the way, we spy a tanker truck, painted in the aquamarine with white lettering of the well-known classic Laddie bottle– no mistaking where that tanker’s from! After gawking for a moment (it’s cold after all) we reach the grain building.
In some single malt distillery tours, you might feel privileged to simply see the giant grain bins, looming twenty feet high or taller and filled with barley ready to be ground up and mashed. But here at Bruichladdich, Carl indulges us, taking us up a steep, narrow, and mildly treacherous set of open-steel stairs to an elevated walkway running along a row of bins—roughly the size of a schoolbus– and affording easy access to the top. A small hole in each allows us to peer in and see that some are completely filled with malt.
Part of the ethos of Bruichladdich is its fanaticism for local barley and releasing certain expressions made from the grain production of just a single local farm. That is, terroir to an extreme. Unlike many of the Islay distilleries who malt at Port Ellen Maltings, Bruichladdich’s maltings (even of Islay Barley) is done in Saladin boxes at Bairds of Inverness, in the Speyside region of the Scottish mainland.
The bottom of the grain bins funnel into a lengthy square box that carries grain away to the mill room. Bruichladdich’s mill is a sight to behold! Here, you won’t find the de rigueur, electric driven, tank-like Porteus malt mill found all over Scotland. Instead, step back into time, practically pre-electricity. The room is filled with wooden boxes and chutes, oversized drive wheels and wide and narrow belts connecting it all. The mill itself, made by Robert Boby, is driven by these belts. At one point, Carl throws a switch to bring the operation to life. It was loud, and it was glorious! Truly a peek back into how it was like before servo motors and computers became commonplace in distillery operations.
Mash Tuns
In an adjoining building and up another set of steel stairs is the mash tun, where the milled barely is combined with water and cooked. This is no ordinary stainless steel, flying saucer-like mash tun though! Peering into the huge open-top tank, it’s hard to take your eyes of the collection of curved rakes, armored with dozens of malevolent looking tines. Each rake is connected to a shaft driven around the circumference of the tun by gears straight out of an old-time cartoon. Had such things as Victorian horror films existed, this contraption would have been featured prominently. It appears to be ruthlessly efficient at churning the water and milled barley into mash, something we experienced firsthand when the mash man turned it on for a bit.
While gawking at the mash rake, hot water poured into the tun from a large pipe above. Carl led us over to the console where the operator can quickly see exactly how full the tun is by perhaps the world’s most homespun gauge: a long, vertical plank of wood with hand lettered ruled markings. Exposed cables connect to the top and bottom of a red arrow that floats up and down according to the fill level of the tank. Talk about old school!
Still on the elevated platform, we move to the next room where six enormous and tall fermentation vats, aka wash backs, are lined up. Because we’re on a platform, we can look directly into the tanks, some of which are busy bubbling away. Mark tells us that they’re made of Oregon pine (a common material in such tanks) and regales us with a story of watching a new tank being assembled in place from giant wooden slats. We also learn that Bruichladdich’s fermentation is roughly twice the traditional duration, but uses less yeast.
Past the stills and through another doorway, we come face to face with Ugly Betty. No, not America Ferrera from the American TV series, but a squat, tank-like still that at first glance looks to be made out of spare parts from a truck junkyard. Unlike the breathtaking, swanlike curves of a normal whisky still, Ugly Betty is covered with seams and rivets. The top of the neck doesn’t transform into a gracefully sloping line arm. No, her top is flat and functional. The one humorous nod is along the topmost section. The name plate includes an image of a voluptuous, white-stockinged woman–the aforementioned Betty–luxuriating in a seductive pose.
Ugly Betty was rescued from the aforementioned nearby distillery which was about to be be bulldozed. Today at Bruichladdich it makes the Botanist Gin. As part of Bruichladdich’s desire to source as much as possible locally, a team of retired botanists scour the Islay countryside collecting the botanicals used in the Botanist infusion. Between the Islay-local flavors and beautiful bottle, Mrs. Wonk is a fan!
Wash & Spirit Stills
Just beyond Ugly Betty is the money shot at Bruichladdich – the two wash stills and two spirit stills used to make Bruichladdich, Port Charlotte, and Octomore. Viewing them from above, it’s hard not to immediately rush down the stairs to the platform that spans between them, covering most of the still body. From that platform below, it’s easy to lean over and peek through the porthole into the interior.
Inside a still at Bruichladdich
The wash stills are around 17,300 liters, while the spirits stills are 12,275 liters. Carl tells us that the base of one of the wash stills dates back to the founding of the distillery in 1881. A pair of comparatively tiny spirit safes sits between each pair of stills. Heading down a final set of stairs to ground level, we get a great view of the brick bases of all four stills clustered together. At one point Bruichladdich’s stills were direct fired and used a rummager chain, but today they’re all steam fired, and the telltale pipes are easy to spot.
Aging Warehouse
From the warmth of the stillhouse, we plunge through the waning sunlight of the cold, blustery day, crossing the courtyard and heading toward the back of the property, where the aging warehouses stand guard on a slight rise. Carl unlocks one heavy wooden door and leads us through the fluorescent lit interior, barrels stacked on their sides, three-high, row after row. Overhead, the curved metal roof gives the impression of an exceedingly large Quonset hut. Glancing at a few labels on the barrel ends, it’s clear we’re in the presence of some seriously old whisky. Mark pops the bung on a few barrels, and we taste, and taste, and taste. Sharing any more would just be cruel to you, dear reader, but it was an afternoon to remember.
The Final Dram
With one final dash across the compound we’re back in the toasty confines of the visitor’s center. Taking a closer look around, we spot hundreds of different bottles lined along the high ceiling, each bearing a different label. Some of these releases are from existing stock that predates Mark Reynier’s acquisition. Beyond the mainstay products like the Laddie, with its iconic aquamarine bottle, the distillery has also launched hundreds of small batch releases over its roughly fifteen year of restarted operations—each represented with a bottle here.
Distillery guests have the chance to acquire several of these rare expressions, including bottling and labeling their own bottles. These single-cask expressions are known as the Valinch bottlings. In the visitor’s center that day are two barrels making up the current Valinch offerings — one holding a peated Port Charlotte, the other with unpeated Bruichladdich. I obviously didn’t pass up the opportunity and bottled both to bring home: A ten-year aged Port Charlotte and a twenty-five year Bruichladdich, distilled in 1990 and aged for 25 years in a sherry hogshead.
We left Bruichladdich with smiles on our faces, our hearts warmed by whisky and gratitude for all that Carl Reavey had shared with us. Our time at Islay was sadly drawing to a close. Awaking the next morning, we had no idea if our ferry off the Island had been canceled, thanks to storm Gertrude which caused all manner of planes, trains, and automobiles (and ferries) all over the country to be canceled far and wide. Although we made it off Islay (to our huge surprise), we wouldn’t have been terribly sad had it been canceled, letting use our additional day to soak up even more of the magical island. Even as I type this, I’m wistful for our time there and plotting our return. Meanwhile, dear reader, our single malt distillery posts now move to Speyside, starting with the legendary Glenfiddich. Stay tuned!
Barrels at Bruichladdich
Author mpietrekPosted on October 12, 2016 June 9, 2018 Categories distillery, Scotch whisky distillery, ScotlandTags bruichladdich, featured
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LaDarien Griffin
Saint Louis Billikens at St. Bonaventure Bonnies 3/17/2019
Big Sky - Semifinal 2 (win) at Big Sky - Semifinal 1 (win) 3/16/2019
Bonnies rout Rhode Island to reach A-10 championship game
By Denis P. Gorman Mar. 16, 2019 03:40 PM EDT
Big 12 - Semifinal 2 (win) at Big 12 - Semifinal 1 (win) 3/16/2019
Bonnies top George Mason behind Welch's career high 20
George Mason Patriots at St. Bonaventure Bonnies 3/15/2019
Stockard scores 20, St. Bonaventure locks up 4th in the A-10
SAINT BONAVENTURE, N.Y. (AP) — Courtney Stockard scored 20 points and had seven assists, Amadi Ikpeze's left-handed hook in the low post was the go-ahead and St....
St. Bonaventure defeats George Washington 64-58
Associated Press Mar. 02, 2019 06:24 PM EST
WASHINGTON (AP) — Osun Osunniyi recorded 18 points and 16 rebounds to carry St. Bonaventure to a 64-58 win over George Washington on Saturday. LaDarien...
Stockard leads St. Bonaventure past Duquesne 68-47
ST. BONAVENTURE, N.Y. (AP) — Courtney Stockard had 21 points as Saint Bonaventure easily beat Duquesne 68-47 on Wednesday night. LaDarien Griffin had...
Poyser leads St. Bonaventure past Fordham 74-53
NEW YORK (AP) — Jalen Poyser had 20 points as Saint Bonaventure routed Fordham 74-53 on Saturday. Poyser made 4 of 6 3-pointers. Courtney...
Griffin carries St. Bonaventure over St. Joseph's 76-51
PHILADELPHIA (AP) — LaDarien Griffin recorded 16 points and 10 rebounds to lead Saint Bonaventure to a 76-51 win over Saint Joseph's on Tuesday night. ...
Defense shines as VCU routs St. Bonaventure 85-55
ST. BONAVENTURE, N.Y. (AP) — Sean Mobley recorded 12 points as VCU easily beat Saint Bonaventure 85-55 on Saturday. Marcus Santos-Silva added 11 points...
Dayton outlasts St. Bonaventure 89-86 in double overtime
ST. BONAVENTURE, N.Y. (AP) — Ryan Mikesell matched his career high with 21 points, leading six Dayton players in double figures, and the Flyers outlasted St....
Rhode Island tops St. Bonaventure behind Russell, Martin
KINGSTON, R.I. (AP) — Fatts Russell and Tyrese Martin scored 18 points apiece and Rhode Island beat St. Bonaventure 75-63 on Wednesday night. Cyril...
Griffin, Osunniyi lead St. Bonaventure past Saint Joseph's
ST. BONAVENTURE, N.Y. (AP) — LaDarien Griffin scored 19 points on 8-of-12 shooting and freshman Osun Osunniyi had his second double-double of the season to help St....
Syracuse cruises to 81-47 win over St. Bonaventure
By Mark Frank Dec. 29, 2018 04:29 PM EST
SYRACUSE, N.Y. (AP) — A year ago St. Bonaventure got off to strong start in its upset overtime win against Syracuse at the Carrier Dome. What a...
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Kris Wilkes Rob Edwards Zylan Cheatham Kimani Lawrence Romello White Jaylen Hands Sports Men's college basketball College basketball Basketball College sports Men's basketball Men's sports
Pac-12 Arizona State UCLA
Arizona State beats UCLA 83-72 in Pac-12 quarterfinals
By JOHN MARSHALL - Mar. 15, 2019 02:01 AM EDT
Arizona State's Zylan Cheatham attempts a shot around UCLA's Cody Riley during the second half of an NCAA college basketball game in the quarterfinals of the Pac-12 men's tournament Thursday, March 14, 2019, in Las Vegas. (AP Photo/John Locher)
LAS VEGAS (AP) — Arizona State appeared to be in good shape before heading to Las Vegas for the Pac-12 tournament.
A trip to the semifinals after a hard-fought win over UCLA should all but lock the Sun Devils' bid up.
Romello White scored 19 points, Rob Edwards added 15 and Arizona State withstood UCLA's second-half push for an 83-72 victory in the Pac-12 tournament quarterfinals Thursday night.
"It's a big step. It means a lot," Arizona State coach Bobby Hurley said. "We played in a lot of big games this year, a lot of high-level teams. We've been in this spot throughout the year, and this team has a great leadership and great resolve and desire to win. All those things were on display tonight."
The second-seeded Sun Devils (22-9) dominated the first half and stretched their lead to 23 early in the second, but let UCLA back in it by going nearly nine minutes without a field goal.
Arizona State settled itself after the long drought and held off the Bruins to earn a spot in Friday's semifinals against sixth-seeded Oregon. Zylan Cheatham had 13 points and 13 rebounds, and the Sun Devils shot 49 percent.
Seventh-seeded UCLA (17-16) looked sluggish early after playing the night before, but used a big run to trim into Arizona State's lead to nine.
Kris Wilkes keyed the second-half run, scoring 17 of his 25 points in the final 20 minutes, but the Bruins were never able to make it back from the big early hole. Jaylen Hands added 21 points for UCLA.
"The obvious difference in the game was the last four minutes of the first half," UCLA coach Murry Bartow said. "But these guys have never wavered, they've never backed down. They've competed hard, they've played hard."
The Sun Devils had some head-scratching losses during the regular season, including at home against Washington State. Arizona State closed the season strong, though, five of its final six games to earn the No. 2 seed in the conference tournament.
UCLA looked like it was going to cruise into the quarterfinals, building a 26-point lead against Stanford, but allowed the Cardinal to creep back into it before winning 79-72.
The Bruins opened the quarterfinal game casting too many long range shots and fell into an eight-point hole. UCLA worked its inside-out game to cut into the lead, but went cold again as Arizona State closed the first half on a 14-0 run.
Kimani Lawrence capped the run by fumbling the ball, gathering it up again and hitting an off-balance 3-pointer at the buzzer to put the Sun Devils up 45-29.
"They can be a very streaky team. They're very dynamic and when they get going, they're pretty darn good," Bartow said. "And they just in that stretch really got going."
Arizona State kept humming to start the second half, hitting five of its first seven shots to push the lead to 23.
But then UCLA picked up its defensive intensity and had a better rhythm to its offense, using a 13-0 run to pull within 59-49.
Arizona State broke its long field goal-less stretch when UCLA was called for goal tending on Cheatham's drive — a shot that had no chance of going in — and another goaltend on White's jump hook put the Sun Devils up 72-58 with five minutes left.
"I thought at times in the game we forget what kind of got us there, and that was getting the ball inside to Romello and Zylan," Hurley said. "Both of those guys had great individual games, both scoring and rebounding."
UCLA made a big run after an awful first half, but ran out of gas down the stretch.
Arizona State played well at the start and the finish to add another notch to its NCAA Tournament resume.
UCLA may get an invite to a smaller postseason tournament.
Arizona State plays No. 6 seed Oregon in the semifinals.
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Vindy.com
Blitz Live
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Tom Herman Jalen Hurts CeeDee Lamb Chris Brown Caden Sterns Sports College sports College football Football
Oklahoma Big 12 Texas
Texas defense going from bad to worse at midseason
By JIM VERTUNO - Oct. 14, 2019 04:57 PM EDT
Oklahoma quarterback Jalen Hurts (1) runs the ball against Texas during an NCAA college football game at the Cotton Bowl on Saturday, Oct. 12, 2019, in Dallas, Texas. (Nick Wagner/Austin American-Statesman via AP)
AUSTIN, Texas (AP) — The defensive numbers for No. 15 Texas are bad and getting worse.
After losing to No. 5 Oklahoma on Saturday, the Longhorns rank last in the Big 12 in pass defense and total defense, and their current pace of 453.3 total yards allowed per game would break some dubious records set during the disastrous three years of the Charlie Strong era.
What shocked coach Tom Herman the most about the 34-27 defeat was how easily the Sooners pushed around, ran through or simply ran past the Longhorns (4-2, 2-1 Big 12).
Texas gave up 276 yards rushing and struggled to contain quarterback Jalen Hurts, who also threw for 235 yards. Sooners wide receiver CeeDee Lamb left defenders flailing in his wake.
"We got exposed by some really good athletes. But we've got some good athletes ourselves that we need to teach how to tackle better," Herman said Monday.
The Longhorns knew they were in for some growing pains this season with eight new starters on defense. Herman had downplayed the big changes by noting many of the new starters had seen plenty of playing time. And he said he wasn't losing sleep as injuries started picking off more starters in the secondary; all Big-12 safety Caden Sterns didn't play against Oklahoma.
Some of those ugly defensive statistics come after three games against some of the most explosive offenses in the country in LSU, Oklahoman and Oklahoma State.
But getting pushed around all day by the team Texas is supposed to be challenging for the Big 12 title came as a surprise.
"It was the first time we got out-physicalled on both sides of the ball that I can remember," Herman said. "That's not us."
Herman blamed some of the poor tackling on his decision to limit tackling in practice the last couple of weeks.
"It was not a great decision," Herman said. "It showed."
There was more bad news in the secondary Monday: safety Chris Brown's fractured forearm will need surgery and he is likely out for several weeks.
A pair of early turnovers against Oklahoma kept Hurts from turning the game into a rout in the first quarter. But even when the Texas offense finally starting moving the ball in the second half, the defense never could dial up the key stop it needed in the second half.
Herman noted the Longhorns scored 24 points after halftime. So did Oklahoma as Hurts and the Sooners answered every second-half Texas scoring drive with their own.
"We got our hands on (Hurts) him quite a bit, slippery dude back there," Herman said. "We got to him, we didn't get him down."
Beating Oklahoma would have put Texas in the driver's seat to the Big 12 title game in December. Now they'll have to fight their way through the rest of the schedule to get there, where a rematch could await. Texas and Oklahoma met twice last season with the Longhorns winning the mid-season matchup in October and Oklahoma getting its revenge in the Big 12 championship.
Texas hosts Kansas (2-4, 0-3), one of the worst offensive teams in the country, this week.
"The sun came up, which is a good thing," Herman said. "There is zero sense of panic, there is zero sense of woe is me."
More AP college football: https://apnews.com/Collegefootball and http://www.twitter.com/AP_Top25
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Tajh Boyd
Photo by Chris Trotman/Getty Images
Clemson using former QB Tajh Boyd in practice to emulate Ohio State’s J.T. Barrett
Former Clemson quarterback Tajh Boyd, a key figure in the rise of the Clemson program in recent years, was back at Clemson’s practice this week as the ACC champion Tigers prepare for a College Football Playoff semifinal matchup with Ohio State, but Boyd was not there merely as a spectator or for words of encouragement. Boyd was there to practice as a member of Clemson’s scout team, taking on the role of Ohio State quarterback J.T. Barrett.
Clemson had @TajhB10 practicing at scout team QB today, playing the role of Ohio State QB J.T. Barrett
— Gene Sapakoff (@Sapakoff) December 16, 2016
The idea of using former players to help out on the practice field has been a little bit of a debating point recently. Last month, Alabama head coach Nick Saban battled back at criticism he faced for using former Alabama players Trent Richardson and Blake Sims on the scout team. The NCAA does allow for former players to participate in practices, so long as the practice time is limited and not announced publicly beforehand. This has been criticized by some, including Notre Dame head coach Brian Kelly.
For what it is worth, Ohio State head coach Urban Meyer was intrigued by the use of former players when word of Saban’s practice methods became public.
Tags: J.T. Barrett, Tajh Boyd, Trent Richardson
Ex-Clemson QB Chad Kelly tweets he’s landed at Ole Miss
By John TaylorDec 11, 2014, 8:58 AM EST
Eight months after his unceremonious departure from Clemson, it appears as if Chad Kelly has landed on his quarterbacking feet.
In a tweet posted to his Twitter account Wednesday, Kelly, the nephew of Miami great and NFL Hall of Famer Jim Kelly, indicated that he would be transferring to Ole Miss after spending the 2014 season at the JUCO level in Mississippi. Kelly ultimately opted for the SEC school over Indiana and Virginia Tech.
Alabama was also visited on at least a couple of occasions prior to Kelly’s decision, which was made after spending the past two days in Oxford. Additionally, he had held offers from Florida State, Michigan State and Purdue.
All I Can Say Is HottyToddy!!!!!! It's A Great Day To Be A Ole Miss Rebel !!!! Can't Wait To Be A Rebel !!!! #HottyToddy
— Chad Kelly (@ChadKelly_11) December 10, 2014
Kelly is expected to participate in spring practice with the Rebels next year. With Bo Wallace out of eligibility, Kelly will compete with Ryan Buchanan and DeVante Kincade for the starting job. Both players shared backup quarterback duties this season as freshmen, with Buchanan attempting 22 passes and Kincade 17.
Clemson head coach Dabo Swinney announced April 14 that Kelly had been dismissed from the team for “conduct detrimental to our program.” Kelly, benched following a couple of interceptions, verbally sparred with assistant coaches during the spring game, which triggered the dismissal.
Kelly, along with Cole Stoudt and DeShaun Watson, had been part of a three-headed competition to replace long-time starter Tajh Boyd prior to getting the wrong end of Dabo’s boot.
A four-star member of the Tigers’ 2012 recruiting class, Kelly was rated as the No. 4 dual-threat quarterback in the country and the No. 1 player at any position in the state of New York. Kelly will have two years of eligibility remaining beginning in 2015.
Tags: Bo Wallace, Chad Kelly, Clemson, Cole Stoudt, Deshaun Watson, Mississippi, Tajh Boyd
Ex-Clemson QB Chad Kelly tweets he’s visiting ‘Bama again
Back in June, erstwhile Clemson quarterback Chad Kelly visited Alabama before heading off to the Mississippi junior college he is playing for in 2014.
Three months later, however, the nephew of former Miami Hurricane and Buffalo Bill great Jim Kelly still has his eyes on the Tide.
In a tweet posted to his personal Twitter account early Friday afternoon, Kelly revealed that he will again be visiting the Tuscaloosa school. Just when and why he will be visiting again is unknown, although he could be in town for the Tide’s home opener against FAU Saturday.
https://twitter.com/ChadKelly_11/status/507944043171840000
In a subsequent tweet, Kelly also expressed some level of interest in Florida State — while also stating that he’d picked a very interesting game involving the Seminoles to attend.
Kelly is already has two games into his JUCO career, passing for 385 yards and four touchdowns Thursday night in helping top-ranked East Mississippi push its record to 2-0 on the season. Regardless of how well he performs in this JUCO stint, however, he’ll need to be thoroughly vetted by whichever FBS team ultimately brings him in.
A four-star member of the Tigers’ 2012 recruiting class, Kelly was rated as the No. 4 dual-threat quarterback in the country and the No. 1 player at any position in the state of New York. After playing at the JUCO level in 2014, Kelly will have two years of eligibility remaining beginning in 2015.
Tags: Chad Kelly, Clemson, Cole Stoudt, Tajh Boyd
CFT 2014 Preseason Preview: ACC Predictions
By Kevin McGuireAug 22, 2014, 10:10 AM EDT
As the 2014 season draws near, we peek into our crystal ball and guess project how each of the five major conferences will play out. Today, we will be examining the ACC.
And while we’re at it, check out our CFT 2014 Preseason Preview Repository for our team’s looks at the upcoming season.
1. Florida State (Last year: 14-0; beat Auburn in BCS Championship Game)
It is easy to make the Seminoles the chalk favorite when evaluating the rest of the ACC. Despite losing some key players from a national championship roster, Florida State returns Heisman Trophy winning Jameis Winston and a deep roster that has benefitted and prepared for this moment since the day Jimbo Fisher took over as head coach. The depth is there with loads of quality all around. Karlos Williams should have a big year at running back and Winston’s top targets in the open field will be Rashad Greene and tight end Nick O’Leary. The defense has a few holes to plug, but that should not be of much concern. Florida State looks to have the top unit or second-best unit in the entire ACC at every position on the field. There is not one game on the 2014 schedule Florida State should not be the favorite in, and they could keep this winning streak going into the playoffs. This team is clearly in College Football Playoff or bust mode with this amount of talent and the level of expectations in Tallahassee. Of all teams around the country, Florida State looks to be the most likely to be able to afford a blip in the loss column and still be invited to the playoff. But who can beat them? Anybody?
2. Clemson (Last year: 11-2; beat Ohio State in Orange Bowl)
The distance between Clemson and Florida State at the top of the Atlantic Division is not as widespread as last season’s meeting might suggest, but it did widen a bit heading into 2014 with the loss of Tajh Boyd and Sammy Watkins. Having Vic Beasley back on defense is rather nice. Offensive coordinator Chad Morris could have his work cut out for him in 2014 and Clemson could fall behind early if adjustments are not made. Getting to October with a winning record is not exactly a given with road trips to Georgia and Florida State lined up. Clemson should be a better team by the end of the season once they go through some growing pains early on.
3. Louisville (Last year: 12-1; beat Miami in Russell Athletic Bowl as member of AAC)
This Louisville team may be a far cry from the team we saw a year ago, but they could have a better debut season lined up compared to last year’s ACC rookies at Syracuse and Pittsburgh (and they both went to a bowl game and returned home with a win). The question is what does Bobby Petrino to get the Cardinals off on the right foot and can he continue to work some quarterback magic as the Cardinals enter the post-Teddy Bridgewater era? For starters, he feeds Dominique Brown and Michael Dyer on the ground and gets the ball to DeVante Parker through the air. Will Gardner will be the likely heir to Bridgewater’s throne under center, with just 12 pass attempts last season. The defense should be prepared for an adjustment period after returning juts four starters from last season.
4. Syracuse (Last year: 7-6; beat Minnesota in Texas Bowl)
Syracuse turned out to be a nice little surprise last season, but running back Terrell Hunt is no longer a secret. The Orange will let him carry the offense with his legs and his arm once again. If he can cut down on the interceptions and tack on a few more touchdowns through the air he will give defenses a little something extra to think about. With 15 starters back, the Orange look to have a good amount of experience on both sides of the football. They are not at a level ready to compete for a top spot in the division, but Syracuse could make a push for a third place finish if some pieces come together. The Orange have a schedule that could set up for a great start, but a challenging October will see Syracuse go through some rough spots. How they play through it will tell how their season will end.
5. Boston College (Last year: 7-6; lost to Arizona in Advocare V100 Bowl)
Steve Addazio has already breathed new life into this program, but what happens this season could be crucial. Boston College only brings back a handful of players from last season’s 7-6 squad, and they must find a way to replace 2,000-yard rusher and Heisman Trophy finalist Andre Williams. The primary running duties will likely be handed off to Myles Willis, and quarterback transfer Tyler Murphy from Florida should embrace a fresh opportunity with a head coach who knows all about him. The spring showed Boston College will once again be likely to rely on the running game, but help could be on the way in the passing game with some receivers getting into the mix.
6. North Carolina State (Last year: 3-9)
The 2013 season was a painful one for the Wolfpack, somewhat literally. With a rash of injuries across the roster, NC State hardly got a chance to see what it could do with new head coach Dave Doeren on the sideline. With any luck that should change this season, with 14 starters due to return this season. There is plenty of work to be done on offense and defense in Raleigh, but having a steady quarterback situation with the transfer of Jacoby Brisset from Florida could help.
7. Wake Forest (Last year: 4-8)
New head coach Dave Clawson will have to be patient as he takes over a Wake Forest team in need of improvement across the field. The offense has averaged fewer than 19 points per game each of the past two seasons. Can that possibly go one more year? Competing in this division does not make anything easier for the Demon Deacons. They could jump out to a promising start (3-1 is not completely unrealistic), but once ACC play opens it could be a long fall.
COASTAL DIVISION
1. North Carolina (Last year: 7-6; beat Cincinnati in Belk Bowl)
The biggest thing going for North Carolina is momentum. After getting off to a rough start in 2013 (1-5), the Tar Heels kicked things in gear and ended the season winning six of the final seven games of the year, including a bowl victory. Larry Fedora finally seems to have things in order for a potential run to a division title, and he does so with 15 starters coming back this season. Marquise Williams will keep the dual-threat going for the Tar Heels after leading the team in rushing in 2013 and second to Bryn Renner in passing, but getting running back TJ Logan more involved should be in the plans. North Carolina may be a little in development on the defensive line, but the linebackers and secondary are in really good shape this fall.
2. Miami (Last year: 9-4; lost to Louisville in Russell Athletic Bowl)
It is hard to believe but Miami is entering its 11th season as a member of the ACC and is still searching for a trip to the ACC Championship Game. Could this finally be the year for the Hurricanes? Al Golden certainly has a running back to lead his offense there with Duke Johnson and the defense did put up some better numbers in 2013 compared to 2012 by knocking off roughly four points and 60 yards per game. And for the first time in a while Miami posted back-to-back seasons with a positive turnover margin. Want more? The offense has increased its average scoring each season Golden has been in Miami. Yet, they can’t seem to take a firm grasp on the Coastal Division. Why? Inconsistent play. Miami will be challenged early with road games at Louisville and Nebraska and a home date against Arkansas State is no guarantee. Miami also catches Florida State on the schedule, which could hurt their chances in the division race when other possible contenders skip FSU (and Clemson).
3. Virginia Tech (Last year: 8-5; lost to UCLA in Sun Bowl)
Virginia Tech returns nine starters on offense, but the Hokies break in a new starting quarterback. Fortunately, transfer Michael Brewer is not without experience and could be ready to step right into action in Blacksburg. The offensive line has just one hold to fill as well, so stability and uniformity should not be a concern. Virginia Tech’s biggest concern will just be scoring points after averaging just 22.5 points per game last season. And that’s the catch. Virginia Tech only allowed 19.3 points per game last season, so the Hokies probably should have won more than eight games. There is a chance to get off to a good start too, because the road trip at Ohio State looks much more manageable now with Braxton Miller out for the season.
4. Pittsburgh (Last year: 7-6; beat Bowling Green in Little Caesars Pizza Bowl)
Pittsburgh loses a monster on the defensive line with Aaron Donald now in the NFL, and the secondary is extremely thin in light of some offseason news, so to say the defense is a concern is putting it nicely for the Panthers. The Panthers also allowed more points per game than they scored, which tends to be a rarity for a team with a winning record. If the defense can clamp down just a bit more, Pittsburgh could easily play their way to a Coastal title, although they will win ugly at times. Pittsburgh has young receiver Tyler Boyd, already one of the top receivers in the ACC, and a steady running stable of James Conner and Isaac Bennett. The schedule is also extremely favorable for Pittsburgh, with no Florida State or Clemson and home games against Virginia Tech, Georgia Tech and Duke.
5. Duke (Last year: 10-4; lost to Texas A&M in Chick-fil-A Bowl)
Let us not attempt to take anything away from the great work done in Durham by David Cutcliffe and his Blue Devils the last two seasons. Duke going to back-to-back bowl games was something that could once only be dreamed of. Can they get back to the postseason for a third straight year? Absolutely, but will the rest of the division and the typical football powers rebound a little to block a return trip to the ACC Championship? Duke was set to return 14 starters, but injuries have already taken a toll with an ACL tear to All-ACC linebacker Kelby Brown and another to tight end Braxton Deaver. On top of that, Duke lost quarterback Brandon Connette to a transfer to Fresno State. All is not lost though. Duke still has receiver Jamison Crowder, one of the best in the ACC, and the schedule avoids Florida State and Clemson once again. No school in the country will have an easier October either.
6. Georgia Tech (Last year: 7-6; lost to Mississippi in Music City Bowl)
Georgia Tech’s strategy will be the same as it has always been under head coach Paul Johnson; Run, run, option run. Will the Yellow Jackets be able to use that offensive style effectively enough to take the heat off of Johnson? The depth on offense is not great, although six starters return from 2013. One starter not back this season is quarterback Vad Lee, who decided to transfer this offseason. That opens the door for sophomore Justin Thomas under center, and he played sparingly last season. The big concern will be the defense. Georgia Tech allowed just 22.8 points per game last season, the lowest average since 2008, but just four starters return for the new year. Georgia Tech may still have enough to make a run at the wide-open Coastal Division (avoiding Florida State on the schedule helps, and they get Clemson at home).
7. Virginia (Last year: 2-10)
If there is one coach that is latched into the hot seat in the ACC, it may just be Virginia’s Mike London. The head coach of the Cavaliers. Virginia lost their top offensive player in tight end Jake McGee (he went to Florida), so the need for returning players to step up in 2014 cannot be overstated. Virginia does return eight starters on offense, with a handful of young players scattered throughout. Running back Kevin Parks should be the focus of the offense after a 1,000-yard season with 11 touchdowns. The defense returns nine starters from 2013, and the hope is playing experience last season will help slow down a trend in allowing more points per game each of the past three seasons. The defense was gashed for 404 yards per game last season, the highest per-game average dating back to 2007. One positive might be the number of sacks (28) was the highest sack total for Virginia since recording 29 in 2008. But Virginia has a long way to go to improve on two wins from last season.
(Click HERE for the CFT 2014 Preseason Preview Repository)
Tags: Al Golden, Andre Williams, Bobby Petrino, Boston College, Brandon Connette, Braxton Deaver, Braxton Miller, Bryn Renner, Chad Morris, Clemson, Dave Clawson, Dave Doren, David Cutcliffe, DeVante Parker, Dominique Brown, Duke, Duke Johnson, Florida State, Isaac Bennett, Jacoby Briskett, Jake McGee, Jameis Winston, James Conner, Jamison Crowder, Jimbo Fisher, JMU, Karlos Williams, Kelby Brown, Kevin Parks, Larry Fedora, Louisville, Marquise Williams, MIA, Michael Brewer, Michael Dyer, Mike London, Myles Willis, Nick O'Leary, OSU, Paul Johnson, Pittsburgh, Rashad Greene, Sammy Watkins, Steve Addazio, T.J. Logan, Tajh Boyd, Teddy Bridgewater, Terrell Hunt, Tyler Boyd, Tyler Murphy, UNC, UVA, Vad Lee, Vic Beaseley, Vic Beasley, VT, Will Gardner
CFT Preseason Top 25: No. 16 Clemson
By Kevin McGuireAug 13, 2014, 2:12 PM EDT
2013 record: 11-2 overall, 7-1 in ACC (2nd in Atlantic division)
2013 postseason: Orange Bowl vs. Ohio State (40-35 win)
2013 final AP/coaches’ ranking: No. 8/No. 7
Head coach: Dabo Swinney (51-23 overall; 51-23 in 6 years at Clemson)
Offensive coordinator: Chad Morris (4th season at Clemson)
2013 offensive rankings: 56th rushing offense (175.62 ypg); 9th passing offense (332.9 ypg); 9th total offense (508.5 ypg); 8th scoring offense (40.2 ppg)
Returning offensive starters: 4
Defensive coordinator: Brent Venables (3rd season at Clemson)
2013 defensive rankings: 53rd rushing defense (155.69 ypg); 16th passing defense (200.6 ypg); 24th total defense (356.3 ypg); 24th scoring defense (22.2 ppg)
Returning defensive starters: 7
Location: Clemson, South Carolina
Stadium: Memorial Stadium (81,473; Grass)
Last conference title: 2011
At first glance it may look as though Clemson is likely to be in a bit of rebuilding mode after losing some talented players (including Tajh Boyd, Sammy Watkins and Roderick McDowell) but the Tigers return more seniors in 2014 than any previous season in the Dabo Swinney era. This year’s senior class needs eight wins to set a new school record for wins by a recruiting class, and that certainly looks attainable this season. Cole Stoudt is ready to take over the responsibility as starting quarterback after playing the role of Boyd’s understudy each of the past three seasons. The strength of Clemson could actually come on the defensive side of the football, with a deep defensive line led by defensive end Vic Beasley, who had 13 sacks last season. This Clemson team may not be as good as they have been in recent seasons, but Swinney’s recruiting in recent years have assured Clemson of a very good team once it gets going.
Clemson plays in the same division as Florida State. With as far as Clemson has come in recent seasons, the bar has been set to a height that may not be able to be cleared by Clemson this season, in part because they happen to play in the same division as the best team in the country (and defending national champions, and Clemson has to play on the road in Tallahassee). It could be a rough start for this Clemson team with road games at Georgia and Florida State in September, so it may be unfair to truly judge Clemson until later in the season. Clemson should be one of the best teams in the ACC by the end of the season, but they will likely be playing from behind Florida State the entire way.
How much will Clemson have in the tank at the start of the season. As just referenced above, the Tigers are going to be thrown right into the fire in September with rod games at Georgia, a team some expect to compete for the SEC East and perhaps even the SEC championship this fall, and later at Florida State, defending ACC and national champions and looking prime for a repeat bid out of the gate. Clemson could very well lose those two games, but will they be able to at least make them look respectable? No coach or player will take much solace in a lose, but proving worthy of going toe-to-toe with Georgia ad Florida State regardless of the outcome could go a long way in setting the tone for the remainder of the season. Clemson beat Georgia last year in a wild game at home, but failed to show up for the home game against the Seminoles. Revenge is one thing, but respect is an entirely different aspect.
MAKE-OR-BREAK GAME: vs. South Carolina
Regardless of what happens against Georgia or Florida State in September, the time has come for Clemson to prove it can compete with and beat South Carolina. Even Clemson’s best teams the past few years have been crippled by their in-state rivals from the SEC. Clemson has lost this game five straight years, and those games have not been all that close either. Each game has been decided by a minimum of 10 points, giving Steve Spurrier and his program some in-state bragging rights. Clemson gets this year’s meeting at home, and it would be a great way for the Tigers to put a bow on what could turn out to be a double-digit win season.
HEISMAN HOPEFUL: Defensive end Vic Beasley
We know that defensive players are probably never going to win the Heisman Trophy, but it should not go without mention just how good Vic Beasley is for the Tigers. He could have joined Boyd and Watkins in the NFL Draft this past spring but he opted to return for one more year at Clemson, and that is fantastic news for the Tigers. If he gets off to a fast tart in high-profile games at Georgia and Florida State, and helps Clemson’s defense lead the way to victories in each, then the campaign will quickly emerge as the latest defensive hopeful to snag the Heisman.
Tags: Brent Venables, Chad Morris, Clemson, Cole Stoudt, Dabo Swinney, Roderick McDowell, Sammy Watkins, Tajh Boyd, Vic Beasley
Clemson using former QB Tajh Boyd in practice to emulate Ohio State’s J.T. Barrett December 17, 2016 1:34 pm Ex-Clemson QB Chad Kelly tweets he’s landed at Ole Miss December 11, 2014 8:58 am Ex-Clemson QB Chad Kelly tweets he’s visiting ‘Bama again September 5, 2014 2:36 pm CFT 2014 Preseason Preview: ACC Predictions August 22, 2014 10:10 am CFT Preseason Top 25: No. 16 Clemson August 13, 2014 2:12 pm Five questions for the ACC Football Kickoff July 19, 2014 2:30 pm Report: ex-Clemson QB Chad Kelly visited Alabama June 4, 2014 2:22 pm Clemson adds seldom-used Stanford QB May 1, 2014 1:21 pm JUCO ranks next up for booted Clemson QB April 30, 2014 5:56 am Is Chad Kelly’s apology to Clemson too little, too late? April 16, 2014 7:51 pm Clemson names Cole Stoudt starting QB; big shoes to fill left by Boyd April 15, 2014 5:31 pm Hot-tempered QB Chad Kelly kicked off Clemson roster April 14, 2014 5:21 pm Academics sideline Clemson’s Germone Hopper for rest of spring March 25, 2014 11:57 am Malzahn won’t allow Nick Marshall to work with QB guru March 3, 2014 8:28 am Future Heisman candidates from the recruiting class of 2014 February 25, 2014 8:13 pm Report: Former Alabama RB Kamara visited Clemson February 1, 2014 2:30 pm Auburn’s Dee Ford leads South defense to 20-10 victory in Senior Bowl January 25, 2014 7:09 pm Clemson DE Vic Beasley to return for his senior year January 15, 2014 8:14 pm As expected, AJ McCarron will skip Senior Bowl January 15, 2014 11:51 am Dabo Swinney thinks OC Chad Morris will stay at Clemson January 11, 2014 9:25 pm
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Importance of Universities in Communities - 4:37
Doug Byerly, Councilman, Lock Haven
https://comcastnewsmakers.com/Videos/2017/10/15/importance-universities-communities
Host Candace Kelley talks with Doug Byerly, Councilman, Lock Haven, PA, about the importance of universities in communities, at the recent Pennsylvania Municipal League Annual Summit.
Hosted by: Candace Kelley Produced by: Freedom Newsmakers Team
#Pennsylvania #General Interest
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Standing up for Pennsylvania’s third-class cities is among the work of the Pennsylvania Municipal League, a nonprofit, non-partisan organization. Host Sheila Hyland and guest Sal Panto Jr., PML Pres. and Easton PA Mayor, discuss examples of PML’s support across PA. Recorded at the PML’s Annual Summit at the Majestic Theatre in Gettysburg Borough. easton-pa.org
https://comcastnewsmakers.com/Videos/2019/10/24/Sal_Panto_PML_2019
Fighting to Make Latino Voices Heard in Southwestern PA
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Casa San Jose (or House of St. Joseph) fights to make the voices of the Latino community heard in Southwestern PA - promoting integration, self-sufficiency & advancing the cause of reforming immigration policy. Guest is Monica Ruiz, Executive Director. Sheila Hyland hosts. Recorded at the Xfinity Store, McCandless Crossing, Pittsburgh, PA. casasanjose.org
https://comcastnewsmakers.com/Videos/2019/9/1/Casa-San-Jose
Role of the Commonwealth’s County Commissions Explained
Role of the Commonwealth’s County Commissions Explained - 3:47
The Commonwealth’s County Commissions have many responsibilities that most people don’t think about – from election systems and processes to the opioid epidemic. Lisa Schaefer, Acting Executive Director Appointee, County Commissioners Association of Pennsylvania explains. Jill Horner hosts. pacounties.org
https://comcastnewsmakers.com/Videos/2019/10/1/Lisa_Schaefer
Zero Waste Legislation
Zero Waste Legislation - 4:02
Pennsylvania State Representative Perry Warren explains a package of bills including the water bottle reduction bill that would reduce waste through water bottle filling stations in government buildings. Recorded December 5, 2019.
https://comcastnewsmakers.com/Videos/2019/12/6/BC191205-8
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Kevin Feige Once Said Both Sony and Disney Knew “Unprecedented” Deal Was the “Best Thing for Spider-Man”
By Cameron Bonomolo - August 25, 2019 08:00 pm EDT
Before the public divorce now threatening to tear Tom Holland’s Spider-Man from the Marvel Cinematic Universe, Sony and Marvel parent company Disney once agreed an “unprecedented” pact between the rival companies was “the best thing for Spider-Man.”
“This was a very unique scenario, in large part thanks to [producer] Amy Pascal, and then [Sony chairman] Tom Rothman, the people at Sony, the people at Disney, who knew and really believed this was the best thing for Spider-Man,” Feige said in a 2017 interview with Screen Crush when promoting Spider-Man: Homecoming, the first Spidey solo produced under a five-movie deal that allowed the Sony-controlled character to exist and operate within the Disney-owned MCU.
That deal, Feige added, went “very smooth.” It was in the best interest of not just Peter Parker — who would for the first time exist in a universe shared by other Marvel superheroes on the big screen — but Sony and Disney, who would enjoy great success from the mutually beneficial deal.
“And egos and lawyers and all that other corporate stuff that you would think would hinder it, it was all very smooth. Sort of shockingly so,” Feige said. “People find that interesting, and maybe unprecedented, but it all really came down — from my point of view — to a creative vision for what to do with this character.”
Holland’s rebooted Spider-Man joined the MCU in Disney’s Captain America: Civil War and headlined Sony’s Homecoming before appearing alongside Earth’s mightiest heroes again in Disney’s Avengers: Infinity War and Avengers: Endgame. Sony’s second picture, Spider-Man: Far From Home, would mark the end of the deal.
According to a recent report from Variety, both parties returned to the table to renegotiate a deal as long as six months ago. Claims from inside sources have been contradictory: one insider close to the deal claimed Sony didn’t move to act on re-upping the deal despite Disney’s efforts to keep the character, and another said it was Disney who was “no longer interested” in loaning out Feige to work on IP under Sony’s control.
That same report from Variety said multiple insiders reported Rothman was willing to up Disney-Marvel’s stake to 25%, up from the reported 5% of first dollar gross; a report from Deadline said it was Disney who asked for a 25% stake and co-financing deal for Sony movies involving Marvel and Feige, who masterminded Homecoming and Far From Home — the latter going on to become Sony’s highest grossing movie ever.
Worse still, another report claimed Rothman and Sony — hot off the successes of Venom and the Oscar-winning Spider-Man: Into the Spider-Verse — believe they no longer need Marvel or Feige. (Rothman once conceded Sony “deferred the creative lead to Marvel” on Spider-Man because Feige and his studio “know what they’re doing.”) The Tom Hardy-led Venom launched “Sony’s Universe of Marvel Characters,” to be populated by some of the roughly 900 characters whose screen rights are controlled by Sony; planned spinoffs include Kraven the Hunter, Black Cat, Silk and Morbius, the latter now being readied for a July 2020 debut.
Asked about the still unresolved split at D23 Expo over the weekend, both Feige and Holland gave diplomatic answers — even if Holland, in his video interview, did appear to glance off-camera a total of three times.
“Basically, we’ve made five great movies. It’s been five amazing years,” Holland told EW. “I’ve had the time of my life. Who knows what the future holds? But all I know is that I’m going to continue playing Spider-Man and having the time of my life. It’s going to be so fun, however we choose to do it. The future for Spider-Man will be different, but it will be equally as awesome and amazing, and we’ll find new ways to make it even cooler.”
And Feige — reportedly caught in the crossfire of a warring Sony and Disney, each under the respective charge of Rothman and Alan Bergman — said the original deal left him with a feeling of “gratitude and joy.”
“We got to make five films within the MCU with Spider-Man: two standalone films and three with the Avengers. It was a dream that I never thought would happen,” Feige told EW. “It was never meant to last forever. We knew there was a finite amount of time that we’d be able to do this, and we told the story we wanted to tell, and I’ll always be thankful for that.”
But that story has not been told in full, as evidenced by the jaw-dropper cliffhanger that ended Far From Home. In July, before the public learned talks between Sony and Disney broke down, Feige teased his plans for Spider-Man 3 — plans that included a Peter Parker story that’s “never been done before on film.”
“It’ll be fun to see Spidey back in his element, out of the shadow of Tony, out of the shadow of the other Avengers, as his own man now, as his own hero,” Feige said in that July interview. “And yet now facing his own challenges that aren’t coming from Avengers fighting, like [Civil War], or aliens coming, like [Infinity War] or [Endgame]. It’s all Peter focused and Peter based.”
Both Sony and Disney continue to know Spider-Man in the MCU — where he’s been set up as its new face following the passing of mentor Iron Man (Robert Downey Jr.) — is the best thing for the character.
Fans have expressed their discontent by waging war online, taking to social media with anti-Sony and anti-Disney sentiments alike; when word first broke, it ignited a passionate fanbase to launch a Sony boycott that includes swearing off Spider-Verse sequels and the Andy Serkis-directed Venom 2.
The first Sony-Disney deal was unprecedented and at one time considered little more than amazing fantasy. But as the character at the heart of this tug of war understands better than most, with great power must come great responsibility — and because Spider-Man has become such an integral part of the MCU, made possible only through the combined efforts of Disney and Sony, it’s the responsibility of both sides to do what’s right.
Chris Hemsworth Teams With NatGeo for Real-Life Superhero Docu-Series Limitless
People Are Super Confused Why The Incredible Hulk is Trending
Marvel Studios Rumored to Be Actively Casting Hulkling
New Black Widow Toys Could Spoil Big Plot Detail
Spider-Man Fan Imagines the MCU Debut of the Sinister Six With Epic Logo
Sony Sneakily Hinted at Plans to Bridge Its Spider-Man Universe With the MCU Years Ago
Is Marvel Setting Up the Future of the MCU With Empyre?
ComicBook Nation Episode 98: DC’S Crisis on Infinite Earths Spoilers & Bad Boys 3 Review
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Editors Hideaway Download Forum FM19 and Older
Football Manager Game Help Forums
Editors Hideaway
[FM 2016] Ultimate Stars and Legends Game (1880's to 2016)
By Fenech, November 7, 2014 in Editors Hideaway Download Forum FM19 and Older
fm legends
si games
izagooner
Team: do you need to ask
OK great work mate hope your back next year
Fenech
Team: Chelsea
Managing: Chelsea
Just now, izagooner said:
Doubtful lol
you know you want to lol
just loaded up the update in the editor... 1700 players with a PA of 170 or above and loads more besides great effort .. Richard Hofmann beast
37 minutes ago, izagooner said:
Thanks 2048 legends and stars and counting
Fenech ...... Luc Nilis should be at Anderlecht not Genk https://en.wikipedia.org/wiki/Luc_Nilis
aveago
No class of 92, Phil Neville and Nicky Butt not in there.
maybe next year http://www.pesmitidelcalcio.com/viewtopic.php?f=19&t=630
ill add them in for the final update
18 minutes ago, Fenech said:
Hoped you might say that no more from me now just going to wait patiently Once again a big thanks for all of your effort with this
1 minute ago, izagooner said:
thanks mate, i really appreciate the support.... and it means alot. It's good to know that people appreciate it. Well worth the wait Boro is next
UpTheBoro
You're a good man! I look forward to the final update
600 games for Middlesbrough set to return...
7 England Caps - the equivalent of about 80 caps today
Reginald Garnet Williamson
Team: Don't give this sucker no
Managing: Statue, give him guts!
yes I agree, best thing for a game ever. Love it.
Oh my! Despite knowing the incredible effort you put into your database, I kind of assumed Boro would be half-arsed (possibly due to my constant and annoying requests ), but then you screenshot Reggie! You are still clearly putting the research in. Although I've been born and raise on the likes of Juninho, Emerson and Ravanelli, it's amazing to see other have recognised our history.
The uneducated probably don't realise Brian Clough was a record breaking striker before he became one of the most recognisable Managers in history, or that Graeme Souness was voted out greatest ever player, or that Jack Charlton's promotion team was feared by most, or than John Hickton had the hardest shot known to man, or that Wilf Mannion even existed!
....Or, That Christian Vieri still claims that Juninho is the most gifted player he ever played with (and he played with the likes of Ronaldo and Roberto Baggio). If he didn't break his leg in his first year at Atletico Madrid he truly would've been one of the first name in this database, not one of the last.
Anyway, I'm delighted you have decided to include the Mighty Boro in you epic database! You, Sir, Are a LEGEND!!!
EDIT: Sorry for the Borefest, I just love my team!
Edited August 9, 2016 by UpTheBoro
19 minutes ago, UpTheBoro said:
Each club is heavily researched before they return and i don't do things by halves, so you can expect the best possible middlesbrough team..
What can you tell me about Bernie Slaven?
Geoff Hurst, Bobby Charlton, Ian Rush, Thierry Henry and Cliff Bastin are widely known as some of English football’s most lethal goal scorers. Each has topped the goal-scoring charts, and their record-breaking exploits are regularly mentioned.
But one name you’re less likely to hear is George Camsell. This is strange, as he has more career goals in English football than any of the players just mentioned by quite a distance.
George Camsell is the boy who just couldn’t stop scoring. He is also largely forgotten – not only by the English game but, some might say, by Middlesbrough FC and its supporters, the same club for which he scored 345 career goals between 1925-1939, including a club record 63 goals in one season.
Outside the Riverside Stadium stand the original gates from the club’s previous home, Ayresome Park. On either side of the gates stand two giant bronze statues, legends of not only Middlesbrough FC, but of England’s national team of years gone by.
One is of former Boro and England forward Wilf Mannion, nicknamed the “Golden Boy”. The other is “gentleman” George Hardwick, England fullback and wartime captain of Great Britain.
Absent is the record-breaking Camsell, English football’s fifth-highest goal scorer of all time. He chalked up a club record 345 career goals, with 235 of those coming in the top flight of English football, and had an equally illustrious career with the national team, scoring 18 goals in nine games between 1929-1936. That’s more career and top-flight goals than Charlton, Law, Bastin, Lofthouse, Matthews, Rush, Cole, Henry – and almost everybody else.
So why have most people never heard of Camsell, and why is he not celebrated today?
One obvious reason is the fact that he played so long ago. He started his career at Durham City in 1924-25 and moved to Middlesbrough the following season for £500. Today you will struggle to find anyone living who actually saw him play. Cigarette cards, old photographs, history books and folklore are Camsell’s popular legacy – this, and some grainy footage on YouTube of him scoring for England against Scotland at Wembley, and another clip of him training at Ayresome Park is all there is to be found. Somehow, however, other pre-WW2 players like Dixie Dean, Steve Bloomer, Geordie Favourites Hughie Gallacher and Jackie Milburn are more remembered and revered.
If the question came up in a pub quiz, most people would probably name Dixie Dean or Jimmy Greaves as English football’s all-time top scorer. In fact, that honour goes to Arthur Rowley, who had 434 career goals between 1946 and 1964, although he is probably not mentioned as much as the better known Dean, Greaves or Steve Bloomer, who follow him in the record books. Remarkably, Camsell, fifth on the list, is only seven goals behind Bloomer and 12 behind Greaves. The number-two all-time top scorer, Dean – the most famous striker of his day – remains as the scorer of the most league goals (60) in a season. And some could argue was also Camsells nemesis.
Regular penalty-taker Dean, who was desperate to surpass Camsell’s record of 59 (set the previous season), broke it during the 1927-28 campaign for Everton, the eventual League champions.
Benny Yorston, George Camsell and Bob Baxter training at Ayresome Park
Camsell himself did not consider penalties to be “proper” goals, so he refused to take them. If another story by an ex-teammate is to be believed, it was because Camsell had missed a penalty earlier in his career and took such a dressing-room ribbing that he vowed never to take another.
But even for Boro fans, plenty of others are mentioned before Camsell. You will hear tales passed down from grandfathers about the local legend, “Golden Boy” Wilf Mannion, who represented Boro between 1936 and 1954, save for the war years when he was off fighting in France and Italy. He scored 99 goals. Or another Boro goal machine, Brain Clough, who played for the club between 1955 and 1961 and scored 197 goals. Local boys Mickey Fenton; Jackie Carr and his brothers; Alan Peacock; and even Alf Common – the first £1000 footballer – are mentioned more often than Camsell. Could it be because Camsell wasn’t born by the Tees, and therefore isn’t thought of as one of the fans’ own?
Even with more modern Tessiders goal-scoring heroes – like John Hickton, Bernie Slaven, Fabrizio Ravenelli and fans favourite Juninho, who was voted the club’s best-ever player by supporters – George Still tops the goal lists in the club’s record books.
He took the club to two promotions; was its all-time top scorer (345 goals); scored the most goals in a season (63) for the club; was the top scorer for 10 seasons running; and still holds the record for most hat tricks in a season (9), part of a career total of 24.
As you can see by the chart on the right, Camsell’s goal-scoring record in his 14 seasons with Middlesbrough was phenomenal.
Camsell, from Framwellgate Moor in County Durham, worked in the mines at age 13 and was allegedly originally discovered during a kick-about at the local pit one afternoon during a strike. Legend has it that he didn’t even kick a ball until he was 18.
The versatile Camsell was equally comfortable scoring on a cold wet night on a muddy pitch in the northeast amateur leagues as he was a sunny afternoon on the Wembley baize for England.
BECOMING A LEGEND…
Originally a winger, Camsell’s goal-scoring exploded when he was drafted to replace the injured Jimmy McClelland at the start of 1926-27 during an early-season slump for Boro. After missing the first four games, Camsell managed to bag a record 59 league goals in 37 games (and 63 goals in all competitions) to help make Boro champions. Described by Brian Clough as “the toughest player in the football league” Camsell was a complete all-rounder, able to score with both feet and head regularly from every angle, inside and outside the penalty area.
With the nation’s favourite, Dixie Dean, playing for Everton and Camsell plying his trade in the unglamorous northeast, Dean was seen as the poster boy for English football alongside Cliff Bastin, Arsenal’s own goal machine of Chapman’s glory days. Both were England regulars compared to Camsell. With so few international fixtures compared to modern football and with the England team of the day being picked by an FA committee, it helps explain why Camsell was only picked 9 times over a span of 7 seasons.
If Camsell was playing and scoring goals at the same rate today, he could be playing in the Champions League with Real Madrid or Barcelona, commanding a £50m transfer fee and earning £150k per week. As it was, he lived in a small house on a terraced street within walking distance of Ayresome Park and drove an old Morris Eight car.
Camsell was only 22 when he arrived at Middlesbrough in 1925. He stayed until the end of his career in 1939. Camsell had played away to Liverpool in the second game of the 1939-40 season when WW2 broke out and officially ended football for seven seasons. On Saturday, 3 September 1939, after the third game of the 1939-40 season, all football in Great Britain was halted. War just had been declared, and large gatherings were banned.
WAR YEARS AND AFTER FOOTBALL…
But some football did continue of course. Camsell continued to represent Boro in northern leagues and cups for a further three years, until the 1941-42 season. He appeared 28 times and scored a further 19 goals while playing with Mannion, Harold Shepherdson and guest players including Matt Busby from Liverpool. Camsell would have been approaching 40 years of age the last time represented Middlesbrough.
After his playing days, Camsell worked for the club as a coach, chief scout and assistant secretary before retiring in December 1963. On his retirement, he was presented with a television as a thank-you for dedicating four decades of his life to the Middlesbrough Football Club.
In March 1966, George Camsell died in the town’s General Hospital, adjacent to Ayresome Park where he had scored so many goals – close enough to hear the roar of the Holgate end one last time. He was 63 years old.
It’s highly unlikely that any of Camsell’s goal-scoring records will ever be broken for MFC. He is that standout player from a club’s past who did something extremely special and should not be forgotten.
Newcastle fans still worship Wor’ Jackie Milburn. Everton still speak of Dixie Dean, and Derby celebrate Steve Bloomer. Middlesbrough should keep the memory of George Camsell alive and celebrate his amazing legacy and what he once did for this great football club. We should also follow suit and erect a statue for the club’s greatest goal scorer in its 139-year history – not just to celebrate, but to inspire others to do the same. Still, we may never see his like again.
Some bigger clubs claim that smaller clubs lack history. Well, Middlesbrough certainly has some history, all right. They just don’t shout about it !
Ladies and Gentleman - I am proud to present, the finest striker ever to play in Middlesbrough, the finest england striker you never heard of,
THE BOY WHO COULDN'T STOP SCORING!
Bittah Dreamer
I know you have your own way of looking at these things, but are some of the U.K. Based players not a little over powered?
E.g. Ivan Campo has 180 CA/PA and 20 for passing? He was a good player for Bolton - but he still wasn't one of the top players in the league at that time. And he was mainly a squad player at Madrid, with only 4 caps for Spain (at a time when they weren't as strong as they have been in recent years).
Robin Friday had the same CA and PA as Pippo Inzaghi. While Friday might have been an very talented player, he was uncapped and played at 4th, 3rd and second division levels and even then his record comes nothing close to Inzaghi's (league, continental and international titles).
I realsie inzaghi wasnt wasn't an around player so his stats can only go so high, and not arguing he should be higher. Rather that a player untested at the highest levels and without an international recognition shouldn't be so high.
Perhaps a lower CA with a high PA to reflect his wasted potential.
2 hours ago, Bittah Dreamer said:
Hi Bittah,
As you know I recoded the whole game and we had all these debates out in 2014
I have a totally different way of viewing the ratings system to SI.
However i am always willing to listen... I don't think any player is overpowered based on my ratings system... however no-one is perfect especially in a database of this size.
You have to take into consideration that every single player is heavily researched before a rating and stat is given and unlike some players in the normal game, no player that I have coded is left to chance...
Ivan Campo was a great player and imo a 20 for passing... now you have to bear in mind that there is more than one stat for each player and the stats must be balanced within a certain current ability and therefore you can't be exact, but you can be as realistic as possible and there are so many factors that must be taken into consideration before applying each stat to a player.
I don't create a player to suit a certain role, I dont create a player based on who they played for and how much they achieved in their careers, as there are many players in the case of ivan campo who might not have had the luck to be at the right at the right time and we all know how many titles shearer would have won had he gone to united. campo mate was a great player.
I create the players only after heavily researching them and i give the stat as realistic as possible based on my ratings system which i created, and in 2014 i explained this and I explained that I believe the players is a bigger difference in the top 10 per cent, than in the 10 per cent below that and below that....
My ratings system is mathematically based for ability and potential and i prefer it to the ratings system in the normal game.
I have raised Inzaghis potential ability slightly and he is now 22 instead of 24.
I am leaving campo alone.
In terms friday, 180 is still 20 below the best possible 20, and in my opinion those 20 points are bigger than the 20 point that go down to 160..
so to give you an idea of my mind, 155-165 is more championship player.
180 is a good international player, so after researching friday, he had that ability mate, but where inzaghi has a massive adv is he got the lucky breaks, he has a much better personality, id be surprised if friday wasnt more of a liability than anything else.
You can t just base it on the career, there are many players unheard who were simply unbelievable because they just didnt have that career, but when i research i search everywhere and i find out everything or i dont create the player... and every player is created exactly as much as possible to the exact ability and potential of the player and they start again and this time maybe other players get the breaks instead and i try to be as fair as possible within my ratings system.
so the question i ask you, is the players in the normal game underrated? that is a matter of opinion...
i am happy with my version of the ratings and its mathematical system.
Edited August 10, 2016 by Fenech
CasperAscanius
I dont understand why Ebbe Sand not be find good enough to be in Schalke 04. Many people from Denmarks Euro Squad from 1984 and 1992 and World Cup Squad from 1986 and 1998 also missing . Many stars on this teams
9 minutes ago, CasperAscanius said:
send me the names of the players and ill add them to my list mate.
Leitch91
Just downloaded this, loving the look of it so far!
Is there any chance of increasing the legends in the Hibernian side? Stanton, Bremner & Reilly are there however there are a number of players I would love to see in there having had a look at some of the players you have included for other SPFL teams (Hearts, Celtic, Rangers & Aberdeen)
Joe Baker, Eddie Turnbull, Willie Ormand, Gordon Smith, Bobby Johnstone, Keith Wright, Franck Sauzee, David Murphy, Erich Shaedler, Peter Cormack, Jimmy O'Rourke, Russell Latapy, Derek Riordan, John Blackley, Arthur Duncan, Pat McGinlay, Rob Jones, John Hughes, Gordon Rae, Gordon Hunter, Mickey Weir, Andy Goram, Jim Leighton to name just a couple .
I cannot even begin to understand how much time/effort has been put into a database like this and can only thank you for taking the time to do so and I would absolutely love it if you could include those players as well!
5 minutes ago, Leitch91 said:
I'll add these and hibernian to my list
Just now, Fenech said:
Excellent, thanks a lot! Do you want me to break them down by position? Is it easier for you to have a squad of some sort to put together? Sorry for the questions!
If you want to suggest 25 players with a balance of playing positions since 1880 then you can do, i will be heavily researching them myself as well, so that we can find the best possible team for them since 1880
2 minutes ago, Fenech said:
I'll do that no problem, would you prefer me to PM or just post in here?
22 minutes ago, Leitch91 said:
Either way, whichever you prefer...
14 hours ago, Fenech said:
https://en.wikipedia.org/wiki/UEFA_Euro_1984_squads . https://en.wikipedia.org/wiki/UEFA_Euro_1992_squads https://en.wikipedia.org/wiki/1986_FIFA_World_Cup_squads https://en.wikipedia.org/wiki/1998_FIFA_World_Cup_squads
- https://en.wikipedia.org/wiki/Ebbe_Sand - info about Sand and his Schalke stats
I also seen Martin Jørgensen plays for Inter but he has only played in Udinese an Fiorentina in Italy
5 hours ago, CasperAscanius said:
I have checked and Martin Jorgensen plays for Udinese.. so I dont know maybe inter signed him?
I know we had this debate in 2014 and in know you believe in the system you have its your DB and with the work youve done it's definitely your call to make
without knowing your system, I still have to disagree with this. Regardless of how you've coded it, mathematically or otherwise, it's still ultimately a highly subjective call on what a players ability is - and no matter how you do it people will have differing views.
Personally though I do think that there might be an element of over romanticisation here.
Ivan Campo's stats put him at world class level - but he was never that. You say he didn't have the luck to be at the right place at the right time - but he was. He was at Real Madrid, but wasn't good enough to establish himself. As you say, 180 is a good international player - he wasn't that though as he only 4 caps testify to. His present stats suggest one of the best defenders of his era - but I have never seen anybody credibly claim that.
You can't compare him to Shearer - not only did he actually perform to an exceptional lever, the only reason he never made it to a "big" club is because he didn't want (though his move to then money bags Blackburn was hardly small time). It's well documented that Ferguson tried to sign him but got knocked back repeatedly.
Equally with Friday - he started off with big clubs but for whatever reason he couldn't make it there. He had the chance to prove himself but couldn't take it - whether that was due to attitude or ability I can't tell.
You our can argue he was capable of plying international football but we have know way of knowing if he could have replicated his Div 4 or 3 form there. It's one thing to impress in the lower leagues playing with relatively weak defenders and make things look easy - it's another to do it when faced with elite defenders.
When I raised Pippo Inzaghi, I wasn't saying he needed a bump - because I think 180 suits him. He was a legendary player - but he wasn't an all round player. He was a phenomenal goal scorer and penalty box player, and did a few things to the very highest level - but was otherwise limited.
But it one thing about Inzaghi is that we know he was tested at the very highest levels and passes with flying colours. It's ine thing to do it against a Division 4 defence - it's another to do it against the likes of the very best defences in what was then an extremely competitive Italian league with notorious defensive talents.
It's harder to score 10 goals in the premiership than it is to score 20 in Division 4, so just because he did it in the alter division doesn't mean he could have done it in the latter. The ste up is huge - ask Jamie Vardy. It took him time to adjust to the step ups in his career and his first season in the premiership was prett meh.
So if Friday was to thrive in the premiership or at international level he would have needed to step up his game - to learn how to compete against better, stronger, more disciplined and tactically aware defenders - and do so on a one of basis. What he did in Division 3 wasn't good enough for division one (as it was then).
Perhaps he could have made the step up - but performing at that lower level isn't sufficient to say he was as good as top level internationals and European players.
If if you had given him a lower CA and the potential to get to the top, I would agree as it would be acknowleding that he was an unfulfilled talent with the potential to reach the top. Of course to realistically reflect him, he mental attributes would mean he would likely never reach that (much like the way Ravel Morrison never turns good in FM despite his potential).
23 minutes ago, Bittah Dreamer said:
Hi Brittah,
I don't think there is that much difference in the way we view things. Nor is there that much difference between the way I code the players and the players are normally coded although I do prefer my mathematical system and ratings system.
Upon reflection you are right about campo, perhaps i am being a bit romantic in regards to him, i would normally have put him at 170, and that is where he is now.
In regards to Filipo, i was right in the first place to put him at 180 and that is where he is now..
In regards to Friday, I was imagining what he would have become, but then he would of had a totally different personality and as you said would have had to make the leap up in class maybe two or three times,,,, so with that in mind he is now 14 at reading with a potential of 175 to give him a better chance of reaching it... although as you said with that personality i doubt he will now.
even though i strongly believe in my method and ratings system, i am always willing to listen to constructive feedback and change things if necessary. i am not a closed book by any means of the imagination. Even though this is my project, it is also the communities project because this thing is bigger than you or I. It has to be right and im not surprised with over 2048 legends and stars & Counting if we get one or two that need adjusting.
Thanks for the feedback...
I tried to avoid spoilers on PA's etc, but I do have to say knowing Campo was a 180 made me feel a little sick inside lol, he was not a wonderful player.
1 hour ago, Citizen Kane said:
Fair enough, he is a 170 and that is what i normally would have given him, i have no idea why i gave him 180, but problem solved..
Hi UptheBoro
I have the information I need on Bernie Slaven now so no need to worry
@ Fenech
what skin are you using on all your screens?
edit: I saw now, you didn´t include John Toshack from Liverpool? And Ray Clemence at Tottenham? He´s a real Liverpool legend
Edited August 11, 2016 by Forest
22 minutes ago, Forest said:
John is on my list and ray clemence is there, but he is at Tottenham
You have to appreciate that liverpool have two fine keepers in elisha scott, the best of them and bruce grobbelaar, they dont need a third one.
yes I understand, but Clemence is my all time favorite so I signed him Ray Kennedy maybe also missing, but otherwise very good squad at Liverpool
btw what Skin are you using?
4 minutes ago, Forest said:
Ray Kennedy is on my list
I use the ICON only SIDEBAR (MOD) skin.
you got a link? i use the default dark but my faces of the players are very small and not like yours
http://www.mediafire.com/download/pm5dlx05doex7yr/icon_sidebar.zip
maybe consider https://en.wikipedia.org/wiki/Martin_Dahlin
On 11/8/2016 at 09:34, Fenech said:
https://en.wikipedia.org/wiki/Harald_Nielsen - I think you need this on for the Bologna team
Sorry Fenech, totally missed your post asking for information on Bernie Slaven. Glad you've found what you need.
Funnily enough, I was sat next to him and had a little chat with him in Pizza Hut last Wednesday (he's always in Pizza Hut!).
No Steve Bloomer guy was a goal machine.
On 12/08/2016 at 19:08, Citizen Kane said:
On 13/08/2016 at 02:57, CasperAscanius said:
8 hours ago, UpTheBoro said:
next time you see him you can tell him he is playing again! lol
1 hour ago, aveago said:
Sure but he will be playing for Derby County.
First of all there will be an update before the final update soon.
This update will include the following changes, but not limited to:
* A Full 25 man Middlesbrough Team
* All starting finances back to normal
* Wage expectations of players lowered substantially and much more reasonable
* Players will cost slightly less to purchase too.
* Middlesbrough now in the premiership with Southampton dropping down to the championship
* Wages lowered across the board to reflect the drop in player/agent expectations.
Also I need to finish this project so with that in mind I will be taking no more requests for players or teams. as i have enough as it is now.
Once this update is released, there will be one final update and then that will be it. There will be no further updates. my work will be over.
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Fintech: California Pushes New Fintech Regulations
January 13, 2020 | FinTech, Investments, News
Gavin Newsom plans to spend more money on regulations
The State of California could soon overhaul the regulatory oversight of financial technology companies. Governor Gavin Newsom released details of his 2020-2021 budget. Inside, the proposal includes a provision to make the California Department of Business Oversight as the regulator of fintech companies. The agency would also regulate debt collectors, credit reporting agencies, and other firms tied to consumer finance.
The state would rename the agency of the Department of Financial Protection and Innovation (DFPI). In addition to regulatory efforts, the new agency would aim to increase innovation across the state.
State of California and Fintech Oversight
The remodeled agency would have expanded powers to address “abusive” acts or financial practices. It would also focus on identifying and policing unfair and deceptive acts and practices (UDAP).
The state of California has made this proposal as a direct response to Newsom’s belief that the Federal government hasn’t done enough to address consumer protection. Newsom believes that the Trump administration has limited government oversight and reduced the efficiency of the Consumer Financial Protection Bureau.
“They’re getting out of the financial protection business. We’re getting into it,” Newsom said at a press conference.
“We’re going to protect consumers from unfair and deceptive practices better than we have,” he later said.
The new department would also have a four-person panel dedicated to fintech innovation. It would also aim to liberalize banking laws that would allow fintech firms to operate across the United States while still reporting to the Department of Business Oversight.
Newsom’s press conference on Friday lasted nearly three hours as he outlined the state’s $222 billion budget. Newsome referenced President Donald Trump repeatedly during the speech. He mentioned Trump on every policy issue, including healthcare, climate change, school lunches, and homelessness. Newsom also argued that California aims to assert itself and address the things that he believes the Federal government cannot.
Recent: FinTech: Ripple Targets SWIFT in Brazil
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Such is the power of Kyle Bass, the hedge fund manager who correctly predicted the crisis from US subprime mortgages in 2007. The Hong Kong Monetary Authority deemed it appropriate…
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The Murder of Couriers - look mum no hands
Inside the world of courier riding
Tuesday 31 Mar '20 | 7:00pm look mum no hands
Join us for a pay-by-donation screening of Murder of Couriers on Tuesday 31st March in collaboration with Cycle to the Cinema.
"Murder of Couriers documents the lives of a group of bike messengers over a nearly three-year span."
Roll down for a pay-by-donation screening of Murder of Couriers on Tuesday 31st March from 6:30pm at our cycling / cafe / bar on 49 Old St. EC1V 9HX in collaboration with Cycle to the Cinema.
This film was made by couriers, about couriers, for a wide general audience and offers the chance to experience a lifestyle that not many get the privilege to enjoy.
Doors 18:30, we will start the film at 19:00.
Run time is 1hr 34 mins. Please note we will have a 15 min booze break half way through the film.
We serve craft on draught, natural wines, Square Mile coffee and food is available until 9pm (we’re open until 10pm).
Murder Of Couriers
Murder of Couriers documents the lives of a group of bike messengers over a nearly three-year span.
Buy tickets for The Murder of Couriers - look mum no hands ()
31 Mar '20 | 7:00pm
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Sigur Rós’ majestic live performance with the LA Philharmonic is now online — watch
The sprawling set includes new arrangements from Dan Deacon, Nico Muhly, and Owen Pallet
by Randall Colburn
Photo by Lior Phillips
In April, Sigur Rós played three nights at the Walt Disney Concert Hall with the LA Philharmonic, during which the Icelandic artists would feature new arrangements from the likes of Dan Deacon, Nico Muhly, Owen Pallett, as well as film scorer David Lang and composer Anna Meredith, among others.
Now, a full recording of the April 14th has been released, featuring newly edited and mixed audio. Watch it above, preferably while indulging in some of the band’s Sigurberry Gumdrops.
This December, Sigur Rós’ will launch its inaugural Norður og Niður arts festival in Reykjavik.
Concert Footage
Icelandic Rock
New Arrangements
Guardians of the Galaxy Vol. 2 soundtrack coming to vinyl and cassette
ASAP Rocky and ASAP Ferg reveal new video for “Wrong” — watch
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Three Black Cats by Maud Lewis
mixed media on board
signed to the right
11.5 x 12.5 ins ( 29.2 x 31.8 cms )
Sold for $21,240.00
Sale date: May 28th 2019
Acquired directly from the artist (1960s)
Private Collection, Halifax
Executed on the artist’s signature beaver board, “Three Black Cats” presents as one of Maud Lewis’ most coveted serial images. The rounded cats sit perched on the grass, framed by the overhang of cherry blossoms above them and the cheery tulips below, a visual reminder of the artist’s affinity for the animals. Indicative of Lewis’ earlier work, this piece has a more square justification and has been signed by the artist as “Lewis”, a typical action the artist took prior to her sweeping popularity.
Current SalesHighlightsWatch Artist
The simplicity of Maud Lewis’ paintings, brushed initially with scrounged paint from local fishermen onto ubiquitous green boards and postcards, continue to evoke feelings of innocence, of child-like exuberance as enduring as the spring times she loved to paint. Her works continue to capture audiences intrigued by everyday scenes as diverse as hard-working oxen and whimsical butterflies.
Maud Dowley Lewis was born March 7, 1903 in South Ohio, a community near Yarmouth. Her father Jack would provide a moderately prosperous living as a respected craftsman, making harnesses and serving as a blacksmith. Agnes, her mother, favoured artistic pursuits including painting, folk carving and music. Born disfigured with sloped shoulders and her chin resting on her chest, Maud led a confined but happy home life after she quit school at 14, perhaps in part to escape the mocking of her peers. “What is life without love or friendship?” she once confided to a friend. Her mother lovingly taught her to play the piano before arthritis crippled her hands. Physical deformity may have been her lot, but even more tragic was the loss of both her parents within two years. Thankfully, an aunt who lived in Digby took her in. There she would later answer a newspaper ad that would determine the course of her life. A man named Everett Lewis wanted a housekeeper for his cottage in Marshalltown. She married him in 1938 at the age of thirty-four and would never travel more than an hour’s drive from her birthplace. “I ain’t much for traveling anyway,” she said later, “as long as I have a brush in front of me, I’m all right.”
Although short in stature with hands gnarled by arthritis as the years passed, she stood tall when she plied her brush over green-backed particle board. Everett Lewis, a stingy, parsimonious but certainly hard-working man, kept house and made meals allowing Maud to spend most of her time delving into her world of wonder and creating fanciful works of art. Maud gathered images from her happy childhood and limited excursions in a Model T with Everett to paint cheerful images on dust pans, scallop shells and even on her house. They would settle into a routine where Everett enjoyed peddling and haggling over the paintings Maud would love to paint. The happiness she painted first attracted neighbours, then tourists and eventually even international attention. It started with a Star Weekly newspaper article and then a 1965 CBC Telescope program featuring her unique works. Her notoriety began to bloom like the cherry trees that garnished several of her paintings. Orders came in so fast that the paint hardly had time to dry--one reason you may notice fingerprints on some edges of her paintings.
Her style became as fanciful as her subjects. She painted a world often without shadows, autumn leaves on winter landscapes, and even three-legged oxen. Was she adding humour in her subtle, shy way? Her gentle nature and magnetic smile might give that away. Awkwardly bent over a painting, she may have been squinting and intense, but her inner joy escaped onto her panels with unrivaled determination and vitality. Small wonder her work garnered the attention of even the Nixon White House. Ever pragmatic, Maud wrote to ask that funds be forwarded before she sent the requested two panels to the President! Today her work unequivocally demands status as “important art” in numerous fine-art collections around the world.
Not formally trained, Maud adopted a style that emerged from inside the heart of a true artist. As such, she could produce images of enduring quality and appeal, images that transformed her maritime surroundings into painted visions. The irresistible charm of her art had triumphed over the arrows of adversity.
- Reproduced with permission from Wayne & Jocelyn Cameron
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Governor Wike Reveals Who Only Will Decide Next Rivers Governor
December 17, 2019 December 17, 2019 by DefavouredKings
On Monday, after during a solidarity visit by the Ogoni People at the Rivers State Government House, Governor, Nyesom Wike, declared that he has not promised any ethnic nationality in the state the position of governor.
Wike said only God has the capacity to make any ethnic nationality governor of Rivers State.
He spoke during a solidarity visit by the Ogoni Ethnic Nationality at the state’s Government House Port Harcourt.
According to Governor Nyesome Wike: “Let nobody say that I have met with Ogoni Ethnic Nationality and I promised them Governor. I didn’t promise because I cannot give.
“It is only God that will give the position of Governor. With proper arrangement, things can be done. Don’t say I made a promise, don’t rely on anyone, just work hard. As Nyesom Wike, I can only support, but cannot make anyone Governor.”
ALSO READ: Governor Wike governing rivers state with fear of God – PDP
He urged Rivers people to take him as an example where a leader declared that over his dead body would he emerge governor but he still became.
“Take me as an example. Someone sat here and said over his dead body would I be Governor. Am I not Governor today? I am heading towards eight years.
“Nobody should threaten you that you cannot be Governor. Don’t take the position of God. Don’t allow anyone to take the glory of God”, Governor Wike said.
Speaking further, Governor Wike stated that Senator Magnus Abe would have become the Governor of the state if he listened to his advice and left the then government of Rotimi Amaechi with him.
Read Also 2023: Buhari Assured Nigerians Free, Fair And Credible Election
He noted that with the elections over, it is time for governance. He thanked the people of Ogoni Ethnic Nationality for supporting him to win the election
He urged the people of Ogoni Ethnic Nationality to be united and work together in order to achieve set goals, as well as build bridges across various ethnic nationalities to succeed politically.
The Governor advised Ogoni people with the intention to run for governorship election in the state to be fully prepared to struggle for the position.
He noted that no administration in the state has given Ogoni people the number of appointments his administration has given them.
“No administration in this state has given Ogoni people more appointments than me”, he said
Governor Wike used the forum to intimate the people of Ogoni Ethnic Nationality on the State Government’s decision to acquire Shell’s share in OML 11.”
ALSO READ: Wike Lifts Suspension on Employment at Rivers State University
He regretted the negative propaganda by some people in the area. He advised them not to allow criminals to speak on their behalf.
He said: “We have allowed criminals to speak for us. Some leaders use criminals to speak on their behalf. The next thing you hear, I am an ex-agitator. What are you agitating? You collect money everywhere and become ex-agitator.
“We sit back and sponsor criminals to talk on behalf of Ogoni Ethnic Nationality. How many of you have come out to say what that boy is saying is not correct.”
Speaking during the Solidarity Visit, Gbenemene Tai and Chairman, Supreme Council of Ogoni Council of Traditional Rulers, King G.N.K. Giniwa lauded the governor for his support to the Ogonis. He pledged their unalloyed and unflinching support to the administration.
Read Also BREAKING: Former Minister Decamps to PDP [REASONS]
Presenting the address of the people of Ogoni Ethnic Nationality, Senator Bennett Birabi thanked Governor Wike for the numerous infrastructure put in place in Ogoni land. He also commended Governor Wike for the restoration of peace in the state and Ogoniland.
He also lauded the governor for the acquisition of OML 11 for the benefit of the state and Ogoni people.
Tagged Gbenemene Tai, Governor Nyesome Wike, King G.N.K. Giniwa, Magnus Abe, Ogoniland, Rotimi Amaechi, Senator Bennett Birabi
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Home Pakistan Defence Forum > World Military Forum > Land Warfare >
Komodo 4x4 Tactical Vehicle, Indonesia
Discussion in 'Land Warfare' started by Zarvan, Jan 26, 2016.
Zarvan ELITE MEMBER
+84 / 49,819 / -13
The Rantis Komodo 4x4 wheeled tactical vehicle is designed and developed by Polish weapons manufacturer PT Pindad. The vehicle is offered in a number of variants, which include reconnaissance,armoured personnel carrier (APC), command post, ambulance, rocket launcher, special operations support vehicle (battering ram), and cannon towing.
Designed to transport or launch surface-to-air missiles, the missile launcher platform has been selected by the Indonesian Army, while the special operations support vehicle was ordered by the Indonesian Army Special Forces (Kopassus).
The Indonesian Police Special Forces (Brimob) selected the Komodo APC variant for missions such as search-and-rescue, bomb disposal and riot control.
Development of the tactical vehicle
PT Pindad began the development of the Komodo tactical vehicle in November 2011. The vehicle was introduced during the Ritech Expo 2012 held in Bandung, Indonesia, and the line-up took part in the IndoDefence 2012 exhibition in Jakarta, Indonesia.
PT Pindad signed a memorandum of understanding (MoU) with PT LEN Industri to collaborate on the development of communications systems for the Komodo vehicles in October 2015.
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Komodo armoured vehicle design and features
The Komodo vehicle features an armoured steel hull and offers superior manoeuvrability. It can accommodate up to five personnel.
The vehicle measures 5.65m-long, 2.25m-wide and 2.15m-high. It has an empty weight of 5,800kg and a combat weight of 7,300kg. Its wheel base and wheel tracks are 3.60m and 1.90m respectively.
The rocket launcher, reconnaissance and cannon towing variants are equipped with a four-door double-cab, which can accommodate up to five personnel, while the other variants are provided with a two-door regular cab. The cab features two-piece windshield assembly with ballistic glass. Each door is fitted with a bulletproof glass window.
The on-board navigational and communications systems include AM and FM radio communications, intercom set, global positioning system (GPS), and night-vision goggles (NVG).
The reconnaissance variant is optionally provided with a roof-mounted remote control weapon station to carry a 7.62mm-calibre machine gun for defence against small arms and light vehicles.
"The Indonesian Police Special Forces (Brimob) selected the Komodo APC variant for missions such as search-and-rescue, bomb disposal and riot control."
The missile launcher platform variant can be armed with Mistral surface-to-airmissiles (SAM).
Protection features
The armoured steel hull and bulletproof glass windows protect the crew from 7.62mm armour-piercing rounds. The add-on armour of the cabin provides ensures maximum protection against ballistic threats. The vehicle can be optionally equipped with smoke grenade launchers on the roof.
The Komodo vehicle runs on a four-stroke, inline, six-cylinder diesel engine, which develops an output power of 215HP at a rate of 2,500rpm. The engine is coupled to an optional transmission system, which features six forward gears and one reverse gear.
The vehicle is installed with a rigid axle suspension system and has a power-to-weight ratio of 29.4hp/t. The front suspension employs a bushing arm with coil spring, while the rear suspension uses a trailing arm with coil spring, stabiliser bar and telescopic shock absorber.
The driveline components also include power steering system, 12.5 R20 tyres and hydropneumatic control disc brakes on all four wheels. The vehicle is also installed with two 12V / 100Ah batteries and a 24V / 100Amp alternator.
Komodo tactical vehicle performance
The vehicle's maximum off-road and highway speeds are 50km/h and 100km/h respectively. It can travel at a speed of 80km/h on flat surfaces, and negotiate gradients of 60% and side slopes as high as 30%.
The fording depth is 0.75m and the turning radius is more than 7m. With a fuel capacity of 200l, the Komodo can operate over a maximum range of 450km. It can cross vertical obstacles of 0.4m and trenches of 0.5m. Its approach and departure angles are 45° each.
The Komodo wheeled tactical vehicle variants seen during IndoDefence 2012. Image courtesy of Ominae via Wikipedia.
The Komodo vehicle features an armoured steel hull. Image courtesy of Ominae via Wikipedia.
The Komodo rocket launcher variant is designed to carry Mistral surface-to-air missiles. Image courtesy of Rama via Wikipedia.
http://www.army-technology.com/projects/komodo-4x4-tactical-vehicle/
@Indos @RescueRanger
Indos PDF THINK TANK: ANALYST
Zarvan said: ↑
Once again you post misleading report bro....
PT Pindad is a state owned Indonesia defense company (land specialist)
The monocoque steel body is made by PT Krakatau Steel, Indonesian state owned steel company.
Manufacturer: PT. Pindad (Persero)
Product type: Auxiliary Vehicles
Name: Tactical vehicle
The Komodo is a 4x4 tactical vehicle developed and produced by Pindad.
The creation of the Komodo first started on October 26, 2011 when President Yudhoyono personally visited a PT Indonesian Aerospace weapon system exhibition. In the course of developing the vehicle, Pindad looked at other armored tactical vehicles that were being produced and sold such as the Armored Multi-Purpose Vehicle, the Nexter Aravis and the Sherpa Light family.
Production of the Komodo was based at Pindad's factory in Bandung, West Java. The creation of a working Komodo prototype was completed on March 2012.
The Komodo made its first appearance when Pindad demonstrated the tactical vehicle to visitors at the RITech Expo on September 2012. Production on a working Komodo by Pindad started on October 5, 2012. On November 10, 2012, President Yudhoyono gave the name Komodo to new tactical vehicle at the Indo Defence 2012 Expo & Forum, Jakarta International Expo, Kemayoran, Jakarta.
A production plan of at least 240 Komodo tactical vehicles was planned after it was unveiled in Indodefence 2012.
Pindad has been awarded at the BUMN Award 2013 by the Indonesian government for their contribution in making the Komodo, since 80% of its components are being made locally. Pindad has reported confirmation that there are unnamed countries that are very interested to purchase Komodo tactical vehicles. Pindad has said that possible exports can be done for ASEAN member nations.
The Komodo was designed with a price tag of USD$2-3 million.
According to Pindad, the Komodo's monocoque armored body is bulletproof and it can withstand 7.62 bullets. The Komodo's glass is also made bulletproof.
The Komodo's turbo intercooler diesel engine has a total horsepower of 2500 rpm at 215 ps, allowing the vehicle to achieve the weight ratio of 25hp/ton. The Komodo can carry up to 200 liters of diesel fuel. The vehicle only has a manual transmission system, which consists of 6 forward and 1 reverse gear, allowing the Komodo to have off-road capabilities. Normal cruising range of the Komodo is about 450 kilometers.
The Komodo's off-road capabilities have been tested in various conditions ranging from mountainous terrain to mud and sand.
While most parts of the Komodo are made locally in Indonesia such as the frame, body and design, Pindad has publicly stated that they used imported components such as Hino for machinery parts and Michelin for the tires. Its diesel engines were imported from Renault. The Komodo's monocoque steel body was made locally by Krakatau Steel.
Pindad collaborated with MBDA to create the mobile anti-aircraft SAM variant, which are armed with Mistral SAM missiles. According to the Indonesian military, a total of 56 mobile SAM units are to be made and purchased.
Pindad also collaborated with Nexter to create Komodos that would serves as mobile command and communications vehicles with a total of 8 units being ordered.
The Komodos can be modified by Pindad on the request of their customers.
Variants of the Komodo:
Anti-Terrorist Vehicle
Mobile SAM launcher
http://www.army-guide.com/eng/product5114.html
Nike ELITE MEMBER
Basic APC and recon variant is only costing 800 to 1200 K US dollar each
Mistral carrier is the one who will cost around 2 million US dollar
Jan 1, 2017 #5
durandal FULL MEMBER
Indos said: ↑
/QUOTE]
the price is too high,
the actual price is 2 billion to 3 billion rupiah depending stanag level.
in dollar 200,000 to 300,000 dollars
Otokar Cobra 4x4 Armoured Vehicle
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TUPI 4x4 Light Armoured Vehicle, BrazilBrazil
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Zarvan
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With the logo system designed, the next step was to design print materials that featured a cohesive brand that would create brand recognition with current and potential clients.
GOING RESPONSIVE
Once Cutting Edge had a defined brand, the project progressed to the web design and development phase. One of the main goals of the site was that it would be responsive, or in other words, would adapt to the resolution of the device that visitors were using to view the site. This creates a website that can be viewed on any mobile device without compromising the quality or content.
We'd love to hear about your project.
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In Berkeley, Jordi Savall wanders through the slave trade’s cultural paths
Joshua KosmanNovember 4, 2018Updated: November 5, 2018, 7:28 am
Jordi Savall performed “The Routes of Slavery” at Zellerbach Hall. Photo: Courtesy Jordi Savall
Over the course of 4½ half centuries of unspeakable brutality, the international slave trade created a massive redistribution of the world’s peoples. Entire populations were forcibly relocated from Africa to the New World, and with them went cultural traditions, which then took root in new and inhospitable terrain.
That compelling story peeked through in scattered bits and pieces — sometimes forcefully, more often in desultory fashion — over the course of “The Routes of Slavery,” a 2½-hour musical presentation that arrived in Berkeley’s Zellerbach Hall on Saturday, Nov. 3, for a two-night run in the Bay Area. (The opening, presented by Cal Performances, will be followed on Sunday, Nov. 4, by a reprise in Bing Concert Hall by Stanford Live.)
Conceived and created by the early music pioneer Jordi Savall, “The Routes of Slavery” brought together some two dozen performers — vocalists, instrumentalists, actors and dancers — from both sides of the Atlantic to present a sampling of the enormous range of musics (plural) from this cultural landscape. There were griot songs from Africa, slave songs from the United States, marches and dances from South America, and much more, in a sort of pageant of misery and resilience; in between chapters, actor Aldo Billingslea read historical excerpts on the subject.
The cumulative impact was both affecting and somewhat flattening, as centuries of unimaginable inhumanity — the work progressed chronologically from 1444 to 1888 — blurred into a watercolor of musical experience. One dance or musical sequence gave way to the next, often fading out with a seeming shrug.
There was no evident connection between the spoken selections and the music, nor did the musical miscellany, for all its individual moments of beauty and grandeur, tell a story of cultural transmission. It was simply a sequence of musical offerings, like a leisurely procession through an indifferently curated historical museum.
But if the overall historical context materialized only vaguely, there were still many moments of electrifying beauty and drama. Several of them came from the singer Neema Bickersteth, who deployed her fantastical vocal range alongside a richly spiritual communicative gift to impart pathos and strength to several of the American numbers.
From Mali, the commanding singer Mohamed Diaby, together with the vocal trio of Mamani Keita, Nana Kouyaté and Tanti Kouyaté, conjured up vivid images of the slaves’ ancestral landscape, as did the kora virtuoso and singer Ballaké Sissoko. Brazilian soprano Maria Juliana Linhares brought expressive urgency to songs from the southern hemisphere.
Savall, meanwhile, played the viola da gamba and led accompaniments in ever-shifting configurations by members of his ensemble Hespérion XXI. It was all perfectly stately and polite.
“The Routes of Slavery”: 4 p.m. Sunday, Nov. 4. $32-$102. Bing Concert Hall, 327 Lasuen St., Stanford University, Stanford. 650-724-2464. live.stanford.edu
Jordi Savall maps out the ‘Routes of Slavery’ with music
Bowie, Joni and Leonard: Breathing life into the poetic trinity
In powerful Berkeley recital, piano duo unveil new work by Harrison Birtwistle
Give pianist Igor Levit a big hand for performance at SF’s Herbst Theatre
Joshua Kosman
Joshua Kosman Joshua Kosman is The San Francisco Chronicle’s music critic. Email: jkosman@sfchronicle.com Twitter: @JoshuaKosman
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Promoting the branch lines
Supporting economic growth
Helping deliver improvements
Tarka Line
Exeter – Barnstaple
Avocet Line
Exeter – Exmouth
East Devon Line
Exeter – Axminster
Riviera Line
Exeter – Paignton
Tamar Valley Line
Plymouth – Gunnislake
Looe Valley Line
Liskeard – Looe
Atlantic Coast Line
Par – Newquay
Maritime Line
Truro – Falmouth
St Ives Bay Line
St Erth – St Ives
Home > Our work > Case studies > CreativiTea trains
CreativiTea trains
Inter-generational tea parties on the train to explore memories of the railway and bring people together
Looe Valley Line and Atlantic Coast Line
Great Western Railway Sally Crabtree Eden Project Age UK Local schools
1st, Best Community Engagement
Community Rail Awards 2019
Poet Sally Crabtree sings with local school children on the CreativiTea train
Our CreativiTea trains helped the community to come together in a creative way at onboard tea parties, complete with cupcakes, bunting, arts and crafts and more.
The Creativitea concept was created by Cornwall’s unmistakable pink-coiffeured poet Sally Crabtree who hosted each of the events together with Rebecca Catterall from the Devon & Cornwall Rail Partnership (DCRP).
On the Looe Valley Line, the CreativiTea trains were linked to our heritage project and were a way to tease out memories of local history and culture, to be featured in the wider project, as well as educating young people, who will be the future custodians of the line, about the history of the railway.
On the Atlantic Coast Line (Par-Newquay) the CreativiTea train was linked to social inclusion by working with the Eden Project, a local Age UK group and nearby primary school.
The concept of CreativiTea Trains was developed initially for the Looe Valley Line Heritage project as a way of gathering memories of the line from local people. Drop in events had already been held for local people but the Partnership wanted a way to also engage young people.
Two local schools along the line were keen to be involved and the first stage was for Rebecca Catterall from the Partnership and Sally Crabtree to go into class to teach the children about the history of the line using old photographs that the heritage project had already unearthed. The children were then tasked with coming up with good questions they could ask to find out more about older people’s memories of the line. What type of trains did they remember travelling on for example? What was their earliest memory of travelling on the line?
The time in school was then finished off with a creative aspect where the children designed toppers for cakes which were then printed on edible sugar paper ready to be served at the tea party. After the day in class the pupils were each given an invitation to hand to either a family member or a member of their community to attend a special tea party on the train on Tuesday 12th February 2019.
Trains were run with Duloe Primary School in the morning and Looe Primary School in the afternoon, with 120 people taking part across the day. The proceedings were filmed by local film makers Studio Wallop to allow DCRP to share the event more widely:
The innovative nature of the CreativiTea train concept piqued the interest of the Eden Project, and their Community Network Manager joined the train to find out more. He was so impressed that he collaborated with DCRP to hold a further CreativiTea train as part of Eden’s annual Big Lunch programme.
The Big Lunch is all about getting people together to share food, get to know each other and tackle exclusion and isolation. As before, Rebecca and Sally went into class beforehand but this time rather than teaching the children about the heritage of the line, they created a song called ‘What’s your cup of tea?’ which was all about finding out about people likes and dislikes and getting to know one another.
A local Age UK group was keen to be involved as many of their users had not been on a train trip for many years. The children and adults spent the journey simply eating and chatting and children were moved around so that they were able to speak to lots of different people throughout the journey. The children also performed the song that they had written in class. BBC Radio Cornwall and BBC Spotlight (regional TV news) were on board throughout the journey interviewing young and old for broadcast later that day.
The CreativiTea Trains have been extremely successful in a number of ways. The Looe Valley Line events re-engaged many local people with their railway, with many of the older generation commenting on how long it had been since they had been on the train but what fond memories they had of it from their youth.
The trips also brought to light information for the heritage project which was completely new, such as the fact that flowers were picked in Looe and sent to London by train for sale in Covent Garden, something which has always been suspected but never proved.
This information was included in the heritage project’s mobile phone app for the line, on new interpretation boards at stations and in the CreativiTea Trains film (see above) showcased on YouTube and the heritage project website. One commenter on YouTube said:
“What a lovely heartwarming video, re-living and teaching the young about the past. Really beautiful.”
The film was also shown on a 20-foot screen at the heritage project’s premiere evening at Liskeard Public Hall. Families featured in the film were invited to attend and were among the 100-strong audience at this well-received evening.
On the Atlantic Coast Line, the trip was very different in that none of the people on board had met each other before but the atmosphere was incredible as young and old enjoyed eating, drinking and chatting whilst travelling through the countryside.
The elderly people particularly commented on how much fun they had had and how surprised they were at how much they had to talk about with the children.
The media response to the event with the Eden Project was fantastic with the news item being shown on the evening news that day and broadcast on BBC Radio Cornwall throughout the day.
The Atlantic Coast Line event was also filmed by Great Western Railway and shown at their Community Rail Conference as a way to share best practice with other Community Rail Partnerships.
More from the Looe Valley Line and Atlantic Coast Line
Looe Valley Line heritage project
Carbon Reduction Challenge
The Munchtime Express
Gunnislake tiles project
Petroc College students give Barnstaple station a makeover
Barnstaple’s newest train needs a name
GreatScenicRailways
@dcrailpart
Rail Partnership
railpart@plymouth.ac.uk
Devon and Cornwall Rail Partnership
PL4 8AA
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Applications open for new season of 'Stars of Science' show
Amiri Guard concludes first part of training season
Gulf Cup to be a fine show of entertainment and football
season show applications Stars of Science
Finalists of Season 11
'Stars of Science' – Qatar Foundation (QF)’s edutainment show – is now accepting applications for Season 12, giving aspiring innovators the opportunity to present their ground-breaking ideas to a jury of renowned field experts.
Online applications are open to Arabs all around the world until December 31, QF has said.
Interested participants could become part of the impressive alumni community that has been 11 years in the making, contributing to a culture of Arab scientific excellence. More than 130 innovators representing 18 Arab countries have gained invaluable insights and learned crucial lessons during their time on 'Stars of Science'.
Over the past decade, the SOS alumni community has raised over $14mn in crowdfunding, awards, investment and research grants to refine their inventions and build startups around the world.
This year, Ahmad Nabeel and Fouad Maksoud – both contestants in Season 9 – alongside Hassan Albalawi from Season 7, were recognised as members of the Massachusetts Institute of Technology Innovators Under 35 list in the Mena region. More details on how to apply can be found at www.starsofscience.com
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Detroit Lions sign RB Tra Carson
Don Drysdale - January 7, 2020 0
According to the Detroit Lions, they have signed RB Tra Carson to a Reserve/Future contract. Carson started one game for the Lions in 2019,...
Report: Detroit Lions’ quarterbacks coach Sean Ryan is a wanted man
Arnold Powell - January 7, 2020 0
On Tuesday, news broke that Baylor's Matt Rhule will be the Carolina Panthers next head coach. http://gty.im/1191461532 According to NFL reporter Jason La Canfora, Rhule has...
3 Players the Detroit Lions could target in the 2020 NFL Draft
Well, the 2019 NFL regular season is (mercifully) in the books and the Detroit Lions hold the No. 3 pick in the 2020 NFL...
NFL Draft insider says Detroit Lions could take Tua Tagovailoa with No. 3 pick
On Monday, Alabama quarterback Tua Tagovailoa announced that he is leaving the Crimson Tide and declaring for the 2020 NFL Draft. http://gty.im/1188484176 Ever since the announcement...
Barry Sanders: ‘We’d love to have’ Tom Brady with the Detroit Lions
This past weekend we may have watched an amazing era come to an end as Tom Brady and the New England Patriots lost at...
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Detroit Tigers announce TigerFest has been moved to summer
The annual pre-season celebration of Detroit Tigers baseball has officially been moved to the warmer temperatures of summer. TigerFest will be held during the summer...
Report: Detroit Tigers, Los Angeles Angels discuss trade for Matthew Boyd
According to a report from Jon Morosi, the Detroit Tigers and Los Angeles Angels have discussed a trade for SP Matthew Boyd, though it...
Source familiar with Pistons expresses “confidence” team will trade Andre Drummond
There continues to be speculation swirling around Detroit Pistons center Andre Drummond, who is the subject of trade rumors as the February 6 NBA...
Report: Blake Griffin undergoes knee surgery
Ryan Griffin - January 7, 2020 0
Devastating, but not surprising. The Athletic's Shams Charania is reporting that Detroit Pistons forward Blake Griffin has undergone knee surgery and will have an...
Pistons’ Derrick Rose to compete on NBA All-Star Saturday Night
Per The Athletic's Shams Charania, Detroit Pistons point guard Derrick Rose will be competing in the NBA All-Star Skills Competition that takes place the...
Oddsmakers reveal potential destinations for Pistons’ Andre Drummond
There are currently rumors swirling around Detroit Pistons center Andre Drummond, and where he'll spend the next phase of his career. Of course, Drummond...
NBA drug tests Lakers center following strong game vs. Pistons
Have yourself a good game, and then get drug tested. http://gty.im/1180632230 At least, that's what happened to Los Angeles Lakers center JaVale McGee following Sunday...
It’s Jimmy Howard bobblehead night at Little Caesars Arena
Fans heading down to Little Caesars Arena tonight can take home a souvenir. It's Jimmy Howard bobblehead night as the Detroit Red Wings host...
Jeff Blashill defends Red Wings C Dylan Larkin following Brian Burke’s ‘Keep your mouth shut’ comments
When Detroit Red Wings C Dylan Larkin openly told media members that he preferred rest over playing in the NHL All-Star Game, and that...
A prime coaching candidate for the Detroit Red Wings just became available
For Detroit Red Wings fans looking for their team to make a change at the head coaching position, a prime candidate just became available....
NHL commentator says Red Wings are in a “dangerous place psychologically” under Jeff Blashill
It isn't a secret that the Detroit Red Wings are unfortunately terrible this season. With last night's 4-2 loss to the Chicago Blackhawks, they've...
Red Wings fan wears Steve Yzerman No. 19 Green Packers jersey [Photo]
While browsing Twitter this morning, I stumbled across something that caught my attention...in a bad way. As you can see below, a fan (I assume...
Michigan receiver Nico Collins makes decision for 2020
While the Michigan Wolverines will be without Donovan Peoples-Jones after he declared for the NFL Draft, they'll be getting a valuable member of their...
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Michigan offensive lineman Cesar Ruiz declares for NFL Draft
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Detroit Lions NewsU of M News
Odds released for Jim Harbaugh, two former Detroit Lions head coaches to become Washington Redskins HC
By Arnold Powell
Detroit Lions NewsDon Drysdale - January 7, 2020 0
According to the Detroit Lions, they have signed RB Tra Carson to a Reserve/Future contract. Carson started one game...
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Arnold Powell
On Monday morning, news broke that Jay Gruden had been relieved of his duties as head coach of the Washington Redskins.
For now, Bill Callahan is the interim head coach in Washington, but the question is, who will be the head coach when the Redskins take the field in 2020?
Well, according to betonline.ag, a few names with ties to the state of Michigan have a chance.
Those candidates include current Michigan head coach Jim Harbaugh and former Detroit Lions head coaches Jim Schwartz and Jim Caldwell.
Of the three, Caldwell currently has the best odds at +1800 to land the job while Schwartz is +2000 and Harbaugh is listed at +2500 to leave the Wolverines for the gig.
Here is a look at the full list of odds.
Have something to say? Click here to jump to the comments!
Jim Caldwell
Jim Harbaugh
Jim Schwartz
Previous articleRed Wings Anthony Mantha owns the Dallas Stars twice in 24 hours
Next articleWhat to look out for in tonights Pistons preseason kickoff!
Detroit Lions News Don Drysdale - January 7, 2020 0
Detroit Lions News Arnold Powell - January 7, 2020 0
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Chilaca Chile Peppers
Chilaca chile peppers are elongated pods, averaging 15 to 22 centimeters in length and 2 to 5 centimeters in diameter, and have a curved to flattened conical shape. The skin ripens from dark green to a dark brown-black when mature and is waxy, wrinkled, and covered in vertical ridges. Underneath the skin, the flesh is thin, pale green, and crisp, encasing a narrow cavity filled with many small, flat and round, cream-colored seeds. Chilaca chile peppers can be harvested at multiple stages of maturity, and when young, the pods have a mildly tangy, floral flavor with a heat similar to poblano chiles. As the pepper matures, the flavor deepens into an earthy, slightly sweet flavor with raisin-like undertones and a mild heat.
Chilaca chile peppers are available in the summer.
Chilaca chile peppers, botanically classified as Capsicum annuum, are uniquely flavored, mildly hot pods that are members of the Solanaceae or nightshade family. Native to Mexico, Chilaca chile peppers range 1,000-2,500 SHU on the Scoville scale and are widely used in traditional Mexican cuisine. Translating to mean “old” or “gray hair,” the name Chilaca is derived from the pepper’s wrinkled appearance and is used to describe the fresh version of the pepper. Fresh Chilaca chile peppers are rare in local markets and are more popularly found dried. Once dried, the Chilaca chile pepper is sold under the name Pasilla which translates to mean “little raisin” in Spanish. Also known as Pasilla Bajio, Chile Negro, Mexican Negro, Prieto, and Cuernillo, Chilaca chile peppers are most commonly sold today dried whole or in powdered form and are used in sauces, marinades, and salsas.
Chilaca chile peppers are an excellent source of vitamin C, iron, niacin, and magnesium. The peppers also contain some vitamins B1, B2, and D.
Chilaca chile peppers are best suited for both raw and cooked applications such as grilling, roasting, and baking. The pepper can be used fresh and diced into salsas, blended into hot sauce or cream-based sauces for fish, or used to make an enchilada sauce. Chilaca chile peppers can also be blistered over a grill or gas burner and sliced into strips for vegetable dishes, rice, soups, stews, and casseroles, or they can be roasted and used in tacos, tostadas, tamales, and chile rellenos. In addition to fresh preparations, Chilaca chile peppers are most commonly utilized in their dried form, known as Pasilla, and are either used as a whole pepper or ground down into a powder. The dried powders are typically used for savory sauces to pour over cooked meats and in Mexico, the dried chiles are crushed and sprinkled over tortilla soup. In Mexico, they are also a popular pepper for pickling. Chilaca chile peppers pair well with meats such as pork, poultry, duck, and fish, eggs, garlic, onions, fennel, tomatoes, tomatillos, herbs such as oregano, cilantro, thyme, and parsley, mushrooms, rice, and beans. The peppers will keep 1-2 weeks when loosely stored whole and unwashed in a plastic or paper bag in the refrigerator.
In Mexico, Chilaca chile peppers are considered to be part of the holy trinity of chiles that are used to make mole sauce. Mole originated in the Puebla and Oaxaca regions of Mexico and is derived from the Nahuatl language to mean “concoction” or “sauce.” Often made during holidays or special celebrations like weddings, mole is a smooth sauce comprised of chiles, tomatoes, spices, nuts, and sometimes raisins. Mole recipes widely vary between families in Mexico using different secret ingredients, but the holy trinity of chiles almost always includes ancho, Pasilla, and mulatto chile peppers. Mole is traditionally served over burritos, in tacos, over grilled meats, or over rice-based dishes.
Chilaca chile peppers are believed to have originated in the Puebla region of central Mexico just south of Mexico City and have been cultivated since ancient times. Today in central and northwestern Mexico, Chilaca chile peppers are cultivated primarily in Guanajuato, Valisco, Michoacan, and Zacatecas. While the fresh pepper is localized to markets and home gardens in Mexico, the dried version known as Pasilla can be found through specialty grocers and online retailers in the United States and Europe.
Recipes that include Chilaca Chile Peppers. One is easiest, three is harder.
Food Geeks Chilaca Chile Snack
BrokeAss Gourmet Roasted Butternut Squash and Chilaca Pepper Soup
Sweet Life Salsa de Chile Chilaca
Cadry's Kitchen Light & Creamy Squash Blossom Quesadillas
La Pina en la Cocina Chile Chilaca Con Queso y Crema
People have shared Chilaca Chile Peppers using the Specialty Produce app for iPhone and Android.
Sharer's comments : Chilaca peppers at Buford Farmers Market
La Morenita
La Morenita Market
2434 Jefferson Street Napa CA 94558
Near Napa, California, United States
Chino's Vegetable Shop
Chino Farms
6123 Calzada Del Bosque, Rancho Santa Fe 92067
Near Fairbanks Ranch, California, United States
Sharer's comments : Chilaca Chile Peppers spotted at Chino's Vegetable Shop.
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KDE 4.1 Beta 1 Released
Submitted by Will Stephenson
The KDE Project is happy to set the first beta of KDE 4.1, codenamed Caramel, free today. KDE 4.1 is intended to meet the needs of a broad range of users and we therefore respectfully request you to get testing Beta 1. Beta 1 is not ready for production use but is in wide use by KDE developers and is suitable for testing by Linux enthusiasts and KDE fans.
Highlights of 4.1 are a much more mature Plasma desktop shell that returns much of the configurability that was missing in KDE 4.0, many more applets and look and feel improvements, the return of Kontact and the rest of the KDE PIM applications, and many improvements and newly ported applications. The feature set is now frozen, so the developers look forward to using June and July to metamorphosing your bug reports into rock solid code, completing documentation and translating everything into your language. A series of Bug Days where users can contribute quality assurance to the release will continue towards 4.1's final release on the 29th of July, so watch the Dot for details.
For more details, see the release announcement and info page or if you are at LinuxTag, see KDE 4.1 being presented in Berlin this Friday.
Re: C#
Why do we need a binding for that M$ language? What's wrong with C++?
By Kevin Kofler at Wed, 2008/05/28 - 5:00am
Are you claiming that C++ is as easy to write stuff in as C#?
By anon at Wed, 2008/05/28 - 5:00am
C# is not what a linux or macOSX user may want to have in his
system, and there ia plenty of cause for this.
You're however always free to do yourself bindings for C#, cobol,
fortran and logo languages, nobody will stop you.
i hate c++ and i'm pretty sure there's others like me. anyway just because c#
was conceived by microsuk it doesn't mean that we linuxers can't use it and just for the records i hate windoze so much that i even removed all the windows from my house all i have it's wall:-)
By Darwin Reynoso at Wed, 2008/05/28 - 5:00am
Um, read the reply Richard Dale already provided. The C# bindings help out the QtRuby bindings, so they are good in my book.
Also insert generic "people can spend their free time doing what they want, who the heck are you to say it's a waste of resources which aren't yours".
it's not just wasting personal resources, it's actively helping out a company that stands for everything we as a community are trying to avoid. in general I don't like people complaining about open source either, but in this case, they are actually standing up for it.
By mark dufour at Sun, 2008/06/01 - 5:00am
I'm sorry, I strongly disagree that I'm 'actively helping Microsoft'. And I couldn't care less about 'open source', as I write Free Software, which isn't the same thing.
What we're actually doing is allowing existing C# programmers to write code using the Qt and KDE apis. I would say that we are helping them to transition away from the Microsoft 'eco system' of IDEs and APIs such as Visual Studio and Win32, Winforms etc, and move to tools and frameworks based on Free Software.
It takes much more effort to learn a large framework such as Qt, than it does to switch to another language, such as going from C# to Java. Hence, once these former Microsoft C# programmers have learned how to write Qt/KDE code in C#, they can pick up C++, Python or whatever fairly easily if they want to.
By Richard Dale at Mon, 2008/06/02 - 5:00am
The Qt guys could give you a huge list, they made quite some effort to improve on it. For some reason Qt is not really C++ but requires the code to be pre-processed.
But come on, can't you think of anything? Type (un)safety? Really crappy polymorphism support? What other languages do you know?
By ad at Wed, 2008/05/28 - 5:00am
Konqueror and WebKit
In the announcement it says that "KHTML get a speed boost from anticipatory resource loading, while WebKit... is added to Plasma..."
So is Konqueror going to have WebKit or KHTML?
By Zubin Parihar at Tue, 2008/05/27 - 5:00am
Re: Konqueror and WebKit
There is a webkitpart available which you can select at "File Associations" in systemsettings to be the default renderer for embedded HTML contents (such as the web pages in HTML).
Plasma makes use of Webkit to render Mac OS X Dashboard Widgets (as the quoted text states...). That has nothing to do with Konqueror.
By Stefan Majewsky at Tue, 2008/05/27 - 5:00am
Konqueror ---> khtml
Konqueror uses KHTML, Plasma uses WebKit.
(Ok, you can do bizarre things and use webkit under Konqueror, but you'll lose lots of speed optimizations and other stuff.)
Re: Konqueror ---> webkit
Come on guys, just choose one renderer and let it be webkit. I have a lot more compat issues with konqueror than with safari. Webdev's don't give a damn about khtml compatibility. They do about webkit. Qt choose webkit. It's only logical to follow. Performance? nice, but compatibility is more important!
Just my 2 ct.
By Fred at Wed, 2008/05/28 - 5:00am
"Come on guys, just choose one renderer"
> Webdev's don't give a damn about khtml compatibility. They do about webkit.
They don't. They care about Safari. Incidentally having the same engine does not solve the problem. If at all it makes it easier to "lie" about your real browser identity.
"They don't. They care about Safari. Incidentally having the same engine does not solve the problem."
You're describing something which doesn't get us any further forward in order to try and tell us that the status quo is OK. It most decidedly isn't. The fact is that bug-for-bug compatibility with Safari does count for quite a bit for exactly the reason that the parent has stated - developers care about market share. Do some web developers use user agent strings? Yes they do, but as people use libraries for HTML and JavaScript and write less of it, and owing to the complexity of AJAX, they're being used less and less. The problems now are all about bugs and quirks between different engines. KHTML's bug list is down to user agent strings. Using WebKit gives KDE a far wider pool of web sites that will render well without having to jump on every mole hill in the field, and for those that don't, it gives web developers a far easier avenue to fix their sites and have it render well in any WebKit browser without having to think about it too much.
Continuing to use KHTML isn't going to get us any further forward on that front, and the past few years of Konqueror's limited usage as a web browser should have taught us all that.
By segedunum at Thu, 2008/05/29 - 5:00am
The problem is that you don't get bug for bug compatibility with Safari at all just by using WebKit. WebKit is just the rendering engine of Safari, everything else (e.g. client <-> server communication) can (and already does) behave differently between different browsers using WebKit.
By anon at Thu, 2008/05/29 - 5:00am
"The problem is that you don't get bug for bug compatibility with Safari at all just by using WebKit."
The point is that you have a pretty good shot at it. The situation now is that an undermanned group of people (that are sometimes pretty unresponsive, it has to be said) are having to run around fixing bugs in a rendering engine that few people use, and corner cases are always......just around the corner. There can be no end game to KHTML in terms of it becoming a widely used engine where it will render the vast majority of web pages for people in a confident fashion and where you'll get a KDE web browser that, quite frankly, will be of any use to people.
"WebKit is just the rendering engine of Safari, everything else (e.g. client <-> server communication) can (and already does) behave differently"
I don't see that being a problem in all honesty. The corner cases are in the engine itself. You can work yourself to a set of known issues, and the advantage is that Trolltech are taking the workload on for this.
no magic pony
> The point is that you have a pretty good shot at it.
No you don't. You don't magically get a pony by using QtWebKit. It's a port. It is NOT bug-for-bug compatible with Safari Webkit or feature-for-feature compatible with Safari Webkit.
> The situation now is that an undermanned group of people
If that's going to be your excuse for being unhappy, switch back to MS Windows and just don't use KDE at all. I think only plasma and amorak (which isn't even part of kde proper!) don't fall into the "undermanned" category. Most of the big apps, and the core libs, not just khtml fall into the "need more developers" category. If you want tons of developers and professional marketing, don't use free software.
> "WebKit is just the rendering engine of Safari, everything else (e.g. client > <-> server communication) can (and already does) behave differently"
> I don't see that being a problem in all honesty.
This person is trying to point out /why/ it isn't bug-for-bug compatible. And what all is going to be different from Safari Webkit. And that it is a problem. QtWebkit is a port of safari webkit, and would have to be ported to KDE. Doing so will generate all sorts of your "corner cases". And you already claim there aren't enough khtml developers to deal with what is out there.
So go back to Windows, and be sure to FUD khtml and plasma on your way out. As everyone else in these dot comments seems to be happy to do so. :P
By anony at Thu, 2008/05/29 - 5:00am
Re: no magic pony
"No you don't. You don't magically get a pony by using QtWebKit. It's a port."
*Yes you do*. Repeating the above is not going to magically make it all go away. Yes, it's a port (from the same codebase no less) and that's exactly the reason why you have a shot at it rather than in some totally different and rarely used 'fork' in KHTML that produces corner cases right, left and centre that aren't going to be solved and have no chance of being so.
"If that's going to be your excuse for being unhappy, switch back to MS Windows and just don't use KDE at all."
Boo, hoo, hoo. I don't have to. The fact is that you're never, never have and aren't, going to make KHTML a well supported rendering engine that will be of use to the vast majority of users and web developers out there. The engine that will be used most prevalently within KDE, and in any KDE browser, is the one that has the most support in terms of web pages that people can view well, and the past few years has taught us that that isn't be KHTML. Trying to attack QtWebKit won't change that problem for KDE's users, or KDE's developers trying to get a rendering engine that won't cause them problems for them and their users.
KHTML is a very small island, that hasn't changed and isn't going to.
"I think only plasma and amorak (which isn't even part of kde proper!)"
Rrrrrrrrrrrrright.
"QtWebkit is a port of safari webkit, and would have to be ported to KDE. Doing so will generate all sorts of your "corner cases"."
What are you talking about? QtWebKit exists now, will get developed much further at a pace that KHTML cannot match via upstream code from Trollech, and further upstream from WebKit, and will simply be reused as every other part of Qt is in KDE these days. You make it sound as if there is some insurmountable mountain to get over in terms of porting a Qt component to KDE, which is just plain daft.
"Doing so will generate all sorts of your "corner cases"."
No it won't, and any issues you might have will be far, far, far, far, far smaller than trying to jump on every mole hill in the field and investigate every bug report about a particular site that isn't rendering properly in KHTML. They are exceptionally difficult to debug. You're not going to get any help from any web developers or anyone else in the form of upstream code on that score.
"So go back to Windows, and be sure to FUD khtml and plasma on your way out."
Feel free to ignore the issues as KDE's users and developers leave KHTML behind in favour of something that works for users, and more importantly, has a far, far better chance of continuing to work in the future. The robust 'defence' of KHTML is just a case of 'our ego is bigger than yours' rather than having the best interests of KDE's users and wider developer community at heart.
By segedunum at Fri, 2008/05/30 - 5:00am
you know the problem is if QWebKit was one tenth as good as you sad trolls touted it for monthes, it would stand on its own, just like KHTML does without any of this silly propaganda.
You wouldn't need 30+ lines of strange and insane drivel that seem to obey to some kind of personal obsession (sorry).
The truth is current QWebKit suck. It's slow, buggy, and incomplete.
This state of affair might change. It might not.
It's not like any Trolltech employee as a significant role on the WebKit project or any bearing on its future.
They are all just stub-fillers for features made by Apple employees.
Hardly exciting, and certainly not a guarantee of a perrenial and fully functional "product".
By D. at Fri, 2008/05/30 - 5:00am
"you know the problem is if QWebKit was one tenth as good as you sad trolls touted it for monthes, it would stand on its own, just like KHTML does without any of this silly propaganda."
Very, very, very few people use KHTML at the moment, and it's fair to say that most of KDE's users use Firefox. That's for a reason. Additionally, KDE developers get something that works with QtGraphicsView.
Do the maths. You're right about one thing. KHTML does stand on its own. Very alone, and that's the problem.
"You wouldn't need 30+ lines of strange and insane drivel that seem to obey to some kind of personal obsession (sorry)."
*Shrugs shoulders*. If you're willing to debate it I'm all ears. I'll condense it into something that might make it through your head better - the market decides on the basis of what works best for them, and based on the evidence of the past few years they aren't going to pick KHTML.
"The truth is current QWebKit suck. It's slow, buggy, and incomplete."
If you have something to back that up, I'm all ears. There's a lot of upstream code going into it - most if it from the very people who started KHTML in the first place!!
"It's not like any Trolltech employee as a significant role on the WebKit project or any bearing on its future."
Pfffffffffff. Yer, you're right. Trolltech, Nokia, Apple and all these other people who contribute code to it are just wasting their time when you compare it to the powerhouse of development that is KHTML.
"They are all just stub-fillers for features made by Apple employees."
That's the usual sad line trotted out by Harri Porten and a few others, that WebKit is entirely dependant on the empty stubs that Apple have left for their own features which Steve Jobs has asked for by next week. Well, as I said the market decides and the proof will be in the eating. I don't see QtWebKit having any issues thus far.
See, but virtually nobody uses QtWebKit. Plasma is about the only application based on it. You really don't seem to understand that a port is not an equivelency, and a library is not an application. "Using QtWebKit" is not going to suddenly have the contents of a Konqueror browser look the same as a Safari browser (which does *not* use QtWebKit... it uses WebKit)... it will never do so. Once again, it isn't a magic pony. It's a kit to build your own pony, and the results due to things like different font rendering, network interface and base widgets will mean the two will never look or act the same. Safari doesn't use KIO
QtWebKit is being worked on, and it may replace KHTML at some point, but don't ever think that it will make a bug for bug Safari clone (nor will Epiphany, Android, S60 or any other ported WebKit project). It is already different than WebKit, and attaching it to a different system with different IO system and rendering system will result in a different application no matter how close you want it to be.
Otherwise, if it were this lego like simplicity you seem to think it is... why would it take any effort and new code in the ongoing effort to port it?
Come on guys, why you all are fighthing each other? The fact is: QtWebKit is there, it is not (yet) as good as Safari with WebKit, it might be distributed as KPart for KDE 4.1, but seems the WebKit KPart will only be ready for daily usage for 4.2 onwards.
Meanwhile, KDE will still ship KHTML as the default for Konqueror, providing the best for the user. And even after 4.2, users will be given a choice between that two, I don't know which one will be the default. Those who still want the uber performance of KHTML or those who want compatibility with each website out there.
Just my personal opinion: QtWebKit still needs to mature first, for compatibility, I really should rely on Firefox/Gecko (I try QtWebKit from time to time)
By fred at Fri, 2008/05/30 - 5:00am
"The situation now is that an undermanned group of people (that are sometimes pretty unresponsive, it has to be said)"
I just hope that the KHTML devs can successfully sync directory structure of KHTML and WebKit (and also helped by a GSoC to port WebKit's SVG to KDE) so that both projects can synchronize each other easily (but I guess WebKit won't bother to sync with KHTML...). I guess it would be the best path for KHTML.
And also, having KHTML in our tree IMO won't hurt, WebKit is good, but KHTML is also progressing very nicely. I also hope with the availability of KHTML on Windows can significantly grow KHTML market share.
And also, don't underestimate a small team. I'm so grateful that even though WebKit is there, the KHTML devs still maintain and develop their own baby. As a comparison, just imagine if KOffice devs had dropped KOffice in favor of OOo long time ago, we would not have a hope that someday we can have a viable alternative to a slow and resource intensive office suite.
"I just hope that the KHTML devs can successfully sync directory structure of KHTML and WebKit"
They can't. KHTML is now a fork of WebKit, and as Zack Rusin puts it, not a terribly good one at that.
Yish, people can actually buy THAT line?
By SadEagle at Fri, 2008/05/30 - 5:00am
"Yish, people can actually buy THAT line?"
Yes, because the proof as they say is in the eating. Take a look at the last few years. KHTML has just not emerged into an engine of sufficient reliability and quality for people, and developers, to use confidently enough, and there is no reason at all to believe that situation will change.
I'm not entirely sure how often that needs to be repeated.
Repeating it often doesn't make it any less of nonsense. It's completely and utterly absurd.
"Repeating it often doesn't make it any less of nonsense."
Uh huh. Repeating it isn't going to make it go away.
"It's completely and utterly absurd."
Why? I don't use KHTML because it has a lot of widely recorded issues with browsing a lot of web sites on a day-to-day basis, and KDE developers outside the world of KHTML are reluctant to use it because of that. There's no reason at all that you can point to as to why that situation is going to change.
That is *why* it's not absurd. Did that not become clear at any point?
By segedunum at Sat, 2008/05/31 - 5:00am
"They can't. KHTML is now a fork of WebKit, and as Zack Rusin puts it, not a terribly good one at that."
Nothing is impossible ;) Harri Porten is doing that job (you can see from KDE 4.1 Feature Plan in techbase), I don't know whether it will be ready for 4.1. Also we get one SoC project to port WebKit SVG to KDE/KHTML, seems that it will tremendously help ;).
By anon at Fri, 2008/05/30 - 5:00am
Don't forget that the status quo is the reason why we are able to choose between different browsers since else everybody would be on IE which is still the leading browser.
To if-elif-else Browsers at webpages is not the solution but the problem since that list will always exclude some users and may it only those that depend on the IBM blindreader or another kinder of useragent.
If you look a bit more close at things like ACID1+2+3+n, IE8 quirks vs standard and so on, you may also note, that the general goal is to be independend of browser-implementations and this is the only correct way to go in the long run to prevent incompatibility, to easier the job of webdesigners, to prevent to exclude smaller user-groups and to have real interoperability.
By other anon at Thu, 2008/05/29 - 5:00am
"Don't forget that the status quo is the reason why we are able to choose between different browsers since else everybody would be on IE which is still the leading browser."
There is a balance to be struck between having a choice of rendering engines that open up other platforms for people, and having something that, uhm, works. The status quo just doesn't work for KDE users currently.
For compatibility, I'd rather go for Firefox/Gecko (or even IE, I bet 99% websites out there is compatible with IE :D). I still see some compatibility issues with Safari/WebKit. Also, there is a recent news that a guy from Mozilla is working for Qt/Gecko.
For performance, KHTML is still the winner (especially the latest KHTML from trunk). I still use Konqueror/KHTML as my main browser since it serves me well for my 99% browsing need. And I just fire Firefox when I encounter site which is not compatible with KHTML.
By Another fred at Wed, 2008/05/28 - 5:00am
Same for me. The only place where I need Firefox is the Wordpress post editor, but afaik KHTML now has WYSIWYG editor support, so this might be solved already.
By Stefan Majewsky at Thu, 2008/05/29 - 5:00am
I'm also almost exclusively using Konqueror / KHTML to browse the web, it's simple the fastest I could find and has the nicest rendering in my eyes, leading the pack by a large margin.
Unfortunately ECMAScript / JavaScript support with KDE 3.5's KJS is a bit flaky, but as far as I understand that's not directly KHTML's fould.
I'm looking forward to KDE 4.1 and I'm curious to see how Konqueror has improved. :-)
In case of compatibility problems with web sites I resort to Firefox, but it's just too slow for daily work and many pages get rendered just plain ugly... Maybe Firefox 3 will improve something on that front, I've not tested its betas yet.
By Gunter Ohrner at Sun, 2008/06/01 - 5:00am
Last I heard, qt's webkit was using the same user agent that konqueror was.
Change yours and then you can stop complaining, that's all the site wants.
Of course, then it will look like you're using something that isn't konqueror, so you might as well just go ahead and install internet explorer.
Web developers seem to care very little about standards. And Firefox has written its own. Picking which rendering standard to implement is non-trivial. Deal with that for a while then come back and complain about compatibility.
p.s. qt's webkit != safari's webkit
"Last I heard, qt's webkit was using the same user agent that konqueror was.
Change yours and then you can stop complaining, that's all the site wants.......p.s. qt's webkit != safari's webkit"
I'm afraid that this is the myth that lots of people want to perpetuate, but it simply isn't true I'm afraid. Using the same WebKit engine and code allows for bug-for-bug compatibility with Safari, and with greater market share that counts for a lot, and it's far easier to drive market share up together for the engine. That's why Nokia and lots of others are using it.
Peruse through KHTL's bug list and you'll see that the problems arise from differences and quirks between how KHTML handles certain elements and other engines. Very few, if any at all, of the real problems are down to user agent strings as some people want to pretend.
"Using the same WebKit engine and code allows for bug-for-bug compatibility with Safari"
I'm pretty sure this isn't and will never be true. http://zecke.blogspot.com/2008/01/joys-of-debugging-webkit.html
That doesn't paint a pretty picture.
By jason at Fri, 2008/05/30 - 5:00am
HTML and JavaScript engines never are pretty. Debugging issues with any engine is damn hard, whether it be WebKit or KHTML. In the end' it's a question of what ends up being easiest to work with in the long run, and gives better results.
What happened there was they GIT merged a new branch into QtWebKit, got pointed to a known bug by the Apple people (which affected nightly builds of WebKit and Safari as well) and ended up being OK. In reality, they didn't need to resolve and patch this themselves although they did need to find out what was happening in their port. Try doing this with your own engine that no one else works on.
Unfortunately, this doesn't prove your point at all.
I have been developing web browser components for 9 years. Yes, all the way back when HTML4 was brand new and AJAX wasn't even AJAX (it was all "DHTML" :)
Simply put, having Konqueror use WebKit means that Konqueror and other QtWebKit embedding applications will be running the same rendering engine. This means, if a site fails to load in one, it will fail in the other. The current state of affairs is that Konqueror renders it one way using KHTML (note, badly most of the time) and QtWebKit from a very recent WebKit build (~SquirrelFish checkin time) will render it very nicely. And 3x faster.
To say that it will be bug-for-bug compatibility, is wrong, that is for sure - the abstraction of QtWebKit is different to Safari, so you may see bugs in Qt classes, but then you will also see these in Konqueror, perhaps hidden behind different, confused codepaths. But, WebKit is maintained by Nokia (alone as well as through Trolltech for QtWebKit), Apple and a large team of developers, and the bugfixes and better abstractions will be committed in, and there will be more concerned developers working on WebKit than there are on KHTML.
In fact the blog URL you posted just goes to prove THAT :)
The major benefits will be that Konqueror will develop new features in lockstep with WebKit, and not be a second-rate cousin implementing it's own development path. Rendering, DOM, Javascript and bugfixes can be consolidated, and resource usage reduced (why load two whole rendering engines when you can use one?). Konqueror could concentrate on being the best wrapper around a browser it can be, instead of trying to knock against the status quo. There is no benefit in writing The Best HTML Renderer That Nobody But Konqueror Uses.
I think KDE developers should at least produce some affirmation of their stance on this, and correct the hundreds of not thousands of articles which proclaim that Konqueror is "based on WebKit", when in fact it is based on KHTML which is where WebKit came from. If there is no plan to support WebKit Actual as Konqueror's renderer, then say so. Tell us all, so we can start porting the surrounding Konqueror components into a WebKit-based browser :)
By Matt Sealey, Ge... at Fri, 2008/08/01 - 5:00am
Re: Konqueror ---> khtml
Hmm is flash supported yet? Support for swfdec and/or gnash would be cool...could u puhleeeez cute em? :)
By hihi at Wed, 2008/05/28 - 5:00am
flash is written to work on firefox
and not really anywhere else
at least with newer versions
also, they don't support 64bit systems
complain to them
sorry folks, firefox is THE monopoly today
(but yes, it does work, depending on what version you use)
Re: flash is written to work on firefox
Read again. He was asking for Qt ports/adaptions of swfdec and gnash, which aren't the binary trash Adobe tosses out.
Konqueror can use both KHTML and WebKit, I believe, though WebKit plugin support is still experimental. The added support of WebKit for Plasma is probably for better compatibility with OS X Dashboard widgets.
By Michel S. at Wed, 2008/05/28 - 5:00am
Konqueror has always been technically renderer agnostic. Which is good, since essentially the "free market" (in the form of distros and users) will decide what ends up being the primary renderer of Konqueror. It would've been ugly if what renderer Konqueror used had to be a top-down decision...
Judging from what I've seen blogged about WebKit in Qt 4.5, it sounds like WebKit won't really be ready until then (Qt 4.5 will be probably be late 2008).
Thanks KDE for all your hard work & perseverance!
That is all :)
By Martin Fitzpatrick at Tue, 2008/05/27 - 5:00am
Re: Thanks KDE for all your hard work & perseverance!
By Bram at Wed, 2008/05/28 - 5:00am
(I learned)
By Riddle at Thu, 2008/05/29 - 5:00am
Missing Bits
First of all thank you all who are involved in this wonderful work and for another important beta release.
There are a few things that I am personally missing, they are not vital but nonetheless missing.
Flickr - could somebody tell me where Flickr disappeared to?
Thumbnail preview (composite) doesn't seems to be working although it's turned on and the KWin compositing effects has brought my system to a crawl once again although it was quite fast with previous builds. Anyone here has similar problems?
By Bobby at Tue, 2008/05/27 - 5:00am
no proxy support :'(
Well... I still don't see any word on proxy support in the release notes. More is a pity, but I cannot even try KDE 4.x in a reasonable fashion (well, that is try KDE and KDE programs) without fixed proxy support. I could always use firefox, pidgin, liferea, thunderbird and other non-KDE programs to access the net, but in that case I don't see the point of using KDE. I hope they will fix this soon.
By Dmitriy Kropivn... at Tue, 2008/05/27 - 5:00am
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by Dobber Sports on April 26, 2017
Prospect - Graduates
Auston Matthews, C
Born: 1997-09-17
Hometown: Scotsdale, AZ
Draft Eligible: 2016 by Toronto Maple Leafs, 1st Overall
April 2017 – With his rejection of playing the World Championships, the Matthews rookie season is complete. He came, he scored, he threw some size around, made mistakes, showed growth in the faceoff circle and carried a team into the playoffs (which was well beyond most expectations). The stats are out there to analyze, but we look at what matters. He was a top-20-point producer, his production is sure to grow to point per game and challenge the top 5-10 of any given year and continue to be a top contender in Rocket Richard races for the next several seasons. He finished 8th in shots which is another stat that should swell as he learns to create room for himself and his supporting cast grows and becomes more lethal. The circle was his main drawback. At the start of the season, coach Babcock, defended him with limited faceoff opportunities about 10 per game, by December he was seeing over 15 per contest while winning in the low 40% and at season end he was starting with the puck almost half of the time. He doesn’t have to become a high-end NHL talent on draws, but if he can get to and stay in a mid-50 range he will create much more on offensive zone draws. After watching him game in and game out, especially in the playoffs I found him reminding me of Keith Tkachuk with more offense and none of the extra-curricular activities. Should his career go without any major hitches, he should contend Brett Hull for the top US born producer off all time (unless Patrick Kane gets there first). He doesn’t need further monitoring as everything he does is well documented and analyzed. For fantasy purposes, he should be a top 10 pick in almost any fantasy format going forward. Jason Banks
January 2017 – First and foremost let’s talk production, he is currently on pace for over 70 points thanks in part to a recent hot streak of 11 points in his last seven games. His shot rate is below my earlier prediction but is still high at 3.7 per game, while his minutes per game are increasing due to increased responsibility in the faceoff circle starting shifts in the defensive zone more often. The development curve is hitting new highs nearly every game and has resulted in him hitting the 20-goal mark very early as a rookie. His faceoff winning rate is a bit of a concern at 44.2% but not uncommon for even the best swingmen entering the NHL (John Tavares 47.5% and Sidney Crosby 45.5%). He currently is amongst the top 25 scorers in the league, another season or two he will be amongst the higher end of the top 10. Jason Banks
October 2016 – Well what more can we say about a four goal night. Better than expected (NHL record setting) results for a debut. Matthews was the complete focal point all night any time he was on the ice for viewers and the puck, but somehow managed to find seams in the Sen’s defense which is a skill in itself that is somewhat Ovechkin-like. He put on display his defensive skills a few times as much as his offensive attributes, yet he took responsibility for a soft defensive play that in part, lost his team the match. If the first game is any indicator he is likely to lead the Leafs in scoring as the puck very much follows him if he isn’t carrying it. For those wondering about expectations, lets pencil in 60-65 points which is far more modest than his current 328-point pace. One NHL record to keep tabs on that he may well approach this season is the single season shots on goal record currently owned by Phil Esposito at 550. He registered a half dozen on night one, puts him on pace for 492, which would be good enough for 3rd, sandwiched by Ovechkin’s 08-09 campaign of 528 and head of Ovy’s 446 in 07-08. There is no reason I see that he can’t get 5-8 shots per game even as teams adjust to him. Jason Banks
June 2016 – As expected, the Maple Leafs drafted Matthews first overall. He will make the team immediately and if the Leafs do not sign a center (or trade one), then Matthews – Nazem Kadri – Tyler Bozak will be your 1-2-3 centermen for the Leafs. In an effort to ease Matthews in, Kadri can shoulder the load for the first little while. But Matthews is so good and so ready that he will shoulder his way to the top very quickly. Dobber
June 2016 – Matthews had a draft year for the ages. As an 18 year old he dominated the Swiss League scoring 46 points in 36 games. The Arizona native led team USA twice at international tournaments scoring 11 points in seven games at the World Junior earning the Bronze, and another nine points at 10 World Championship games. Swiss Head Coach Marc Crawford called Matthews the best player in the Swiss League as an 18 year old and Matthews was the best player for USA at the World Championship on a roster that featured several veteran NHL players. Matthews proved to be NHL ready competing all season against former NHL and AHL and pro players in Switzerland and at the World Championship that he will step into a first line job in the NHL immediately. Peter Harling
December 2015 – Auston Matthews will be a vital member of Team USA's entry at the 2016 World Junior Championships in Helsinki, Finland as he returns after representing his country last season. Playing for the Zurich Lions in the Swiss League, Matthews has scored 14 goals and 25 points through 22 games. At the 2015 World Junior event, the Arizona native chipped in one goal and three points in five games for the Americans. Brendan Ross
December 2015 – Born two days past the 2015 NHL Draft deadline, Auston Matthews was unable to challenge Connor McDavid and Jack Eichel for the top spot but he surely would've been in the conversation based on his talents. In a rare move, Auston Matthews opted to play his current 2016 draft season in Switzerland with ZSC of the top professional league and he's established himself as a dangerous offensive threat. Matthews blends imposing size and power with impressive skill to compete as a strong two-way pivot. Possesses terrific hands and strength on the puck as he dominates possession, particularly below the top of the circle. He flashes intelligent vision, good creativity and high-end skating ability which all blend to create an impact forward in all three zones. There are few holes in Matthews game as this toolsy forward possesses all of the attributes that teams seek out in a number one centerman. Deemed NHL-ready, Matthews ability to carry the offence while providing excellent defensive presence makes him a lock to be selected first overall at the upcoming 2016 NHL Entry Draft. Brendan Ross
Fantasy Outlook: A+
Franchise two-way power centerman with point-per-game upside.
Footage:
First 4 NHL goals in first game (the 2nd was the most impressive)
Auston Matthews – First five goals in Europe:
Auston Matthews – 2015 World Junior Highlights:
Buy the latest Fantasy Prospects Report here.
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March 14th, 2017 Cristy "Pandora" Ramadani Tournaments 1 comments
Singsing's stack - Bean breezed through the Kiev Major EU Open Qualifiers
TI6 schedule and format revealed
Invcitus Gaming’s potential has started to surface this season, reaching the top during the China Kiev Major qualifiers. The Chinese team took the top place and seed in the group stage and then became the second of the organization’s teams to lay claim to the main event spot. Xu “BurNIng” Zhilei and company will be heading to the Kiev Major to take place between April 27th – April 30th, joining Wings Gaming, Digital Chaos, Evil Geniuses, Newbee, OG, Team Liquid, Ad Finem, Team VG.J, Team Faceless, TnC Pro, iG.Vitality, Virtus.Pro, Team Secret, Team Onyx and SG esports.
The Kiev Major got a whole lot better with BurNIng and his boys from Invictus Gaming securing a slot at the event. Congrats. #KievMajor pic.twitter.com/UH1BtGiOC1
— Wykrhm Reddy (@wykrhm) March 14, 2017
Invictus Gaming fully emerged from the fog and recent obscurity during the China Kiev Major qualifiers.
After rough stretch and spate of disappointing finishes for the last year, the team faded into the background of the Chinese Dota 2 scene.
Quietly and surely the team has stuck together and continued to grind through – with the most satisfying result – a place in the Kiev Major.
Invcitus Gaming topped the group stage with a 7:2 record. In the playoffs, they continued to show dominance and power, but fell to their sister team iG.Vitality in the upper bracket finals, losing out on seizing the first qualifying slot.
In the lower brackets they faced ViCi Gaming in a three game battle. Following two hard fought matches for each team, Invictus Gaming sealed the deal and their fate in the deciding game in only 24 minutes. Led by a Burning on Vengeful Spirit, the team snatched away any hopes left for ViCi Gaming.
Their win secured them a place among the best at the Kiev Major.
All 16 teams are now officially decided and getting ready to prepare.
Invictus Gaming China Kiev Major qualifiers winners
Burning at The Summit 3
Invictus Gaming had a very difficult time last year. After a disappointing 12th place finish at TI5, the team was once again subject to nonstop roster changes and instability – resulting in little to no achievements. It marked the first time that the organization and Luo “Ferrari_430” Feich did not participate in the Internationals since TI1.
The iconic and TI2 championship organization has made some drastic changes to their roster for the upcoming Fall Major 2016 season, adding famed veteran Xu “BurNIng” Zhilei and Fu “Q” Bin to the squad, moving Ou “Op” Peng up from IG.Vitality.
At the end of August, Luo “Ferrari_430” Feichi left Invictus Gaming after more than 5 years with the organization.At this time it is unknown as to the future status of the highly acclaimed ‘pianist’.
Chen “Rong” Jingwu and Zhao “qd” Shungeng have also been replaced on the squad, leaving Lin “Xxs” Jing and Ye “BoBoKa” Zhibiao left on the lineup.
Introduced to DotA by his friends, at the end of 2007, it wouldn’t be until his last DotA 1 team, DK, transitioned to Dota 2 that Burning would make his first splash into the scene. The Chinese star stayed with DK until after TI4, when he left the team after a fourth place finish, and decided to retire from competitive play temporarily. Burning is regarded as one of the best and most experienced carry players in the world, probably the most famous Chinese Dota 2 player of all time, considered by many a legend. With such steep and enormous revere from others and a nickname of B-God. He is the exemplification of consistency and superior performances. He has an exceptional ability to farm while still remaining active in the game, by supporting his team quickly in fights and taking objectives when necessary.
Q kicked off his professional Dota 2 career playing for the LGD youth squad in 2014. He transitioned with his teammates when the squad decided to go solo, under the CDEC tag. As CDEC’s captain, Q has outdrafted even the best teams in the world at TI5. His selections and leadership for execution is flawless. There is little doubt that his team respects and follows his calls and foresight.
Op has moved up from IG.Vitality to the main squad. He started his career in Dota 2 in March 2016 with the organization.
The team has stayed together since – despite subpar and disappointing results. Their commitment seems to be starting to pay off with a fourth place Dota2 Professional League Season 2 – Top at the start of the new season, 1st-2nd place in the Dota 2 Asia Championships 2017 China Qualifier and fourth place at Dota Pit League Season 5.
Invictus Gaming roster
Xu “BurNIng” Zhilei
Ou “Op” Peng
Lin “Xxs” Jing
Fu “Q” Bin
Ye “BoBoKa” Zhibiao
China Kiev Major qualifiers China Kiev Major qualifiers China Kiev Major qualifiers China Kiev Major qualifiers China Kiev Major qualifiers
Kiev Major
The Kiev Major is scheduled to take place between April 27-30th at the National Palace of Arts, in Kiev, Ukraine. National Palace of Arts is one of the main theater venues in Kiev, Ukraine. It was opened in 1970 with a seating capacity of almost 4,000 in the main concert hall – approximately the same size as Wang Theater where the Boston Major was held this last fall.
In the past, StarLadder i-League StarSeries Season 2 hosted CS:GO at the event successfully.
The event will be hosted by PGL and will be the last Major ore-TI7.
Kiev Major teams
Kiev Major dates
The Kiev Major group stage will take place starting April TBA.
The Kiev Major main event will take place between April 27-30th at the National Palace of Arts, in Kiev, Ukraine.
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Comments: In a field in which two books tied for first place, another was given the nod as the third place finisher, and a number were listed as finalists, I'm not entirely sure what designating Lavie Tidhar's novel Osama as an "honorable mention" was supposed to mean. Did the judges intend to recognize Osama as an implied fourth place finisher in the balloting? Did they mean to say that Osama isn't really a science fiction novel but they wanted to recognize Tidhar's accomplishment anyway? As with so many things about the Campbell Awards, the answer to these questions seems likely to remain a mystery.
(tie) The Highest Frontier by Joan Slonczewski
(tie) The Islanders by Christopher Priest
Embassytown China Miéville
Dancing with Bears by Michael Swanwick
Home Fires by Gene Wolfe
Robopocalypse by Daniel H. Wilson
Seed by Rob Ziegler
Soft Apocalypse by Will McIntosh
This Shared Dream by Kathleen Ann Goonan
Osama by Lavie Tidhar
Musical Monday: Magic (MTG): The Rap by Remy Munasifi
I will now make an admission that may damage my gamer geek credibility: I have never played Magic: The Gathering. I have, however, played other collectible card games - my favorites are the Babylon 5 CCG and Steve Jackson Games' game of conspiracy and world domination Illuminati: The New World Order (usually abbreviated INWO). CCGs are addictive, and can be expensive. They are also insanely fun for people with obsessive personalities like me.
Remy's rap, like all of his other songs, is brutal and accurate. This is probably because Remy has experience playing a game that some have called "cardboard crack". One can almost learn how to play Magic by watching the video, and one certainly gets a good feel for how a game plays out. Plus, Remy makes it funny to listen to. So for anyone who ever spent hours crafting a new deck for their favotire CCG, this week's Musical Monday selection is Magic (MTG): The Rap.
Previous Musical Monday: I Will Sing a Lullaby by Paul & Storm
Subsequent Musical Monday: We Are Star Dust by Symphony of Science
Remy Munasifi Musical Monday Home
Posted by Aaron Pound at 1:00 PM 0 comments
Notice: Sporadic Posting Ahead
Starting today, June 24, 2012, I will be at Camp Olmsted in the Goshen Scout Reservation near Lexington Virginia until June 30, 2012. For anyone unfamiliar with Goshen (which I am guessing means most of the people who read this blog), it is in the mountains of Virginia in the middle of nowhere. This means I will have limited, if any, access to the internet. Consequently, posting for the next week will be sporadic at best.
Labels: Notices
Book Blogger Hop June 22nd - June 28th: The Sevens Are a Secret Society at the University of Virginia
Jen at Crazy for Books has restarted her weekly Book Blogger Hop to help book bloggers connect with one another. The only requirements to participate in the Hop are to write and link a post answering the weekly question and then visit other blogs that are also participating to see if you like their blog and would like to follow them. A complete explanation of the history and the rules of the Hop can be found here.
This week Jen asks: Do you immediately write a review upon finishing a book or do you wait and write multiple reviews at once?
I try to write my reviews as soon as I can after finishing a book, so that I have the material fresh in my mind when I write. I usually have a backlog though, because I read faster than I can write. Right now, I'm several books behind.
Go to previous Book Blogger Hop: The Six Are Superhumans in Flow My Tears, the Policeman Said
Go to subsequent Book Blogger Hop: Eight Is the Second Magic Number in Nuclear Physics
Book Blogger Hop Home
Labels: Book Blogger Hop, Meme
Follow Friday - The U.S.S. Enterprise is CVN-65
It's Friday again, and this means it's time for Follow Friday. There has been a slight change to the format, as now there are two Follow Friday hosts blogs and two Follow Friday Features Bloggers each week. To join the fun and make now book blogger friends, just follow these simple rules:
Follow both of the Follow My Book Blog Friday Hosts (Parajunkee and Alison Can Read) and any one else you want to follow on the list.
Follow the two Featured Bloggers of the week - Books and Blossoms and Head Stuck in a Book.
Put your Blog name and URL in the Linky thing.
Grab the button up there and place it in a post, this post is for people to find a place to say hi in your comments.
Follow, follow, follow as many as you can, as many as you want, or just follow a few. The whole point is to make new friends and find new blogs. Also, don't just follow, comment and say hi. Another blogger might not know you are a new follower if you don't say "Hi".
If someone comments and says they are following you, be a dear and follow back. Spread the love . . . and the followers.
If you want to show the link list, just follow the link below the entries and copy and paste it within your post!
If you're new to the Follow Friday Hop, comment and let me know, so I can stop by and check out your blog!
And now for the Follow Friday Question: If you could “unread” a book, which one would it be? Is it because you want to start over and experience it again for the first time? Or because it was THAT bad?
I've read plenty of bad books: Pureheart (read review), Dragons in the Valley (read review) and everything else by Donita K. Paul, Seven Wings and the Bleeding Twin Flowers (read review), and so on and so forth. But as bad as they were, I wouldn't pick any of them to "unread". Instead, I'll pick the sequels to Rendezvous with Rama: Rama II, Garden of Rama, and Rama Revealed. Why? Because the first book by Arthur C. Clarke is a classic of science fiction, while the sequels (written two decades later in collaboration with another author) are awful enough that they tarnish the first one.
Go to previous Follow Friday: My First Computer Was a Commodore 64
Go to subsequent Follow Friday: Order 66 Directed the Clone Troopers to Kill the Jedi
Follow Friday Home
Labels: Follow Friday, Meme
Review - The Wizard in the Tree by Lloyd Alexander
Short review: Mallory finds a wizard hidden in a tree. They have adventures.
In an old oak tree
A sleeping wizard awakes
Magic is fading
Full review: Lloyd Alexander wrote consistently good children's fiction, usually with an element of fantasy. While The Wizard in the Tree is not up to the level of the Chronicles of Prydain, it still holds up as a well-written tale of a hapless wizard losing his powers and the young girl who discovered him.
The story begins when Mallory, a young village girl, discovers Arabicus, a wizard who has been trapped in an oak tree since he broke the rules concerning harming living things. She frees him, and discovers that he was trapped while on his way out of our world into a place where all magical creatures retreated long ago. Soon enough, they discover that Arabicus' magic is fading away and he will die if he doesn't leave.
Unfortunately, Mallory and Arabicus run afoul of the greedy village squire, who is trying to industrialize the town and make himself rich. Mallory and Arabicus lurch from silly adventure to silly adventure. The tone is much more light-hearted than the Chronicles of Prydain - the villains don't, for example, burn people alive as they do in The Book of Three (read review) and much more like most young adult adventure fantasy. The problems are those a villager would encounter, and the villains are venal rather than vile. The book is fun, but it is not anything more than that.
Lloyd Alexander Book Reviews A-Z Home
Labels: Book Reviews, Fantasy Fiction Reviews, Young Adult Fiction Reviews
Review - The Foundling and Other Tales of Prydain by Lloyd Alexander
Stories included:
The True Enchanter
The Rascal Crow
The Smith, the Weaver, and the Harper
The Truthful Harp
Coll and His White Pig
Full review: The Foundling is a collection of short stories set in the same fictional world as the Chronicles of Prydain, and featuring several of the same characters (or, in some cases, their ancestors). The stories in this book are not strictly necessary, but offer back story and character development for several of the secondary characters. Stories featuring Dallben, Coll, Fflewddur Fflam, Doli, and Kaw as well as Eilonwy's mother appear. A dark story concerning the sword Dwrnwyn, and a fairy tale-like story involving Arawn's theft of human knowledge are also featured.
For the most part, the stories are all quite brief, filling in the gaps of the Chronicles of Prydain with a story structure like folk tales. In The Foundling Alexander borrows from some Irish myth to tell the tale of how Dallben obtained his great knowledge, and also, in a very Celtic turn of events, the price that is exacted from him in return. The Stone is a little morality tale in which a farmer earns a favor from Doli and demands in payment a stone that will prevent him from aging. As is typical in tales like these, the enchanted boon turns out to be a decidedly mixed blessing.
One of the few stories that doesn't feature any of the characters from the Chronicles, The True Enchanter instead features Angharad, Eilonwy's mother. A headstrong young woman, Angharad is informed by her mother that she must marry an enchanter, and despite her reluctance begins to entertain suitors. In succession, Gildas, Grimgower, and Geraint try to win her hand - the first by conjuring darkness and snow, the second by summoning monsters, and the last by telling stories of nature and beauty. In the end, Angharad gets her way and true magic and love wins out. The Rascal Crow features Medwyn, a character who played a minor role in the Chronicles, but focuses on Kadwyr, an arrogant crow who refuses to heed Medwyn's warnings about Arwan's designs upon he and the other animals of the forest, spurning the offers of assistance proffered by Medwyn's other charges. Because this is a morality tale, this comes back to haunt Kadwyr, but because this is a humorous tale, he doesn't learn the lesson one would expect.
The darkest tale in the collection, The Sword provides background concerning the king that constructed the Spiral Castle and owned the magical blade Dyrnwyn and how his body came to be where Taran found it in The Book of Three. It is a story of hubris and injustice followed by madness and death. The Smith, the Weaver, and the Harper is another dark tale that details how Arawn deceived men and stole the tools that held the secrets of their crafts by playing upon their greed. The tale ends on a note of hope as the power of men to find beauty and resist the power of the Dark Lord is demonstrated.
The final two stories in the collection connect directly to the Chronicles. In the first, The Truthful Harp, we learn how Fflewddur Fflam gave up his kingdom, took up a life as a wandering bard, and obtained his magical harp. As happens so often in Alexander's tales, Fflewddur dreams of being heralded for famous deeds and doesn't realize which of his actions truly have value until he learns wisdom. The last story in the collection is Coll and His White Pig, which tells the tale of how Coll rescued Hen Wen from the clutches of Arawn. Although Coll is declared to be a stout warrior in the story, it is not the strength of his arm that wins him his pig back, but rather his kindness and generosity, plus a little bit of luck, which results in his obtaining help from some unlikely new friends.
While this collection is not as good as the series it supports, all of the tales are well-told, and each adds a little bit to the overall picture of Prydain. As a person who loved the five book series, the only thing I didn't like about this book is that there weren't more stories to read.
Previous book in the series: The High King
Labels: Book Reviews, Fantasy Fiction Reviews, Short Fiction Reviews, Young Adult Fiction Reviews
Musical Monday: I Will Sing a Lullaby by Paul & Storm
Caution: This week's Musical Monday installment may cause members of the Michigan House of Representatives to clutch their pearls in horror, get the vapors, faint, or possibly even have a heart attack or an aneurism. Be warned.
On June 20th, 2012, while criticizing a bill that was yet another effort to evade the legal requirements of Roe v. Wade, Michigan state representative Lisa Brown said " "I'm flattered you're all so concerned about my vagina. But no means no." This simple statement of truth caused the all-male Republican leadership of the state house to spin themselves into a pearl-clutching tizzy of outrage over the fact that a mere woman had the temerity to tell the truth about their blatantly unconstitutional and anti-woman legislation.
So Republican leadership barred her from speaking stating that Brown (and another legislator who had tried to introduce a bill that would bar vasectomies except where necessary to protect the life of the patient) "will not be recognized to speak on the House floor today after being gaveled down for their comments and actions yesterday that failed to maintain the decorum of the House of Representatives."
This, predictably, sparked criticism of the Michigan House leadership,for their ban on the use of the word "vagina" in discussing legislation aimed at regulating, well, vaginas. In response, the Republican lawmakers decided to double down on their silliness by proffering mealy mouthed weasel-worded excuses explaining that they didn't ban her for using the word "vagina", but rather for the way she used the word vagina. To quote Ari Adler, press secretary for Michigan House Speaker James Bolger, "It was the context in which it was used and the way it was used, that was the problem." So apparently using the word "vagina" in the context of legislation involving vaginas is the problem? Or maybe Brown's "breach of decorum" was in pointing out that as a woman, she does indeed possess a vagina?
Of course, Adler's excuse is simply nonsense, and the attempted obfuscation is simply pathetic. Republican lawmaker Rick Johnson dug the hole deeper when he attempted to explain by saying, "That comment would be very inappropriate. You have young children? Is that something you want them to hear from your state rep?" In response, I have to say that I don't find the comment to be inappropriate given the legislation being discussed at the time, I have children (my youngest is currently twelve, which I think does count as "young children"), and I think that a state representative using the correct anatomical term in a discussion about legislation relating to medical practices is exactly what I would want them to hear.
So, in honor of the leadership of the Michigan House of Representatives who apparently get the vapors and faint when they hear the word "vagina", I am featuring Paul & Storm's ode to female lady parts I Will Sing a Lullaby.
Previous Musical Monday: I Am Glad, 'Cause I'm Finally Returning Back Home by Eduard Khil
Subsequent Musical Monday: Magic (MTG): The Rap by Remy Munasifi
Location: Seattle, Washington.
Comments: In 2012, for reasons unknown, the Best Magazine and Best Book Publisher or Imprint categories dropped off of the roster of the Locus Awards. As with all of the previous times that categories have vanished without warning, I have no idea why this change was made, or what it signifies. Given that these two categories were reinstated in 2013, their disappearance is even more mysterious.
1. Embassytown by China Miéville
2. 11/22/63 by Stephen King
3. Rule 34 by Charles Stross
4. The Children of the Sky by Vernor Vinge
5. Leviathan Wakes by James S.A. Corey
6. Dancing with Bears by Michael Swanwick
7. Grail by Elizabeth Bear
8. Deadline by Mira Grant
9. Home Fires by Gene Wolfe
10. Vortex by Robert Charles Wilson
11. Earthbound by Joe Haldeman
12. Firebird by Jack McDevitt
13. The Clockwork Rocket by Greg Egan
14. The Islanders by Christopher Priest
15. Heart of Iron by Ekaterina Sedia
16. Daybreak Zero by John Barnes
17. This Shared Dream by Kathleen Ann Goonan
18. 7th Sigma by Steven Gould
19. All the Lives He Led by Frederik Pohl
20. Wake Up and Dream by Ian R. MacLeod
21. The Courier's New Bicycle by Kim Westwood
22. Zone One by Colson Whitehead
1. A Dance with Dragons by George R.R. Martin
2. Among Others by Jo Walton
3. Snuff by Terry Pratchett
4. The Wise Man's Fear by Patrick Rothfuss
5. Deathless by Catherynne M. Valente
6. The Kingdom of Gods by N.K. Jemisin
7. The Magician King by Lev Grossman
8. The Heroes by Joe Abercrombie
9. The Folded World by Catherynne M. Valente
10. The Cold Commands by Richard K. Morgan
11. Raising Stony Mayhall by Daryl Gregory
12. The Uncertain Places by Lisa Goldstein
13. Redwood and Wildfire by Andrea Hairston
14. Heartless by Gail Carriger
15. Professor Moriarty: The Hound of the D'Urbervilles by Kim Newman
16. The Dragon's Path by Daniel Abraham
17. The Alchemists of Kush by Minister Faust
18. Briarpatch by Tim Pratt
19. Mr. Fox by Helen Oyeyemi
20. The Fallen Blade by Jon Courtenay Grimwood
21. The Hammer by K.J. Parker
22. Mistification by Kaaron Warren
1. The Girl Who Circumnavigated Fairyland in a Ship of Her Own Making by Catherynne M. Valente
2. Planesrunner by Ian McDonald
3. Akata Witch by Nnedi Okorafor
4. Goliath by Scott Westerfeld
5. Miss Peregrine's Home for Peculiar Children by Ransom Riggs
6. The Freedom Maze by Delia Sherman
7. Abarat: Absolute Midnight by Clive Barker
8. Daughter of Smoke & Bone by Laini Taylor
9. Across the Great Barrier by Patricia C. Wrede
10. A Monster Calls by Patrick Ness
11. Red Glove by Holly Black
12. Mastiff by Tamora Pierce
13. The Highest Frontier by Joan Slonczewski
14. Huntress by Malinda Lo
15. Beauty Queens by Libba Bray
16. The Boy at the End of the World by Greg van Eekhout
17. Across the Universe by Beth Revis
18. Scrivener's Moon by Philip Reeve
19. Eona by Alison Goodman
1. The Night Circus by Erin Morgenstern
2. Mechanique: A Tale of the Circus Tresaulti by Genevieve Valentine
3. Soft Apocalypse by Will McIntosh
4. God's War by Kameron Hurley
5. Ready Player One by Ernest Cline
6. Of Blood and Honey by Stina Leicht
7. The Tiger's Wife by Téa Obreht
8. The Girl of Fire and Thorns by Rae Carson
9. Seed by Rob Ziegler
10. The Desert of Souls by Howard Andrew Jones
11. Debris by Jo Anderton
12. Low Town by Daniel Polansky
13. Blood Red Road by Moira Young
1. Silently and Very Fast by Catherynne M. Valente
2. The Man Who Bridged the Mist by Kij Johnson
3. Kiss Me Twice by Mary Robinette Kowal
4. The Ants of Flanders by Robert Reed
5. The Affair of the Chalk Cliffs by James P. Blaylock
6. The Ballad of Ballard and Sandrine by Peter Straub
7. The Man Who Ended History: A Documentary by Ken Liu
8. The Ice Owl by Carolyn Ives Gilman
9. Gravity Dreams by Stephen Baxter
10. The Men from Porlock by Laird Barron
11. Near Zennor by Elizabeth Hand (reviewed in Errantry: Strange Stories)
12. The Adakian Eagle by Bradley Denton
13. Rampion by Alexandra Duncan
14. Blue and Gold by K.J. Parker
15. A Brood of Foxes by Kristin Livdahl
1. White Lines on a Green Field by Catherynne M. Valente
2. The Summer People by Kelly Link
3. What We Found by Geoff Ryman
4. Underbridge by Peter S. Beagle
5. The Copenhagen Interpretation by Paul Cornell
6. The Choice by Paul J. McAuley
7. Fields of Gold by Rachel Swirsky
8. The Dala Horse by Michael Swanwick
9. The Book of Phoenix Excerpted from The Great Book by Nnedi Okorafor
10. The Maltese Unicorn by Caitlín R. Kiernan
11. A Long Walk Home by Jay Lake
12. Purple by Robert Reed
13. Clean by John Kessel
14. The Little Green God of Agony by Stephen King
15. Six Months, Three Days by Charlie Jane Anders
16. The Old Man and the Martian Sea by Alastair Reynolds
17. Late Bloomer by Suzy McKee Charnas
18. A Small Price to Pay for Birdsong by K.J. Parker
19. The Last Ride of the Glory Girls by Libba Bray
20. My Husband Steinn by Eleanor Arnason
21. Laika's Ghost by Karl Schroeder (reviewed in Clarkesworld: Issue 100 (January 2015))
22. Blackwood's Baby by Laird Barron
23. The Cold Step Beyond by Ian R. MacLeod
24. The Projected Girl by Lavie Tidhar
25. The Vicar of Mars by Gwyneth Jones
26. The Ki-Anna by Gwyneth Jones
27. Ghostweight by Yoon Ha Lee
28. Mysteries of the Old Quarter by Paul Park
29. Steam Girl by Dylan Horrocks
1. The Case of Death and Honey by Neil Gaiman
2. The Paper Menagerie by Ken Liu
3. The Cartographer Wasps and the Anarchist Bees by E. Lily Yu
4. The Bread We Eat in Dreams by Catherynne M. Valente
5. The Way It Works Out and All by Peter S. Beagle
6. And Weep Like Alexander by Neil Gaiman
7. Tidal Forces by Caitlín R. Kiernan
8. The Brave Little Toaster by Cory Doctorow
9. The Invasion of Venus by Stephen Baxter
10. Valley of the Girls by Kelly Link
11. After the Apocalypse by Maureen F. McHugh
12. Dolly by Elizabeth Bear (reviewed in Asimov's Science Fiction: Vol. 35, No.1 (January 2011))
13. Attlee and the Long Walk by Kage Baker
14. For I Have Lain Me Down on the Stone of Loneliness and I’ll Not Be Back Again by Michael Swanwick
15. Goodnight Moons by Ellen Klages
16. Pug by Theodora Goss
17. Ascension Day by Alastair Reynolds
18. Daddy Long Legs of the Evening by Jeffrey Ford
19. Younger Women by Karen Joy Fowler
20. Mulberry Boys by Margo Lanagan
21. Smoke City by Christopher Barzak
22. The Corpse Painter's Masterpiece by M. Rickert
23. The Server and the Dragon by Hannu Rajaniemi
24. Slow as a Bullet by Andy Duncan
25. The Sandal-Bride by Genevieve Valentine
26. Woman Leaves Room by Robert Reed
27. Movement by Nancy Fulda
28. The Patrician by Tansy Rayner Roberts
29. And Go Like This by John Crowley
30. Tying Knots by Ken Liu
1. The Bible Repairman and Other Stories by Tim Powers
2. After the Apocalypse: Stories by Maureen F. McHugh
3. Sleight of Hand by Peter S. Beagle
4. The Collected Stories of Carol Emshwiller, Volume 1 by Carol Emshwiller
5. Two Worlds and In Between: The Best of Caitlin R. Kiernan (Volume One) by Caitlín R. Kiernan
6. Paradise Tales by Geoff Ryman
7. The Collected Short Works of Poul Anderson, Volume 4: Admiralty by Poul Anderson
8. Kurt Vonnegut: Novels & Stories 1963-1973 by Kurt Vonnegut
9. Gothic High-Tech by Bruce Sterling
10. When the Great Days Come by Gardner Dozois
11. The Inheritance and Other Stories by Robin Hobb (aka Megan Lindholm)
12. Yellowcake by Margo Lanagan
13. Unpossible and Other Stories by Daryl Gregory
14. Love and Romanpunk by Tansy Rayner Roberts
15. Somewhere Beneath Those Waves by Sarah Monette
16. The Monkey's Wedding and Other Stories by Joan Aiken
17. TVA Baby and Other Stories by Terry Bisson
18. The Universe of Things by Gwyneth Jones
19. Matilda Told Such Dreadful Lies: The Essential Lucy Sussex by Lucy Sussex
1. The Year's Best Science Fiction: Twenty-Eighth Annual Collection edited by Gardner Dozois
2. Welcome to Bordertown edited by Holly Black and Ellen Kushner
3. Engineering Infinity edited by Jonathan Strahan
4. Steampunk!: An Anthology of Fantastically Rich and Strange Stories edited by Kelly Link and Gavin J. Grant
5. Eclipse Four edited by Jonathan Strahan
6. The Weird edited by Ann VanderMeer and Jeff VanderMeer
7. The Thackery T. Lambshead Cabinet of Curiosities edited by Ann VanderMeer and Jeff VanderMeer
8. The Best Science Fiction and Fantasy of the Year Volume Five edited by Jonathan Strahan
9. Life on Mars: Tales of the New Frontier edited by Jonathan Strahan
10. Naked City: Tales of Urban Fantasy edited by Ellen Datlow
11. Year's Best SF 16 edited by David G. Hartwell and Kathryn Cramer
12. Teeth: Vampire Tales edited by Ellen Datlow and Terri Windling
13. The Book of Cthulhu edited by Ross E. Lockhart
14. Ghosts by Gaslight edited by Jack Dann and Nick Gevers
15. Subterranean: Tales of Dark Fantasy 2 edited by William Schafer
16. The Best Horror of the Year: Volume Three edited by Ellen Datlow
17. Blood and Other Cravings edited by Ellen Datlow
18. The Year's Best Science Fiction & Fantasy: 2011 Edition edited by Rich Horton
19. Happily Ever After edited by John Klima
20. A Book of Horrors edited by Stephen Jones
21. The Mammoth Book of Best New Horror: 22 edited by Stephen Jones
22. The Year's Best Dark Fantasy & Horror: 2011 Edition edited by Paula Guran
1. Evaporating Genres: Essays on Fantastic Literature by Gary K. Wolfe
2. Becoming Ray Bradbury by Jonathan R. Eller
3. Musings and Meditations by Robert Silverberg
4. In Other Worlds: SF and the Human Imagination by Margaret Atwood
5. Sightings: Reviews 2002-2006 by Gary K. Wolfe
6. Pardon This Intrusion: Fantastika in the World Storm by John Clute
7. Nested Scrolls: The Autobiography of Rudolf von Bitter Rucker by Rudy Rucker
8. Denying Science by John Grant
2. Masters of Science Fiction and Fantasy Art edited by Karen Haber
3. Out of This World: Science Fiction But Not As You Know It edited by Mike Ashley
4. A Tolkien Tapestry: Pictures to Accompany The Lord of the Rings by Cor Blok
5. Jeffrey Jones: A Life in Art by Jeffrey Jones
6. Hardware: The Definitive SF Works of Chris Foss by Chris Foss
7. Fantasy+ 3: Best Hand-painted Illustrations edited by Vincent Zhao
8. Exposé 9: Finest Digital Art in the Known Universe edited by Daniel Wade
2. Jonathan Strahan
4. Ann VanderMeer and Jeff VanderMeer
7. John Joseph Adams
8. Sheila Williams
9. Catherynne M. Valente
10. Terri Windling
13. Liz Gorinsky
14. Gavin Grant and Kelly Link
16. William Schafer
17. Neil Clarke
18. Patrick Nielsen Hayden
22. Alisa Krasnostein
23. Jeremy Lassen
24. Sharyn November
26. Teresa Nielsen Hayden
1. Shaun Tan
3. John Picacio
7. Stephan Martiniere
9. John Jude Palencar
11. Thomas Canty
14. Phil Foglio
16. Leo Dillon and Diane Dillon
17. Daniel Dos Santos
18. Tom Kidd
19. Yoshitaka Amano
21. Vincent Chong
22. (tie) Boris Vallejo
(tie) Brom
25. Todd Lockwood
Awards - Very British Science Fiction
The Arthur C. Clarke Award is a relatively recently created annual award that is given to the best science fiction novel first published in the United Kingdom in the previous year. Established by a grant provided by Arthur C. Clarke, the award was first given in 1987 to Margaret Atwood for The Handmaid's Tale, her dystopian tale of misogynistic theocracy. Atwood, somewhat predictably, was shocked to discover that she had written a science fiction novel, and has spent the last several years dismissively pooh-poohing the entire genre, which has alienated a large cadre of her potential readers (go to list of Arthur C. Clarke Award Winners).
The winning book is chosen by a panel of judges drawn from from the British Science Fiction Association, the Science Fiction Foundation, and SF Crowsnest. The winner is given a prize consisting of a number of pounds sterling equal to the current number of the calendar year (i.e. in 1987, for winning the award she was horrified to receive, Atwood was given 1,987 pounds sterling). You can find the official website for the award here.
1987 Arthur C. Clarke Winner: The Handmaid's Tale by Margaret Atwood
Labels: Arthur C. Clarke Award Reviews
Book Blogger Hop June 15th - June 21st: The Six Are Superhumans in Flow My Tears, the Policeman Said
This week Jen asks: Do you belong to a book club, either online or in real life?
No. Yeah, I know, it's a pretty boring answer, but it is the only truthful one I can give.
Go to previous Book Blogger Hop: Leeloo Was the Fifth Element
Go to subsequent Book Blogger Hop: The Sevens Are a Secret Society at the University of Virginia
Follow Friday - My First Computer Was a Commodore 64
Follow the two Featured Bloggers of the week - Candace's Book Blog and Patch of Sky.
And now for the Follow Friday Question: Happy Father’s Day! Who is your favorite dad character in a book and why?
Maybe it is because I've been posting reviews for the Chronicles of Prydain series (read reviews), but I'm going to go with the elderly enchanter Dallben and the warrior-turned-farmer Coll as my favorite "dad characters", even though technically neither of them are a dad. In the books, Taran is an orphan brought up at Caer Dallben under the enchanter's care with Coll's assistance, so they more or less fill in the role of "adult guardians" for the hero. They are kind, patient, and loving towards a headstrong and foolish boy, doing their best to guide him with the wisdom that comes from age and experience, but smart enough to know when to step back and let him make his own mistakes.
Go to previous Follow Friday: The Offspring of a Donkey and a Horse Has Sixty-Three Chromosomes
Go to subsequent Follow Friday: The U.S.S. Enterprise is CVN-65
Posted by Aaron Pound at 1:38 PM 12 comments
Review - The High King by Lloyd Alexander
Short review: Arawn reaches his hand out to take Prydain in his grasp. Taran and his friends must struggle and sacrifice to stop him.
The white pig banner
Rallies the free to Taran
Kill the cauldron born
Full review: This is the last book of the main story of the Chronicles of Prydain, and a worthy climax to the series. The bulk of this book describes the war between Arawn and the rest of Prydain, led by High King Math, Prince Gwydion, and the rest of the Sons of Don. Taran and his companions gather together the people he had befriended on his many journeys in the previous books and join Math and Gwydion's side, fighting under Taran's banner of a white pig.
Much of the war goes badly for the heroes: they are betrayed by those they depended upon, sacrifices must be made, good people fall. For a book aimed at a younger audience, the book is definitely dark, and the war quite brutal; many characters who have been in the series for numerous books must give up things that are precious and valuable to them, and many others die. Finally, through a twist that was quite a surprise to me when I read the book the first time (albeit when I was much younger), Arawn is defeated.
But that's not the end. And in many ways, the elements of the book that follow Arawn's defeat are the most important part of the book - the choices and sacrifices Taran and his friends must make in victory are the most critical, and without them, the book (and in many ways, the entire series) would have been a throwaway piece of fluff. In the end, Alexander shows that although victory has its rewards, it definitely has a price that must be paid, both to achieve it and after it has been attained.
Previous book in the series: Taran Wanderer
Subsequent book in the series: The Foundling and Other Tales of Prydain
Labels: Book Reviews, Fantasy Fiction Reviews, Newbery Medal Book, Young Adult Fiction Reviews
Review - Taran Wanderer by Lloyd Alexander
Short review: Taran searches for his heritage and along the way inadvertently finds the man he is meant to be.
To find his parents
Taran quests across the world
And then finds himself
Full review: Of the five books that make up the Chronicles of Prydain, this one is the most oddly structured. It is also my favorite. Following the events in The Castle of Llyr, Taran decides he must find out about his true parentage and sets out accompanied by Gurgi. First he seeks out the witches of the Marshes of Morva, but since they will only trade for information (and being poor, Taran has nothing to trade), he settles for being told of the magical Mirror of Llunet faraway in the mountains, which he is told will show his true heritage. He shelters with a farmer, settles a dispute for King Smoit, rescues Doli and the fair folk from the power of the evil wizard Morda, runs afoul of the mercenary Dorath, lives with Craddoc, a farmer he believes is his father, and studies the trade crafts of smithing, weaving, and pottery with master craftsmen from the Free Commots. Taran finds the Mirror, a pool of still water in the cave, but it is destroyed by Dorath after Taran views only a glimpse, which reveals only his own reflection.
Taran in this book is a direct contrast to the Taran of The Book of Three. While Taran in The Book of Three wanted to become someone else: A hero, a warrior, someone famous and rich; the Taran in this book is looking for who he really is. Where Taran in The Book of Three jumps without thinking and fails at almost everything he tries, Taran here is wise enough to accept instruction, and consequently, ends up succeeding at almost every task he takes up. Without realizing it, Taran has grown up and become the hero he wanted to be. In Taran Wanderer, Alexander has created an almost perfect coming of age story, showing how a child becomes an adult, and how finding oneself is the most important element of that journey.
Previous book in the series: The Castle of Llyr
Subsequent book in the series: The High King
Musical Monday: I Am Glad, 'Cause I'm Finally Returning Back Home by Eduard Khil (with an assist from the crew of the Enterprise)
Ray Bradbury died this week, so the natural thing to do for Musical Monday would be to post Rachel Bloom's Fuck Me, Ray Bradbury as the featured song this week. However, I already posted that song on October 18th, 2010, and I don't like to repeat myself.
Instead, I'll feature a song from another man who passed away this week: Eduard Khil, who is probably more familiar to people now as "Mr. Trolololo", singing I Am Glad, 'Cause I'm Finally Returning Back Home, which most of you will probably recognize better as the "Trolololo Song". Just to add some more science fiction flavor, in the attached video Mr. Khil gets an assist in his performance from Captain Kirk, Mr. Spock, Doctor McCoy, and the rest of the bridge crew of the U.S.S. Enterprise. The song itself is apparently the result of a dispute between the song's composer Arkady Ostrovsky and the Lev Oshanin, lyricist he normally worked with. Purportedly Oshanin claimed that a composer wasn't as important as a lyricist, and to get back at him, Ostrovsky decided that the song would be just fine with no lyrics. The intended lyrics supposedly told the tale of a cowboy returning to his home, and from what little there is available of them, were pretty bad, so the song is probably better without them. And if the song had had lyrics, then it would have been just another forgettable piece of Soviet era pop music.
The performance is gloriously awful, mostly due to the 1970s Soviet sensibilities. With a bad haircut typical of the disco era and a double breasted jacket, Khil wanders out onto a really awful looking set doing some fairly obvious lip-synching. To make the song "cheerful", Khil wears a slightly deranged but oddly beatific expression on his face while going through some stiff choreography. Despite the lack of lyrics, Khil seems to be trying to tell something of a story and infuse some emotion into the performance, which is both unnerving and strangely enjoyable. It is a testament to his talent that despite being hampered by a song with no lyrics and the very worst support that Soviet era television could offer, his performance is actually somewhat enjoyable to listen to. Sadly, Khil died on June 4th (which also happens to be my mother's birthday), but he left us something that will probably endure forever. Or at least until the attention of YouTube is captured by the next thing.
Previous Musical Monday: Skullcrusher Mountain by Jonathan Coulton
Subsequent Musical Monday: I Will Sing a Lullaby by Paul & Storm
Eduard Khil Musical Monday Home
Labels: Meme, Musical Monday, Star Trek: The Original Series, Videos
Book Blogger Hop June 8th - June 14th: Leeloo Was the Fifth Element
This week Jen asks: If you were to write a book, what type of book would you write?
This question is almost a gimme for me: A science fiction novel. Whether it would be hard science fiction or a space opera is open for debate, but it would almost certainly be a science fiction novel.
Go to previous Book Blogger Hop: There Were Four Classical Elements Until Aristotle Came Along
Go to subsequent Book Blogger Hop: The Six Are Superhumans in Flow My Tears, the Policeman Said
Follow Friday - The Offspring of a Donkey and a Horse Has Sixty-Three Chromosomes
This week is a little different. The activity is to FEATURE your own blogger on your blog. See below to see who I am featuring!
And now for the Follow Friday Question: There is an ACTIVITY instead of the usual question. The activity is to FEATURE your own blogger on your blog. Tell us about your buddy, or even your favorite blog and feature them. You can tell them you are doing it, or you can just surprise them. Either one - it is YOUR turn to feature someone.
So, who am I featuring today? Julia Rachel Barrett of Julia Barrett's World.
Why? Because she is one of the nicest people in the blogging world, leaving great comments and pointing people to great blogs all the time. Plus, her own blog is always fun and interesting to read. She is also a pretty damn good writer, with a number of published books under her belt. Most importantly to me, she seems to share my tastes in science fiction and fantasy. Which is, I suppose, a little narcissistic of me to care about, but there you have it. Go read her blog. Follow her on Twitter. What are you waiting for? Go! Now!
Go to previous Follow Friday: Sixty-Two Scared Sigmund Freud
Go to subsequent Follow Friday: My First Computer Was a Commodore 64
Review - The Castle of Llyr by Lloyd Alexander
Short review: Eilonwy must learn to be a lady so everyone goes on a sea voyage to Mona where they run afoul of a giant dwarf and his enormous cat.
Mystic heritage
Aachren kidnaps Eilonwy
Oversized housecat
Full review: This is the third book in the Chronicles of Prydain, and in my opinion, the weakest of the five books. However, the weakest of these five books is still a great book. In the book, Dallben decides that Eilonwy (who has been living at Caer Dallben since the end of The Book of Three) should go to the island of Mona and learn to become a lady. Taran and Gurgi escort her through the journey, and meet Prince Rhun, who captains the ship they take to the island. Once there, Taran finds that both Fflewddur and Gwydion are there too, and Gwydion tells Taran that Eilonwy may be in danger.
Of course, Eilonwy is kidnapped, and the intrepid companions with Prince Rhun and several soldiers set out to find her. Taran, Fflewddur, and Gurgi find an abandoned house, a mysterious blank book, and are trapped by a giant housecat. They escape but are later trapped by a giant dwarf named Glew, and have to escape again. Finally they track Eilonwy to Caer Colur, an abandoned tower by the sea where Aachren has ensorcelled Eilonwy. Secrets are revealed concerning the blank book and Eilonwy's bauble and Aachren's power over Eilonwy is broken.
After the far-reaching adventure of The Book of Three and the intensity of The Black Cauldron, the plot of The Castle of Llyr seems like something of a let down. While the pursuit and recovery of Eilonwy turns out to be a significant affair, the side quests involving the cat Llyan and the dwarf Glew are silly enough to detract from the rest of the story, which gives this tale a light-hearted quality that seems out of place in between The Black Cauldron and Taran Wanderer. On the other hand, if all five books were dark and brooding, then the story would probably be dragged down under its own weight, so the tone of the book is probably necessary.
Previous book in the series: The Black Cauldron
Subsequent book in the series: Taran Wanderer
Posted by Aaron Pound at 9:05 AM 0 comments
Review - The Black Cauldron by Lloyd Alexander
Short review: Arawn has a cauldron that can bring the dead back to life to serve as his soldiers. Taran and his friends have to find a way to take it away from him, even as their own allies betray their cause.
Deathless cauldron born
To destroy the black cauldron
One hero must die
Full review: In the second book of the Chronicles of Prydain, Taran sets out for adventure once more, slightly more prepared than he was in The Book of Three. He is once more accompanied by Gurgi, Fflewddur and Eilonwy, and the whole group is led by Gwydion. Some new characters are introduced: the chief bard Aadon, the cunning King Morgant, the jovial ham-handed King Smoit, and the egotistical prince Ellidyr.
Gwydion has learned that since the Horned King was killed Arawn has been using the magical device known as the Black Cauldron to produce more and more of the deathless cauldron-born warriors. The plot of the novel revolved around the heroes' attempts to recover and destroy the object, preventing Arawn from increasing his army. It turns out that the cauldron has been stolen from Arawn already, but eventually Taran locates it, and bargains with its new owners to obtain it. After various betrayals and deaths, the cauldron is destroyed, but at a significant cost.
For a book aimed at young adults, the book is quite somber. Several notable characters die, characters one thought would be allies turn out not to be, Taran is forced to give up something very valuable, and the Cauldron itself can only be destroyed if someone willingly gets in it while still alive, which will kill them (which draws directly upon the original Welsh legend the cauldron is based upon). Unlike the crappy Disney hack-job movie in which Gurgi came back to life after destroying the cauldron, in the book, the death is irrevocable. While The Book of Three was more of a romp, this book seems to up the ante, showing that defeating Arawn will be neither easy nor painless.
Previous book in the series: The Book of Three
Subsequent book in the series: The Castle of Llyr
Labels: Book Reviews, Fantasy Fiction Reviews, Newbery Honor Book, Young Adult Fiction Reviews
Review - The Book of Three by Lloyd Alexander
Short review: An assistant pig-keeper dreams of becoming a hero. He gets his chance and believes he has failed.
Assistant keeper
For an oracular pig
Not really a hero
Full review: This book kicks off Alexander's Chronicles of Prydain series. The hero is Taran, an assistant pig-keeper who dreams of adventure despite the admonitions of his wiser guardians Dallben and Coll. When Hen Wen, the oracular pig Taran takes care of, escapes, Taran goes off to find her and prevent her being captured by the Horned King, servant of the evil Arawn. On the way, Taran meets the prince Gwydion, the beast Gurgi, gets captured by the evil sorceress Aachren, escapes with the help of the princess Eilonwy and the bard Fflewddur Fflam, finds a magical sword he can't use named Dyrnwyn, wanders into a valley reserved for animals, stumbles into the hidden home of the fair folk, and finally tries (and fails) to use Dyrnwyn and misses the climactic battle of the book.
In short, Taran is about as inept at being a hero as one would expect a farm boy to be. Despite this (or rather, because of this), Taran is an endearing and engaging character and you root for him the whole book. Along the way, Taran (and presumably the reader) learns that being a hero means more than simply being able to swing a sword effectively, and maybe there are qualities that an assistant pig-keeper might display that are, in fact, the hallmarks of a true hero. Although the Chronicles are written for young readers, they are among my favorite books, and are my favorite fantasy series.
Subsequent book in the series: The Black Cauldron
Musical Monday - Skullcrusher Mountain by Jonathan Coulton
There are some love stories that can only be told by certain people. The twisted and beautiful love story in Skullcrusher Mountain could only be told by Jonathan Coulton. An evil super-villainous madman kidnaps the object of his desire and whisks her away to his secret lair and attempts to woo her by making a half-monkey half-pony monster, plying her with wine, and pointing out that the mountain is covered with hungry wolves. The evil genius dreams of taking his love away on a trip under the ocean while his henchmen set the atmosphere on fire. Overall, a fairly standard tale of boy meets girl, boy kidnaps girl, boy makes horrible mutated monster for girl, and boy's army of demented followers ends life on Earth. Pretty boring really. But in Coulton's hands this classic tale of romance really comes to life.
Undead life. Wait, no, that's another song.
Previous Musical Monday: Rhiannon by Fleetwood Mac
Subsequent Musical Monday: I Am Glad, 'Cause I'm Finally Returning Back Home by Eduard Khil
Jonathan Coulton Musical Monday Home
Book Blogger Hop June 1st - June 7th: There Were Four Classical Elements Until Aristotle Came Along
This week Jen asks: BEA Edition – What upcoming releases are you most looking forward to?
I have no idea. Maybe this makes me a lousy book blogger, but I really have no idea what books are schedule to be published in the future. Even when I am a fan of an active ongoing series, such as Naomi Novik's Tremeraire books, I don't actually pay enough attention to know when a new book is coming out. This isn't really unique to books for me though, despite the massive advertising campaigns that movie studios and television networks engage in I usually only have the vaguest idea which movies and programs are due to be released in the near future. Prehaps it is because I have such a huge backlog of books to read and things to watch already. perhaps it is just that I am not very attentive about such things. But the end result is the same: I don't have a clue what releases are upcoming, which pretty much precludes me from looking forward to any particular ones.
Go to previous Book Blogger Hop: The Triluminary Is the Most Sacred Artifact of the Minbari
Go to subsequent Book Blogger Hop: Leeloo Was the Fifth Element
Labels: Book Blogger Hop
Follow Friday - Sixty-Two Scared Sigmund Freud
Follow the two Featured Bloggers of the week - Books of Love and Sinnful Books.
And now for the Follow Friday Question: You are a matchmaker - your goal, hook up two characters from two of your favorite books. Who would it be? How do you think it would go?
I always hate "match-up" questions because I am so very lousy at answering them. For this question I'm going to put together Robert A. Heinlein's Lazarus Long from books like Methuselah's Children and Time Enough for Love and Poul Anderson's character Dominic Flandry from Ensign Flandry and Agent of Terra. This isn't really a romantic pairing, although I expect that in the unlikely event that Flandry suggested some sort of tryst that Long would accept. The real goal is to get two interstellar swashbucklers together and see what kind of mischief they can get up to. I figure that they would mostly get along, although Long would probably chide Flandry for his cynicism and willingness to fight for a government he knows is corrupt, while Flandry would chastise Long for his adherence to unattainable ideals, his hypocritical willingness to participate in efforts to control the politics of multiple universes, and maybe for the occasionally incestuous nature of his promiscuity. Despite their differences, I'm guessing they would become a formidable duo gallivanting about the galaxy and foiling villains and setting things right. Or at least they would find all the bars and drink a lot.
Go to previous Follow Friday: Boudica Rebelled Against Roman Rule in 61 A.D.
Go to subsequent Follow Friday: The Offspring of a Donkey and a Horse Has Sixty-Three Chromosomes
Musical Monday: Magic (MTG): The Rap by Remy Munas...
Book Blogger Hop June 22nd - June 28th: The Sevens...
Review - The Wizard in the Tree by Lloyd Alexander...
Review - The Foundling and Other Tales of Prydain ...
Musical Monday: I Will Sing a Lullaby by Paul & St...
Book Blogger Hop June 15th - June 21st: The Six Ar...
Follow Friday - My First Computer Was a Commodore ...
Musical Monday: I Am Glad, 'Cause I'm Finally Retu...
Book Blogger Hop June 8th - June 14th: Leeloo Was ...
Follow Friday - The Offspring of a Donkey and a Ho...
Musical Monday - Skullcrusher Mountain by Jonathan...
Book Blogger Hop June 1st - June 7th: There Were F...
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Green Family Values: The Power of Youth to Change the World
While stumbling upon the web, I came across the inspiring story of Malawi youth William Kamkwamba on Inhabitat. With all the doom and gloom news of climate change, William Kamkwamba’s ingenuity demonstrates what one person can do to improve their life with green technology. The story also demystifies alternative energy as complex engineering that keeps many Americans from jumping into finding greener methods to power their homes.
Malawi is a democratic, densely populated country in southeastern Africa. The Great Rift Valley runs through the center of the country from north to south. The GDP per capita is $596, and the economy is agricultural, and dependent upon tobacco, sugar, and tea; however, the staple of Malawi’s diet is maize. Many refugees from Mozambique, Rwanda, and Congo have fled to Malawi. One million people in Malawi live with HIV/AIDS. Malawi has been in entertainment news lately, as Madonna has been attempting to permanently adopt a Malawian child. Malawi youth William Kamkwamba’s story deserves media attention, too.
William Kamkwamba has built a windmill to power his home. Having dropped out of school because of a lack of funds, William studied donated books on wind power at his local primary school. Using salvage materials and investing about $16, he built his own windmill through trial and error. The original windmill could power a few light bulbs and a radio, as well as charge a car battery for days when the wind does not blow. According to Inhabitat,
The 12-meter tall windmill (it was originally only 5 meters) is made out of scrap timber. The blades, originally made from PVC, now steel, power a bicycle dynamo, the type that power a bicycle headlamp, which in turn provides electricity to the battery. William uses this energy for his house, as well as to help others recharge their batteries. Just recently, he moved from a car battery to a deep discharge battery, which will help improve with the power storage of his house.
William is now blogging about his experiences. William Kamkwamba’s Malawi Windmill Blog received 113,047 page views in its first month and is now translated to English. On his blog, you can read about his village, how he is spending the money people from the world are donating for his education and improvements for his village and family, his return to school, and the worldwide attention he has received. You can also view pictures of William. To donate to William, visit his blog. A generous donor will match donations of $50 or more.
William offers inspiration of how youth in less-privileged countries can improve their lives with materials on hand, rather than relying on the country’s infrastructure to build coal and oil power plants. William has used his ingenuity to improve his home with green technology. Perhaps he was not thinking of climate change when he set out with his project, but his story demonstrates how individuals can make a difference. I don’t suspect Americans will be erecting homemade windmills in their backyards out of scrap material, yet this story shows what power the youth have to solve our problems.
« When You Are a Hippy Parent….
The Power of Youth to Change Their World »
Kermit says
Wait… so we should all go build windwills from scrap, and this will save the world? We should all live in 3rd world huts, powered by a car battery? You first. You guys truly are idiots.
Jeff McIntire-Strasburg says
If you read all of Jennifer’s post, you’ll see clearly that she’s not suggesting anything like that, nor saying this is the way to save the world.
Perhaps he was not thinking of climate change when he set out with his project, but his story demonstrates how individuals can make a difference. I don’t suspect Americans will be erecting homemade windmills in their backyards out of scrap material, yet this story shows what power the youth have to solve our problems.
Might be a good idea to do that before you start calling names… you’re free to criticize, but please keep it civil.
Jeff McIntire-Strasburg
Green Options
jeff@greenoptions.com
Thanks for writing this article, and bringing attention to William’s site. He is changing the world and has a lot to teach all of us.
http://www.21st-century-citizen.com
Jennifer Lance says
I did live in home powered by a car battery to run one DC light and car stereo for three years. There was no septic, and the bathtub was outside. The house was built by the original homesteaders and was heated by a barrel woodstove. It may have been California and not Malawi, but it was primitive.
I don’t propose William’s windmill saves the world, but it changes his world. I think that when third world countries look for ways to improve their lives and live more like the first world, they do not need to resort to unclean sources of power.
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About Eco Child’s Play
Our ethos is to provide news, information, and opinions on natural, green parenting to help your family live a greener, healthier life! Additionally, we offer personal consulting services to help you achieve your green living goals.
Jennifer is a vegetarian, yoga teacher, gardener, hiker, teacher, and mother that has been living off-the-grid for over 20 years.
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EDGE holds luncheon at Bridgestone Guayule Farm in Eloy
Lab tries to stretch guayule plant into profit
· By TANNER CLINCH Staff Writer -Eloy Enterprise
· Oct 27, 2016
· ELOY — Guayule, an arid desert bush native to Mexico, is being looked at by many companies that use large amounts of rubber to be a good domestic replacement for Hevea trees, commonly known as rubber trees, which are harvested overseas.
There are many small farms scattered across the state that grow guayule. One of the most prominent places for researching the crop is a small farm in Eloy owned by Bridgestone Tires where workers are studying what makes guayule tick.
There is no doubt that the guayule plant can make rubber. In 2015, Bridgestone came out with its first tire that was made wholly of the plants. During World War II America looked into making rubber domestically with the plant after Japan cut off its rubber supply from Malaysia, but the plan was scrapped after the war ended before it picked up steam.
The problem for many companies is how to make farming the plant profitable, which is one of the main problems that researchers at the Bridgestone lab in Eloy are looking at.
The resins from the plant that one uses for rubber are mostly derived from the bark at the stem of the plant, explained Dr. Dave Dierig, a researcher at the facility. This means that what the company needs to satisfy its rubber needs comes from a small part of the plant.
“If you grew cattle specifically just for the tenderloins, you’d never make any money, right?” said Bill Niura, the project lead at the Bridgestone farm, while he explained there conundrum.
So what do you do with the majority of the biomass that comes from farming the plants? There are a couple ideas the people at Bridgestone had, mostly involving turning it into some sort of fuel.
The leftover biomass, which is roughly 80 percent of the plant, is the wood that comes from the stalk and other plant matter, which comes out looking like small wood pellets after it’s done. If you straight up burn it, it will produce 8,000 British thermal units per pound, said Dierig.
This is almost as efficient as burning a pound of coal, which puts out 9,710 BTU’s per pound according to the U.S. Energy Information Administration. Putting this biomass into coal-fired reactors that use high-sulfur coals could also reduce those sulfur emissions, according to Dierig.
Unfortunately, there really isn’t a market in the U.S. for biomass fuel bricks as there is in much of Europe, according to Niaura.
Another avenue they looked into was turning it into fuel for cars by turning it into ethanol. While other biofuels, such as ones made with corn, get a bad wrap for using food crops to burn in vehicles guayule doesn’t have that problem, it’s produced entirely for industrial uses.
The biomass leftover from the rubber-making process can be turned into an alcohol based fuel via fermentation, according to Niaura. Creating a refinery for it on an industrial scale is a whole different demon.
While the people at Bridgestone figure out what to do with all the plants they harvest for rubber, they are continuing to do research on the plant.
The site in Eloy has been operational for a little over three years, studying the different properties of the plants, how different strains grow, which elevation works best and how harvesting times affect plant productivity.
While humans can make many different kinds of rubber synthetically in a laboratory, natural rubber is still the best for many uses. It is stronger in high-force situations than synthetics due to a property called stress-induced crystallization, according to Niaura.
“Nature makes rubber whether it’s on a tree in the jungle or a guayule in Arizona,” Niaura said.
Moving forward in creating a domestic rubber industry is the goal of Bridgestone. It has other competitors, such as Cooper Tires, and other small companies that make other products, such as Yulex, which makes wetsuits out of the guayule.
Arizona will be a center for the production of guayule just because of its natural climate. The weather is the plant’s natural habitat and the PH balance of the soil in places like the Southeast would not be optimal to grow guayule, according to Niaura.
It make take a while for the company to find a the most productive guayule and make it profitable, it takes roughly two years from planting the seed to harvesting the plant.
http://www.pinalcentral.com/eloy_enterprise/news/lab-tries-to-stretch-guayule-plant-into-profit/article_8ad02976-9bd6-11e6-8c1d-a7397b477277.html
Posted in Events Bridgestone, City of Eloy, Economic Development Group
EDGE Holiday Reception
Walls go up at Phoenix Mart!
Written by Belinda Akes
The next membership luncheon is Thursday November 16th at Robson Ranch. The president and CEO
The next membership luncheon is Thursday September 21st at Robson Ranch. Mayor Craig McFarland will
The next membership luncheon will be on Thursday August 17th at Robson Ranch in Eloy.
CASA GRANDE — “It’s about time!” That was how Pinal County Supervisors Chairman Todd House,
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Lit Mags
Reading Into Everything.
The Loneliness of the Long-Distance Bus Ride
0% of article read
“We Are the Ones on the Bus,” short fiction by Matthew Baker
May 28, 2018 - Issue No 14
Matthew Baker
We Are the Ones on the Bus
We have been on the bus for years. The bus is modern, a double-decker coach with a narrow stairway, and can accommodate exactly one hundred passengers, not including the drivers. Each of us has a seat. Above each seat is a switch for a light and a vent for air, heating or cooling depending on the climate. Beneath each seat is an outlet for chargers and a space for a bag, about the size of an average backpack. The cushions on the seats have vibrant patterns, vaguely reminiscent of the carpeting in movie theaters. The bus is neither comfortable nor uncomfortable. The bus is neither spacious nor cramped. The bus is approximately half full. At the front of the bus is a trash receptacle, where crumpled wrappers and peels and rinds can be thrown away after meals have been eaten. At the back of the bus is a bathroom, which has a mirror where makeup can be applied in the morning and removed in the evening. We sleep in the seats, using bunched towels for pillows, sometimes wadded jackets or sweatpants. People in cars occasionally stare at us before passing us on the highway.
None of us were born on the bus. Each of us chose to board, climbing onto the bus at a desolate stop on a foggy turnpike, or a dusty road, or a sunny lane, or a rainy intersection, hurrying down the aisle with a furtive glance at the other passengers. We have been on the bus ever since. Some months ago an elderly passenger with silver stubble and tortoiseshell eyeglasses who was known to have a fondness for salted caramel candies suffered a massive coronary and perished on the stairway, spilling a handful of caramels onto the steps, and was removed from the bus later that night by a pair of paramedics, but other than that none of us have ever died on the bus. Each of us possesses a ticket, with the glorious destination printed in metallic lettering beneath the name of the company. Some of the tickets have fraying edges, worn apart by superstitious rubbing, while other tickets are in mint condition, kept in wallets for protection. In the years that we have been on the bus we have seen all manner of sights out the windows. Skyscrapers gleaming in cities with magnificent boulevards, picturesque towns, quaint villages, craggy snowcapped mountains tinted indigo by the dusk, grassy rolling hills smoldering pink in the dawn, dew glittering on plains, mist drifting across marshes, sunbathers in bikinis lying on sandy beaches, surfers in wetsuits sitting on rocky outcroppings, dark clouds flickering with heat lightning, hail falling onto streets of bobbing umbrellas, snow flurrying through crowds of hooded parkas, uniformed bands marching in spectacular parades, thrill seekers cheering on carnival rides, anglers fishing from docks crusted with barnacles, horseback riders galloping wildly across windswept ranches, gamblers streaming into shimmering casinos, sunlight sparkling across the chrome hulls in sprawling trailer parks, stars twinkling above glassy lakes teeming with rickety cottages, homey farmhouses with children climbing on rusted tractors, weathered bungalows with children swaying in hammocks between the trees, suburban mansions with children bouncing on trampolines in the yards, people standing near grain silos, people walking around water towers, curving skate ramps spattered with vivid graffiti, ancient railroad bridges overgrown with flowering weeds, fireworks, rainbows, and towering billboards. All noise from outside the bus is muffled. The inside of the bus is profoundly quiet. Conversations are held in hushed murmurs. We wear headphones when we want to listen to music. Music never plays over the speakers of the bus. The drivers rarely make announcements, only when the bus is making a pit stop at a gas station or a rest area, and even then only to announce the time that the bus will depart again. With a sense of reverence, even a feeling of anxiety, each of us makes careful note of the time announced.
We hurry off of the bus the second that the doors accordion apart. Each pit stop is exactly one hour. We have that time, and that time only, to shower, to get haircuts, to wash clothing, to buy food and toiletries and medications. Because these are the only occasions on which we are able to interact with the world beyond the windows of the bus, the pit stops are a powerful experience for us, almost transcendental. After years of nearly constant motion, the sense of motionlessness is disorienting, standing there stock-still in a gas station or a rest area, staring at a colorful display of candy bars, or salted nuts, or ice creams, or greasy frankfurters rotating behind glistening glass. The mystical churning of a slushy machine. The cryptic hum of a soda dispenser. Ordinary people chat and laugh with each other in the aisles. As we shop for supplies, we smile at the ordinary people sometimes, longing frantically for some connection. To feel kinship. To feel companionship. Though we try to look friendly, we can feel that the smiles are frightening, radiating pain and desperation.
None of us have to ride the bus. We have no obligation. We could leave the bus whenever we wanted, could join any of those happy communities of stationary people. But if we left the bus, that would mean we would never arrive where the bus is going. The possibility of reaching that destination consumes us. Casting one last glance at the gas station or the rest area, we climb back onto the bus, and we settle into the seats, hearts full of despair and ambition. The engine comes to life with a roar. The bus glides back onto the highway, and we gaze out the windows at the dazzling blur of neon and fluorescence, the headlights and taillights and glowing signs. The bus may never arrive. We know that. But the bus may arrive. We are exhilarated, are utterly enraptured, by the promise of the tickets that we possess. Even managing to find the bus once was a miracle. Some days ago as the bus pulled out of the parking lot of a truck stop at the designated time, a murmur passed through the bus, scattered gasps and exclamations, and all of us turned toward the windows in shock to see a passenger bolting from the doors of the truck stop a minute too late, her hair still damp from a shower, wearing only shorts and a bra and a single flip-flop, running after the bus with her arms outstretched, waving and pleading for the bus to come back, then stumbling over a curb and collapsing onto the pavement, shaking her head and clutching her chest and weeping as she watched the bus vanish into the distance and we watched her become part of the background. That horrible look on her face, realizing she had been left behind, is the thing that we fear most in the world.
Matthew Baker is the author of Hybrid Creatures, a collection of stories written in hybrid languages, and the children’s novel If You Find This, which was a Booklist Top Ten Debut of 2015 and an Edgar Award Nominee for 2016. His fiction has appeared in publications such as American Short Fiction, New England Review, One Story, Electric Literature, and Best of the Net. Born in Michigan, he currently lives in New York City, where he teaches at New York University. Visit him online at: www.mwektaehtabr.com
“We Are the Ones on the Bus” is published here by permission of the author, Matthew Baker. Copyright © Matthew Baker 2018. All rights reserved.
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Articles Projects About EUROPEA members Events
Contact Facebook YouTube Instagram
Jakob and his NEWSLETTERS
History of EUROPEANews
EUROPEA (l’Europe de l’Enseignement Agricole), established at that famous meeting in Ettelbruck (LU) in January 1993, has always relied on the enthusiasm and voluntary work of people who believed in it. One of them was Jakob Kjaer (DK), who created and edited the EUROPEA Newsletters, the first channel of information within our association. Following his retirement, he handed it over to Georges Demeester (BE) but times were changing and paper based information exchange was quickly replaced by online communication.
Henrik Dethlefsen (DK), former Secretary General on Jakob Kjaer:
“As a Dane I am particularly impressed by Jakob’s energy and commitment. Then secretary of The Danish Association of Agricultural Colleges, he was allowed by the board of that association “to spend a couple of weeks on EUROPEA in 1993″.
With this modest starting point, he involved himself in a lot of international activities among which EUROPEA was the most important. In the following years he served as president, vice president ordinary board member, etc. He was fluent in English, German, French and Italian, which removed many, many obstacles facing him.
And from 1993 till his retirement in 2001 he edited the EUROPEA Newsletters, which appeared three of four times a year in French and in English. He played a similar important role in EUROPEA Denmark, being the Secretary from 1993 through 2001.
Eagerly, he worked for the continuous involvement of Danish agricultural schools in EUROPEA, and I tend to think, that he was particularly proud, when hosting one of the first EUROPEA seminars under the so-called PETRA project. PETRA was financed by the EEC, involved Italy, France, Belgium and Denmark, and aimed at developing teacher training and teaching modules focusing on environmental issues related to agriculture. The first meeting in Denmark was located in Tune 11-16 May 1993, that was immediately before the EUROPEA Tune meeting (Newsletter no.1). “
SALUTE THE FOUNDERS AND LONG LIVE EUROPEA!
Acknowledgements: many thanks to Henrik (DK) 🙂
Learn more about the foundation and the history of EUROPEA – HERE.
Judit Čović
EUROPEA Hungary, leader of the EUROPEA Editorial Group
Henrik Dethlefsen
EUROPEA Denmark
Great memories !! Thank you so much, Madelon for all the help you provided for the EUROPEA Editorial group !!
Yes I do remember this meeting as I was there too. We drank ‘gammeldansk’ and did some singing ... all in the morning around ten.
Europea editors
TeamEngine Admin login
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Implementing gender equality with checklists
Sector gender checklists have been prepared to give concrete recommendations to properly address gender issues in the design of projects across different sectors. They provide a “how to” integrate gender equality and women’s empowerment objectives in a range of sectors, from energy to transport, going by urban development, health and many others.
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The film will follow the women on their journey to form a recycling partnership between neighbourhoods with a history of extreme tension and violence.
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Discover a great variety of news related to Gender and Development on the dedicated section of the Asian Development Bank.
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The model trains teachers to be more gender aware and equips them with the skills to understand and address the specific learning needs of both sexes. It develops teaching practices that engender equal treatment and participation of girls and boys in the classroom and in the wider school community.
Creating a Diversity Hub in an online media for more inclusive news
Gender is now a business critical issue. The online media Campaign is proud to launch, in conjunction with Women Leading Change and Campaign360, their very own Diversity Hub. The teams aim to provide the readers with the latest viewpoints and news from the gender frontlines as the industry builds a sustainable future of equal and fair workplaces.
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Barcelona city hall has built a dynamic map of all the local initiatives encouraging the construction of a more inclusive city: explore on the map a fantastic volume of concrete actions undertaken to fight for the rights of various communities
Minorities / Marginalized groups Gender Citizenship Migration
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Mansfield Park/Chapter XXVI
< Mansfield Park
←Chapter XXV
Mansfield Park by Jane Austen
Chapter XXVI
Chapter XXVII→
8964Mansfield Park — Chapter XXVIJane Austen
CHAPTER VIII.
William's desire of seeing Fanny dance, made more than a momentary impression on his uncle. The hope of an opportunity, which Sir Thomas had then given, was not given to be thought of no more. He remained steadily inclined to gratify so amiable a feeling—to gratify anybody else who might wish to see Fanny dance, and to give pleasure to the young people in general; and having thought the matter over and taken his resolution in quiet independence, the result of it appeared the next morning at breakfast, when after recalling and commending what his nephew had said, he added, "I do not like, William, that you should leave Northamptonshire without this indulgence. It would give me pleasure to see you both dance. You spoke of the balls at Northampton. Your cousins have occasionally attended them; but they would not altogether suit us now. The fatigue would be too much for your aunt. I believe, we must not think of a Northampton ball. A dance at home would be more eligible, and if"—
"Ah! my dear Sir Thomas," interrupted Mrs. Norris, "I knew what was coming. I knew what you were going to say. If dear Julia were at home, or dearest Mrs. Rushworth, at Sotherton, to afford a reason, an occasion for such a thing, yu would be tempted to give the young people a dance at Mansfield. I know you would. If they were at home to grace the ball, a ball you would have this very Christmas. Thank your uncle, William, thank your uncle."
"My daughters," replied Sir Thomas, gravely interposing, "have their pleasures at Brighton, and I hope are very happy; but the dance which I think of giving at Mansfield, will be for their cousins. Could we be all assembled, our satisfaction would undoubtedly be more complete, but the absence of some is not to debar the others of amusement."
Mrs. Norris had not another word to say. She saw decision in his looks, and her surprise and vexation required some minutes silence to be settled into composure. A ball at such a time! His daughters absent and herself not consulted! There was comfort, however, soon at hand. She must be the doer of every thing; Lady Bertram would of course be spared all thought and exertion, and it would all fall upon her. She should have to do the honours of the evening, and this reflection quickly restored so much of her good humour as enabled her to join in with the others, before their happiness and thanks were all expressed.
Edmund, William, and Fanny, did, in their different ways, look and speak as much grateful pleasure in the promised ball, as Sir Thomas could desire. Edmund's feelings were for the other two. His father had never conferred a favour or shewn a kindness more to his satisfaction.
Lady Bertram was perfectly quiescent and contented, and had no objections to make. Sir Thomas engaged for its giving her very little trouble, and she assured him, "that she was not at all afraid of the trouble, indeed she could not imagine there would be any."
Mrs. Norris was ready with her suggestions as to the rooms he would think fittest to be used, but found it all prearranged; and when she would have conjectured and hinted about the day, it appeared that the day was settled too. Sir Thomas had been amusing himself with shaping a very complete outline of the business; and as soon as she would listen quietly, could read his list of the families to be invited, from whom he calculated, with all necessary allowance for the shortness of the notice, to collect young people enough to form twelve or fourteen couple; and could detail the considerations which had induced him to fix on the 22d, as the most eligible day. William was required to be at Portsmouth on the 24th; the 22d would therefore be the last day of his visit; but where the days were so few it would be unwise to fix on any earlier. Mrs. Norris was obliged to be satisfied with thinking just the same, and with having been on the point of proposing the 22d herself, as by far the best day for the purpose.
The ball was now a settled thing, and before the evening, a proclaimed thing to all whom it concerned. Invitations were sent with dispatch and many a young lady went to bed that night with her head full of happy cares, as well as Fanny.—To her, the cares were sometimes almost beyond the happiness; for young and inexperienced, with small means of choice and no confidence in her own taste—the "how she should be dressed" was a point of painful solicitude; and the almost solitary ornament in her possession, a very pretty amber cross which William had brought her from Sicily, was the greatest distress of all, for she had nothing but a bit of ribbon to fasten it to; and though she had worn it in that manner once, would it be allowable at such a time in the midst of all the rich ornaments which she supposed all the other young ladies would appear in? And yet not to wear it! William had wanted to buy her a gold chain too, but the purchase had been beyond his means, and therefore not to wear the cross might be mortifying him. These were anxious considerations; enough to sober her spirits even under the prospect of a ball given principally for her gratification.
The preparations meanwhile went on, and Lady Bertram continued to sit on her sofa without any convenience from them. She had some extra visits from the housekeeper, and her maid was rather hurried in making up a new dress for her; Sir Thomas gave orders and Mrs. Norris ran about, but all this gave her no trouble, and as she had foreseen, "there was in fact no trouble in the business."
Edmund was at this time particularly full of cares; his mind being deeply occupied in the consideration of two important events now at hand, which were to fix his fate in life—ordination and matrimony—events of such a serious character as to make the ball which would be very quickly followed by one of them, appear of less moment in his eyes than in those of any other person in the house. On the 23d he was going to a friend near Peterborough, in the same situation as himself, and they were to receive ordination in the course of the Christmas week. Half his destiny would then be determined—but the other half might not be so very smoothly wooed. His duties would be established, but the wife who was to share, and animate, and reward those duties might yet be unattainable. He knew his own mind, but he was not always perfectly assured of knowing Miss Crawford's. There were points on which they did not quite agree, there were moments in which she did not seem propitious, and though trusting altogether to her affection, so far as to be resolved (almost resolved) on bringing it to a decision within a very short time, as soon as the variety of business before him was arranged, and he knew what he had to offer her—he had many anxious feelings, many doubting hours as to the result. His conviction of her regard for him was sometimes very strong; he could look back on a long course of encouragement, and she was as perfect in disinterested attachment as in every thing else. But at other times doubt and alarm intermingled with his hopes, and when he thought of her acknowledged disinclination for privacy and retirement, her decided preference of a London life—what could he expect but a determined rejection? unless it were an acceptance even more to be deprecated, demanding such sacrifices of situation and employment on his side as conscience must forbid.
The issue of all depended on one question. Did she love him well enough to forego what had used to be essential points—did she love him well enough to make them no longer essential? And this question, which he was continually repeating to himself, though oftenest answered with a "Yes," had sometimes its "No."
Miss Crawford was soon to leave Mansfield, and on this circumstance the "no" and the "yes" had been very recently in alternation. He had seen her eyes sparkle as she spoke of the dear friend's letter, which claimed a long visit from her in London, and of the kindness of Henry, in engaging to remain where he was till January, that he might convey her thither; he had heard her speak of the pleasure of such a journey with an animation which had "no" in every tone. But this had occurred on the first day of its being settled, within the first hour of the burst of such enjoyment, when nothing but the friends she was to visit, was before her. He had since heard her express herself differently—with other feelings—more chequered feelings; he had heard her tell Mrs. Grant that she would leave her with regret, that she began to believe neither the friends nor the pleasures she was going to were worth those she left behind, and that though she felt she must go, and knew she should enjoy herself when once away, she was already looking forward to being at Mansfield again. Was there not a "yes" in all this? With such matters to ponder over, and arrange, and re-arrange, Edmund could not on his own account think very much of the evening, which the rest of the family were looking forward to with a more equal degree of strong interest. Independent of his two cousins enjoyment in it, the evening was to him of no higher value than any other appointed meeting of the two families might be. In every meeting there was a hope of receiving farther confirmation of Miss Crawford's attachment, but the whirl of a ball-room perhaps was not particularly favourable to the excitement or expression of serious feelings. To engage her early for the two first dances, was all the command of individual happiness which he felt in his power, and the only preparation for the ball which he could enter into, in spite of all that was passing around him on the subject, from morning till night.
Thursday was the day of the ball; and on Wednesday morning, Fanny, still unable to satisfy herself, as to what she ought to wear, determined to seek the counsel of the more enlightened, and apply to Mrs. Grant and her sister, whose acknowledged taste would certainly bear her blameless; and as Edmund and William were gone to Northampton, and she had reason to think Mr. Crawford likewise out, she walked down to the Parsonage without much fear of wanting an opportunity for private discussion; and the privacy of such a discussion was a most important part of it to Fanny, being more than half ashamed of her own solicitude.
She met Miss Crawford within a few yards of the Parsonage, just setting out to call on her, and as it seemed to her, that her friend, though obliged to insist on turning back, was unwilling to lose her walk, she explained her business at once and observed that if she would be so kind as to give her opinion, it might be all talked over as well without doors as within. Miss Crawford appeared gratified by the application, and after a moment's thought, urged Fanny's returning with her in a much more cordial manner than before, and proposed their going up into her room, where they might have a comfortable coze, without disturbing Dr. and Mrs. Grant, who were together in the drawing-room. It was just the plan to suit Fanny; and with a great deal of gratitude on her side for such ready and kind attention, they proceeded in doors and upstairs, and were soon deep in the interesting subject. Miss Crawford, pleased with the appeal, gave her all her best judgment and taste, made every thing easy by her suggestions, and tried to make every thing agreeable by her encouragement. The dress being settled in all its grander parts,—"But what shall you have by way of necklace?" said Miss Crawford. "Shall not you wear your brother's cross?" And as she spoke she was undoing a small parcel, which Fanny had observed in her hand when they met. Fanny acknowledged her wishes and doubts on this point; she did not know how either to wear the cross, or to refrain from wearing it. She was answered by having a small trinket-box placed before her, and being requested to chuse from among several gold chains and necklaces. Such had been the parcel with which Miss Crawford was provided, and such the object of her intended visit; and in the kindest manner she now urged Fanny's taking one for the cross and to keep for her sake, saying every thing she could think of to obviate the scruples which were making Fanny start back at first with a look of horror at the proposal.
"You see what a collection I have," said she, "more by half than I ever use or think of. I do not offer them as new. I offer nothing but an old necklace. You must forgive the liberty and oblige me."
Fanny still resisted and from her heart. The gift was too valuable. But, Miss Crawford persevered, and argued the case with so much affectionate earnestness through all the heads of William and the cross, and the ball, and herself as to be finally successful. Fanny found herself obliged to yield that she might not he accused of pride or indifference, or some other littleness; and having with modest reluctance given her consent, proceeded to make the selection. She looked and looked, longing to know which might be least valuable; and was determined in her choice at last, by fancying there was one necklace more frequently placed before her eyes than the rest. It was of gold prettily worked, and though Fanny would have preferred a longer and a plainer chain as more adapted for her purpose, she hoped in fixing on this, to be chusing what Miss Crawford least wished to keep. Miss Crawford smiled her perfect approbation; and hastened to complete the gift by putting the necklace round her and making her see how well it looked.
Fanny had not a word to say against its becomingness, and excepting what remained of her scruples, was exceedingly pleased with an acquisition so very apropos. She would rather perhaps have been obliged to some other person. But this was an unworthy feeling. Miss Crawford had anticipated her wants with a kindness which proved her a real friend. "When I wear this necklace I shall always think of you," said she, "and feel how very kind you were."
"You must think of somebody else too when you wear that necklace," replied Miss Crawford. "You must think of Henry, for it was his choice in the first place. He gave it to me, and with the necklace I make over to you all the duty of remembering the original giver. It is to be a family remembrancer. The sister is not to be in your mind without bringing the brother too."
Fanny, in great astonishment and confusion, would have returned the present instantly. To take what had been the gift of another person—of a brother too—impossible!—it must not be!—and with an eagerness and embarrassment quite diverting to her companion, she laid down the necklace again on its cotton, and seemed resolved either to take another or none at all. Miss Crawford thought she had never seen a prettier consciousness. "My dear child, "said she laughing, "what are you afraid of? Do you think Henry will claim the necklace as mine, and fancy you did not come honestly by it?—or are you imagining he would be too much flattered by seeing round your lovely throat an ornament which his money purchased three years ago, before he knew there was such a throat in the world?—or perhaps—looking archly—you suspect a confederacy between us, and that what I am now doing is with his knowledge and at his desire?"
With the deepest blushes Fanny protested against such a thought.
"Well then," replied Miss Crawford more seriously but without at all believing her, "to convince me that you suspect no trick, and are as unsuspicious of compliment as I have always found you, take the necklace, and say no more about it. Its being a gift of my brother's, need not make the smallest difference in your accepting it, as I assure you it makes none in my willingness to part with it. He is always giving me something or other. I have such innumerable presents from him that it is quite impossible for me to value, or for him to remember half. And as for this necklace, I do not suppose I have worn it six times; it is very pretty—but I never think of it; and though you would be most heartily welcome to any other in my trinket-box, you have happened to fix on the very one which, if I have a choice, I would rather part with and see in your possession than any other. Say no more against it I entreat you. Such a trifle is not worth half so many words."
Fanny dared not make any farther opposition; and with renewed but less happy thanks accepted the necklace again, for there was an expression in Miss Crawford's eyes which she could not be satisfied with.
It was impossible for her to be insensible of Mr. Crawford's change of manners. She had long seen it. He evidently tried to please her—he was gallant—he was attentive—he was something like what he had been to her cousins: he wanted, she supposed, to cheat her of her tranquillity as he had cheated them; and whether he might not have some concern in this necklace!—She could not be convinced that he had not, for Miss Crawford, complaisant as a sister, was careless as a woman and a friend.
Reflecting and doubting, and feeling that the possession of what she had so much wished for, did not bring much satisfaction, she now walked home again—with a change rather than a diminution of cares since her treading that path before.
Retrieved from "https://en.wikisource.org/w/index.php?title=Mansfield_Park/Chapter_XXVI&oldid=4556344"
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KOVALENKO AND GERASKIN SCORE TWO EACH AT KHL ALL-STAR GAME
KHL All-Star Game took place in Astana, Kazakhstan. The game featured selected top players of the Junior Hockey League Challenge Cup Igor Geraskin (Team Kharlamov Division), Nikolai Kovalenko (Team Tarasov Division), German Voloshin (Team Bobrov Division) and Yegor Korobkin (Team Chernyshev Division).
Just like last year, the four division teams faced each other in the semifinal round. Losers went on to battle for the bronze, while winners met each other in the final game to compete for the right to be called the top KHL division.
Skill Competition took place the day before and it was won by Team Kharlamov Division. Although, in the semifinal round Andrei Nazarov’s men lost to Team Tarasov Division in the shootout. Regulation solved nothing and Dmitry Kagarlitsky won it for the team in white jerseys as he scored the decisive shootout attempt.
In the other semifinal game it all went to the shootout as well, since the teams were tied at 5-5 after regulation. Team Chernyshev Division’s 3rd goal of thegame was scored by Stalnye Lisy Magnitogorsk captain Yegor Korobkin. Khabarovsk’s German Voloshin, who competed for Team Bobrov Division, had picked up an assist on Marc-Andre Gragnani’s marker earlier in the game. Team Chernyshev Division won the shootout as Vladimir Tkachyov scored the winner.
Bronze medal game featured the most goals and one of the heroes was Cherepovets native Igor Geraskin. First star of the JHL Challenge Cup game scored two goals, which was as many as Sergei Mozyakin got, and added an assist to that on another JHL alumnus Pavel Varfolomeyev’s marker. Team Kharlamov Division enjoyed an 8-4 win and got bronze medals at KHL All-Star Game.
Team Tarasov Division won KHL All-Star championship title. Loko Yaroslavl forward Nikolai Kovalenko was on the team. Yaroslavl junior hockey school alumnus scored his team’s 2nd and 3rd goals of the game. On the second marker he was assisted by one of Lokomotiv professional team’s leaders Brandon Kozun. Yegor Korobkin picked up a helper on Yegor Martynov’s goal for Team Chernyshev Division, which finished second at the All-Star tournament.
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« Trayvon Martin
Grada Kilomba on racism in Europe »
The Broken Africa stereotype
Tue Mar 13th 2012 by abagond
Somewhere in Africa in a place called Kenya
The Broken Africa stereotype is one of the main ways Americans picture Africa: a violent hellhole, savage and cruel, a place of war, genocide, famine, slums, disease, failed states, refugee camps, etc. Aids, malaria and Ebola. Idi Amin, Mugabe and now Kony. Rwanda and Darfur. Somali pirates. Corrupt government officials. Child soldiers. Black men raping virgins to spread Aids. The heroes of this piece? White saviours, like Bono and Miss Jolie.
White people to the rescue!
Africa was, is and always shall be backward. Anything good in Africa comes from outside. Africans can never do anything right – and never will. James Watson, co-discoverer of DNA who should know a thing or two about genes, said he was:
I used to think this picture was a side effect of the Western press, which makes a living off of bad news, and Western NGOs, which make a living off of helping the helpless – making Africa the Country into a land of bad news and helpless people. Not so: the stereotype goes way back, to the 1700s, to the days of the slave trade.
War, famine, disease and evil men are found throughout the world and throughout history, not just in Africa. So why does the image of a Broken Africa stick?
The Rule of How Mud Sticks:
When blacks do something bad or whites do something good, it is largely due to inborn qualities – like “black” crime and “white” inventions.
When blacks do something good or whites do something bad, it is an exception or largely due to circumstances – like black inventions and white crime.
This creates an imbalanced, racist picture of Africa:
Mugabe? Proof that blacks are unfit for rule. Hitler? A madman.
The Rwandan genocide kills 800,00 Tutsis? Proof of how violent Africans are. The German genocide kills 6 million Jews? That was an exception. The Germans killed 100,00 Hereros in Namibia? Another exception.
Middle-class Nairobi or Luanda? Exceptions. The slums of Nairobi and Luanda? Proof of how screwed up Africa is.
African civilizations? They tell us nothing. Primitive tribes in out-of-the-way places? The True Africa.
Like most stereotypes it is two parts self-serving lie and one part projection:
Projection: It was the West that broke Africa. It was the West that was savage. It was the West that could not run things properly. Before whites showed up Timbuktu had more people than London and its schools were better known at the time than Oxford and Cambridge. After whites appeared over 17 million died in the slave trade and the slave wars.
Self-serving lie: The stereotype did not arise till the 1700s to excuse the slave trade – and later grew in strength during the white rule of colonialism. That Africa is poorer than Europe and North America has nothing to do with whites robbing it of human labour and mineral wealth. No, Africa is broken by nature.
Picture credits:
The first picture was taken by photojournalist Kate Holt, who works for the British media and NGOs. If you click on the picture it leads to her blog where you can find out more about the picture and about her.
The first two pictures are from Dadaab, a vast refugee camp in Kenya where hundreds of thousands have fled famine and war in Somalia.
The third picture is from a coffee house in an upmarket Nairobi mall – also in Kenya. It is by Noor Khamis for Reuters and appeared in the South African press.
stereotypes about Africa
The Panama Papers – a more objective look at corruption than what the Western press presents.
White paternalism
White saviours and darkies
Chinua Achebe: Africa’s Tarnished Name
Why do whites hate, demonize, fear and look down on blacks?
A bit of realism for those interested in Africa
The Business of Saving Africa
An Open Letter to King Leopold II
“The average African IQ is 70″
Diop: The African Origin of Civilization: Myth Or Reality
Fanon: The So-Called Dependency Complex of the Colonized
on Fri Mar 16th 2012 at 12:39:29 Matari
Truthfully stated, Abagond.
Now let the trolling begin!
on Fri Mar 16th 2012 at 12:54:42 anglesanddimensions
Portraying the affluent class of Africa side-by-side doesn’t negate the fact that the sorry picture of Africa exists. It only serves to show the extreme inequality that exists in the region.
The poverty in Africa is shown with a purpose, and not a humanitarian one. It is used to show that Africans are inherently screwed up, they can’t govern themselves and hence they need American and European [conditional] aid, foreign soldiers on their ground, foreign control on their resources. To back this theory up they show the ‘benevolent whitey’ side by side.
In my country, India, I’ve seen many holding up the 58 dollar billionaires of India when they want to portray their country as a ‘good’ place. Nationalism obscures one to reality and makes them resort to absurdity when someone points out something that’s wrong in their country. Obviously, 58 dollar billionaires are a shame in a country whose 80% live under Rs.20 ($1=about Rs 50) per day.
But there’s one thing that must be mentioned about those who point out that something is wrong in a country – usually they are the ones trying to establish their superiority over another. You will see how the tone changes when you bring up IMF, World Bank, their conditional loans and aids, wars, sanctions etc imposed by the UN, US & Co because those point towards all the evils that their countries are doing, and they know they’re beneficiaries of it.
I have only one thing to say to those in the first world who point towards the poverty in third world countries – protest against your govt policies, stand up against the wars that your countries wage against others(Libya used to be one with a good HDI before Obama & Co. bombed it to the ground, and yes, sponsored the killing of blacks in Libya by the rebels). If you don’t, then stop whining and shove your charity up your backside. Don’t use poor people as an excuse to feel good without doing anything good.
on Fri Mar 16th 2012 at 13:20:15 leigh204
You know what I find repugnant? You see the media showing the likes of Bono and Angelina Jolie shaking hands with some of the populace, “Oh, look. We are trying to make a difference in Africa.” They don’t deserve recognition. Other people have been doing it for years. Did they smile for the camera and get a pat on the back for helping those in need?
on Fri Mar 16th 2012 at 13:22:47 Oyan (@Oy_aN)
I understand that this blog points out what was/is wrong with the evil behavior of Europe/whites and how they mangled and continue to mangle Africa/black, but, what is ‘wrong’ with Africa that this was possible. I was listening to a Youtube vid, and this professor , Dr Amos Wilson, spoke on how Europe attempted this horror on China, was initially successful, but the Chinese were able to repel them. ‘Other’ groups keep coming for us, why is that? There is this parable, “when you act like sheep, people will act like wolves”.
on Fri Mar 16th 2012 at 14:25:42 JC
What are your thoughts on the Arab slave trade? Slavery was not just a phenomenon of the West and Europe.
https://abagond.wordpress.com/2009/10/03/the-arab-trader-argument/
Very interesting article on the “Arab Trader Argument.” It would be futile trying to compare or judge which was worse. My feeling is that the European slave trade is still highly remembered due to the ever-lasting presence of NGOs in Africa, particularly when they are fueled by projections and self-serving lies.
On the other hand there aren’t any current issues that allow bringing up the Arab slave trade.
on Fri Mar 16th 2012 at 15:36:36 lokey
@angelsanddimension
Hello from your fellow countryman :). I dont know if you are in the US or in India, but I guess you got the picture, the Imperial narrative of the colonized has always been designed to shame the colonized into thinking the other (colonizer) is great while making the colonizer feel superior to the colonized.
Gandhi called this phenomena: Drain inspection. The chief artist of this deception against India was an American white woman (who was also a racist, anti-immigrant conservative who would fit right in with the loonatic racists of the tea party of today).
You can read more here: http://www.lehigh.edu/~amsp/2006/02/teaching-journal-katherine-mayos.html
She was hijacked by the British propaganda machine and because she was white and American, most people in the US and UK (and more shamefully our own Indians) brought this racist/biased narrative.
Now you can see that this culture continues by way of rented-negroes (in these case rented-Indians) see here: http://www.bbc.co.uk/news/world-asia-india-17377895
@abagond:
I just looked at the comments, it is hilarious that the Arab trader argument popped up like clockwork. These guys are like automatons!
@ JC
My feeling is that the European slave trade is still highly remembered due to the ever-lasting presence of black people in the Americas.
As if on cue:
http://www.cbsnews.com/8301-31749_162-57398804-10391698/george-clooney-arrested-during-protest-at-sudanese-embassy/
It is becoming so predictable and hollow.
It’s funny, because the time I spent in both Edo State and Lekki Nigeria was simply fantastic. There are many spots that are incredibly modern and over looked, while there were many spots that were poor and over exposed. The people though, were more aware of their situation then the (whites) West give them credit for.
on Fri Mar 16th 2012 at 17:27:45 truthbetold
I will respond later when I have more strength.
My heart is weary from the last post on the killings of our people.
@lokey
Hi!(Punjab? Am from Kolkata) Among the many issues with Gandhi’s observations is that he failed to grasp the cause-and-effect relations and thus reached a wrong conclusion. While I do agree that colonizers and neo-colonizers everywhere try to paint the colonized people as horrid, irrational people unable to govern themselves and I do caution myself and others against accepting accounts by colonizers without solid evidence as they’re most likely liars, I do not agree with the approach taken by Abagond here, or nationalists at home to counter such ‘drain inspections’.
Drains need to be inspected. Not by degenerates like Katherine Mayo who use the drains in order to turn the whole country into a stinky swamp, but by people who would clean the drains up. Katherine Mayo and her likes in the US want to rob people of their sovereignty and exploit them all the while justifying the exploitation with the theory that we’re not fit to govern ourselves.
Yes, India is an extremely poor country. The denial of this fact is denying the truth and supporting the ‘feel good’ feeling propagated by the media in order to keep the countrypeople from a revolution. It is like someone from the slavery era saying that there are slaves who have better masters who don’t beat them up and feed them well and even let them read books. At home CNN does not mention poverty once on TV, in abroad the same CNN is gushing about poverty in third world countries. It’s against the ruling class interest to let the relatively better-off people here who can access TV know how hard the overwhelming majority of the country suffer. In abroad, the ruling class use the ‘drains’ to garner support for all the atrocities they commit in the name of help.
So yes, India is a poor country and I’m an Indian by accident of birth and internationalist by principle living in India. That does not make me or anyone in India superior or inferior to anyone and does not make us deserving of subordination or inherently screwed up. Want proof of how India or Africa came to be so poor? Look at the global powers, the corporations, the international organizations like the UN, IMF, World Bank. Learn some history and you’ll find that we’re not inherently screwed up. Rather, the ones who are trying to portray us as such are. As one commenter commented on this blog yesterday, “there’s no shame being a slave. Only a slaveholder.”
P.S. Gandhi was, without a shred of doubt, a servant of the colonizers. Gandhi opposed the struggle of the Zulus and defended the massacre of the Zulus by the British in South Africa, was racist to the core which is evidenced by his many remarks on the inferiority of the black race, opposed freedom struggles by labourers and peasants in India, openly said that he supported landlordship and opposed any kind of attempts to take away the wealth they held, worked as a recruit agent for the British army and declared that the British rule was a godsend for India. His ‘non-violence’ was only for the Indians struggling for their freedom because he knew if the struggle turned violent, the British would have to flee and the power would be seized by the people instead of the Congress party (created by the British) which existed to serve the interest of the Indian bourgeoisie. Obviously, given the nature of Gandhiism, it would naturally be the philosophy that the ruling class would want the oppressed class to believe in. Oppress without any fear of a backlash – the dream of the oppressor!
on Fri Mar 16th 2012 at 19:12:58 DarqBeauty
This post instantly made me think of this video. -_-
on Fri Mar 16th 2012 at 19:47:03 dave
I’ll concede the point about Mrs. Jolie / Pitt, however, when It comes to Bono I am going to disagree.
He doesn’t just use his celebrity and own money to help others in need in Africa…He does it throughout the world. Not only In America, but his own country of Ireland.
I saw him when I worked at the pentagon after 9/11 (I was there on the smoke cleanup crew.) He was also with Chris Tucker, by the way they looked to be having a ball together laughing and clowning each other. I didn’t get to meet Bono, but later on Tucker was walking around near the Hall of Heroes, which I happened to be cleaning and I met him. He was very nice and he wanted to see the devastation and he told me he offered officials there anything he could do for help to raise awareness by the use of his celebrity. Now why isn’t Chris Tucker and other blacks being yelled at. Why do you guys hate Bono so much. I think he is a nice man.
What about Sean Penn and the work he does in Haiti. Penn also partnered with Spike Lee on that movie he did to benefit with Hurricane Katrina victims.
on Fri Mar 16th 2012 at 19:55:14 brothawolf
I just had to deal with a fool on Colorlines.com who gave me his Western view of Africa as a helpless, corrupt place incapable of of self-governance and self-reliance. He objected to how the Kony 2012 issue is a “white savior” infomercial and the possibility that America’s main interests when it comes to any African nation is to make money from its resources.
It’s amazing what some people will believe without using their heads.
on Fri Mar 16th 2012 at 20:45:46 Tyrone
Africa was turned into a monopoly board by europeans, this fact is omitted from so-called journalism here in the US and abroad. Leaving out this info presents a false narrative to consumers of media, because all consumers of media don’t have the same level of understanding about the issue. If folk haven’t studied the history of what took place via the transatlantic slave trade, they would view africa as continually dysfunctional. It’s not what we see and hear in media, it’s what we don’t see and hear in media that keeps us in the fog. Whites portray native africans as out of control, knowing damn’ well that their race is the source of the problem. This allows them to play the role of “Savior” that we have all come to despise. Brad Pitt, Angelina, Bono, and other bleeding hearts will never be honest about who created the chaos that we see in some african countries, Never!
on Fri Mar 16th 2012 at 21:54:24 Notable Links: 3-16/12 « BROTHA WOLF
[…] “The Broken Africa Stereotype” by Abagond […]
on Fri Mar 16th 2012 at 22:07:30 BROTHA WOLF
on Fri Mar 16th 2012 at 22:15:47 Mel
@Oyan,
Other’ groups keep coming for us, why is that? There is this parable, “when you act like sheep, people will act like wolves”.
I do sometimes feel blacks “welcome” the victim-hood portrayals. I often find it aggravating the way blacks welcome cameras to film them. Those videos of Africans dancing and singing for white audiences annoy me. So do those “news” pieces with black women crying about how “single” /unmarried they are. Why allow mainstream media to victimize you?
What many black people don’t get or understand is that many non-blacks, particularly whites, believe, as a natural rule, that blacks are genetically or intellectually inferior to whites and other groups.
From this “blacks are naturally inferior” belief, they build all their opinions, laws, attitudes, etc about blacks.
I volunteered at a local high school in 2010, and was allowed to sit in on the staff meeting, where the officials discussed “dumbing down of the curriculum.” The school is mostly black and South Asian, and when I asked why they were dumbing down the curriculum (which made it difficult for the kids attending the school to get into universities), the answer was that the kids can’t handle the tougher curriculum, so the solution, naturally, is to dumb it down.
Now, if I were a parent with a kid at that school, I’d be offended that they’re doing this, because I understand why they chose this as a solution…they believe the black and South Asian kids are too dumb.
So Mel, just to be clear, are you’re saying here that you were okay with the dumbing down process (not offended) because you’re not a parent with a child attending that school?
Were any African or South Asian staff members attending that meeting?
on Sat Mar 17th 2012 at 00:37:40 destructure
I used to care about what happened to poorer countries. But this post has really straightened me out. From now on I promise not to give a $#!t.
on Sat Mar 17th 2012 at 01:05:49 Franklin
@ Destructure
If your belief is that flimsy and is swayed that easily then it probably wasn’t genuine in the first place. But that’s me posting as if I has no idea that you were just some dishonest white who’s trying to paint himself as an open-minded person who is now deeply offended because of some cruel boogeymen that he was fighting for.
Abagond, I am glad that you posted this post. Good post.
on Sat Mar 17th 2012 at 02:03:27 Bliff
@mel
the answer was that the kids can’t handle the tougher curriculum, so the solution, naturally, is to dumb it down..
Finally, a sensible school district. Usually, the teachers, administration, community, or white people are blamed, usually in a game of musical chairs which of this takes it’s turn in being blamed. Finally, they have awoke – maybe its the kids.
@anglesanddimensions
58 dollar billionaires are a shame in a country whose 80% live under Rs.20.
You know nothing of the generation of wealth in an economy. The presence of biliionaires, indicates a growing economy. From India’s lower economic base, much money is made by entrepreneurs who create business and start to produce goods for the people. The entrepreneurs can make a lot of money in these intial stages.
those who point out that something is wrong in a country – usually they are the ones trying to establish their superiority …..Don’t use poor people as an excuse to feel good without doing anything good. Not always. There are many honest charitable organizations, nost of them white. Your racist attitude toward them may explain your poor opinion of them. Would you rather we not send the money? Because if that is your attitude, maybe we should not.
Bono and Angelina Jolie shaking hands with some of the populace,… They don’t deserve recognition. The use of celebrities to bring awareness, action, and money has been used very successfully for a wide range of causes. People would normally not listen to simple pleas for help unless there is something that catches their attention – celebrities, pictures of children, or highly polished videos.
So perhaps you should put aside your disdain for white people and think about how the disadvantaged are helped by the celebrities’ efforts. It’s irrelevant whether Jolie and Bono are getting more than their share of publicity.
It’s disgusting to me how many commenters disdain white people so much that they would criticize their efforts to help.
on Sat Mar 17th 2012 at 02:49:09 brothawolf
@Bliff,
But it’s okay to have a disdain for blacks, including Africans, because you, as a so-called race realist, believe they are not as intelligent or sufficient as whites?
I’m just asking.
on Sat Mar 17th 2012 at 02:53:40 leigh204
Pffft. What do I care about white celebrities bringing attention to causes. I personally know people who do a lot more in helping others and don’t go in front of a camera to do it. GTFO.
on Sat Mar 17th 2012 at 03:17:21 FG
Stop blaming Americans for everything and start paying more attention to the problems of your own country!
on Sat Mar 17th 2012 at 03:34:12 DarqBeauty
FG obviously hasn’t read the post and the comments.
on Sat Mar 17th 2012 at 05:15:03 dave
I would like to hear some credit for this man here.
on Sat Mar 17th 2012 at 07:55:21 anglesanddimensions
@Bliff
And your profound knowledge of economics astounds me. For twenty years since neoliberal policies have been adopted India has been experiencing what economists call ‘jobless growth’. Unless ‘growing economy’ means increased economic inequality, I don’t see how we can call the economy of a country which has the highest unemployment rate in 20 years growing. Goods for people? The purchasing power of the common Indian is mentioned in my previous post. Social welfare indicators are indicating the worst in 20 years. Some amount of industrialization is happening all right, but at the cost of farmers and tribals who are displaced from their lands creating several times more jobless and homeless people than the factories can hire. Again there are the huge number of factories that shut down and small businesses are getting wiped out.
Trickle-down economy has failed. It is clear as daylight and anyone with a slightest bit of brain can see why. So we’d better stop being happy about pumping money into the tummy of the super-rich.
Not always. There are many honest charitable organizations, nost of them white. Your racist attitude toward them may explain your poor opinion of them. Would you rather we not send the money? Because if that is your attitude, maybe we should not.
There may be “honest” charitable organizations, but charity is merely a way to keep people from an uprising. Charity does not solve poverty, it keeps a very tiny percentage of people in poverty barely alive. An investigation into the cause of poverty reveals what policies are responsible for it and who wanted to implement those with what intentions. This part gets really uncomfortable for people like you who think you’re doing us a favour by tossing $5 a week at us. That is why people like you will boast of charity but start opposing anyone who will stand up against the cuts in welfare, the liberalization-privatisation-globalization drive. If those organizations really wished to solve the issue of poverty, they would have hit at the core reason of poverty, the international policies, organizations like WB and IMF, imperialist wars, sanctions imposed on countries (US is threatening to impose sanctions on India if the latter doesn’t stop buying oil from Iran) etc. and finally capitalism itself.
So save your favors. Do away with the charity industry by all means. Hardly makes a difference to the poor population, but at least it will stop the people who want to boast to people ‘you know, I donated to the poor kids in Africa, oh how poor they are’ without any significant loss to their lifestyle and all the while supporting the system that keeps their privileges intact and makes the poor people poorer.
on Sat Mar 17th 2012 at 09:48:26 malkia
Thanks for this post! Especially in the wake of that Kony mess and now George Clooney!
@Destructure honestly, I really do wish all of you would leave us alone. Thanks. Your “help” is more about how good you want to feel than about us really. Am not trying to be your feel good moment. I don’t think many Africans like it.
I agree with Mel. A lot of white people do truly believe that black people are inferior. I will not believe otherwise. A couple of things they have said:
1. Oh look at Rwanda, these primitive savages killing each other over some ancient tribal feuds. Never mind that people were fighting over systemic inequality introduced by the Belgians.
2. On critics of Kony 2012: “Well at least we care about your hellhole!” “at least WE are doing something unlike YOU Africans” “Africa is just stuck in the stone age, we should leave those uncivilized people to kill each other”
3. Saw a story on dead elephants on CNN, the white people almost dying over a dead elephant in fact some were saying that they should be moved out of Africa. Next story was on Sudan…”primitive savages” seemed to be the underlying message in their comments.
I could go on and on, but this is the general meme of their arguments.
Finally, Africa does have a lot of problems, I do not deny that. I live here and we are all faced with our problems. But we are more than the sum of our failures.
Here is fact: 8.5 billion dollars worth of diamonds are extracted out of Africa every year. It is enough to wipe out hunger and poverty in Africa.
This is just diamonds. Here is another fact: only an eighth of Africa’s mineral have been discovered. The clamour for Africa’s rare minerals have began. There is no continent like Africa. Congo alone could feed us for 20 years. I wish we could really see how much we have and rise as a people and take fate into our hands.
@Oyan, I agree with you. We as Africans and black people are way too forgiving! Look at the Jews, they did not forgive or forget. We should emulate them!
“But that’s me posting as if I has no idea that you were just some dishonest white”
But of course I’m a “dishonest white”. Is there any other kind? And each one of us is more racister than the next, right? That’s why I came to this blog — to learn da troof.
Yes, yes, yes. A person with no real purpose or argument is using colorful sarcasm as their “Hail Mary Attempt” to sway people’s attention away from that fact. It was only a matter of time.
honestly, I really do wish all of you would leave us alone. Thanks. Your “help” is more about how good you want to feel than about us really. Am not trying to be your feel good moment. I don’t think many Africans like it.
I can assure you that Africa has never been my “feel good moment”. I’ve never been there. Never plan to go there. And I’ve never given a cent to any charity except for those performing medical research. I believe most charities end up making things worse. People shouldn’t become dependent on handouts whether it’s welfare or ‘save the children’. There’s a reason national parks have signs that say, “Don’t Feed the Bears.” It’s bad for bears and its bad for the people feeding them. And it’s just as bad when people get charity.
on Sat Mar 17th 2012 at 18:01:00 Nom De Plume
I’ll say it again. Subscribing to The Africa Channel through my cable company was one of the best things I’ve ever done.
Pffft. What do I care about white celebrities bringing attention to causes.
Pffft yourself. Apparently you don’t care about the disadvantaged either, otherwise, you wouldn’t put down people like Jolie or Bono.
@brothawolf
disdain for blacks….believe they are not as intelligent.
Saying blacks is less intelligent than whites is something I have come to believe as an explanatory principle of blacks, condition. It’s not something I created, nor do I say it in any disdain….it’s just something that’s true and explains an awful lot. You are just shooting the messenger.
I “disdain” I speak of here is those who speak ill of those who are helping. I am criticizing the criticizers for what they are doing – disdaining – not for any of their abilities. People are held responsible for what they do, not for who they are.
neoliberal policies That was India’s first mistake. Should have tried capitalist policies. Works much better.
Trickle-down economy has failed. Don’t think so. The strange term just makes it amenable to ridicule.
Charity does not solve poverty, it keeps a very tiny percentage of people in poverty barely alive. This is all charity could ever be expected to do. Solving poverty comes from the country, their government in its policies, and the people themselves, including developing/adopting a culture of growth.
This part gets really uncomfortable for people like you who think you’re doing us a favour by tossing $5 a week at us No, I personally don’t even do this; hence, no discomfort. I give $0 to overseas charities. They let do it on their own. They constantly criticize USA and Americans, so let them pound salt.
core reason of poverty, the international policies, ….., and finally capitalism itself Lady, I’ll bet you learned your wacko liberal-socialist ways right here in the USA at one of our fine leftist universities. We wouldn’t need any international policies if the poor countries were already doing fine on their own. Capitalism is the GREATEST solution to poverty. Look at Hong Kong, Asian tigers, and China. They are growing due to their adoption of Western (white) capitalist policies.
Do away with the charity industry by all means. Here we agree. YOU can be the one to tell your people you recommended turning down western money because it was given by snotty white people. Then take the first flight out of your country immediately, for your own safety.
stop the people who want to boast to people ‘you know, I donated to the poor kids in Africa Really. You think this is why people do this? Do you think white people are not caring? How RACIST!!!!
on Sat Mar 17th 2012 at 19:13:08 Matari
” I agree with you. We as Africans and black people are way too forgiving! Look at the Jews, they did not forgive or forget. We should emulate them!”
Speaking with my individual POV as a descendant of those kidnapped from somewhere in West Africa, I don’t think Jews are the people we should emulate. Without going into a lengthy post, here’s why.
There exists in a Marvel Comic storyline about a mythical technologically advanced self-sustaining, never colonized, never conquered Kingdom/nation in Africa that’s run by a fictional King/Ruler named T’challa, aka The Black Panther.
This “fictional” Kingdom, an African nation named Wakanda, imo, is closer to who we once were as Africans, (i.e. the Moors ..) in antiquity than the present model of real life Jews.
If we need to emulate someone, let’s model ourselves after own ancestors/people before they were overcome by Europeans.
Even the mythical Wakandan empire is a better role model than modern, present day Israel largely comprised of Ashkenazi Jews. How can it be good for our young to grow up wanting to pattern/model/emulate after a group made up of largely European people? Haven’t we already witnessed enough of the harm internalized racism has pained us?
*Yes, we should never forget ..or repeat our mistakes.*
on Sat Mar 17th 2012 at 19:30:30 vanishingpoint
@Bliff, ever hear of Lauren Gallindo? Jolie’s adoption of her son from Cambodia was tainted, and the facilitator(Gallindo) was arrested and convicted of child trafficking.
http://www.theage.com.au/articles/2004/01/08/1073437411857.html
Also, another saviour, Madonna, took David from Malawi even though he was not an orphan, his father visited him every week and never gave permission for him to be adopted.
I guess splitting up families due to poverty is helpful and good?
@ Bliff
Get a clue:
http://en.wikipedia.org/wiki/Neoliberalism
You’re new around here, aren’t you? And you don’t have a clue as to the kind of person I am so please spare me with the “you don’t care about the disadvantaged either” crap. Again, what do I care about Angelina Jolie and Bono? They’re just a bunch of rich, influential white people who smile for the camera patting themselves on the back for the “good” they’ve done. What a great photo op.
on Sat Mar 17th 2012 at 20:10:16 JC
Don’t forget to add George Clooney to the mix….It’s almost as if he was trying to purposely get arrested this week in Sudan.
Is this supposed to be raising awareness or attention grabbing self-aggrandizement?!?!
(The spirit of Rochester rasps); “Help us, help us lousy nigras sah! What is disgusting is they have neglected to clean up their own back yard whilst helping someone else with theirs. Anything to keep the nigras at home in their place. At the same time you can feel good about yourself for helping the nigras overseas!
Why don’t you go kiss some more white behind?
Thanks white folks! Now can you do for us here at home what you are doing for others abroad?
@anglesanddimensions:
He is smarter than you because he is a white man, never forget that!
But of course I’m a “dishonest white”. Is there any other kind?
If there is I have yet to meet one! Really you sound paranoid.
There’s a reason national parks have signs that say, “Don’t Feed the Bears.” It’s bad for bears and its bad for the people feeding them.
Stop! Will the lunacy never end? What's wrong with you?
People are held responsible for what they do, not for who they are.
If that were true you would stop writing the reams of garbage that you do.
1. So, what you’re saying is that any theory that “proves” the so-called inferiority of blacks and Africans is something you would automatically believe without question? (yes or no) And any proof that counters this is just wrong? (yes or no)
2. No one here has the right to question or criticize anything they find suspicious when it comes to whites always being seen as saviors of Africans even though that not only does it offend, but also raises important questions? (yes or no)
3. If people are held responsible for what they do and not who they are, then:
a. Why can’t we hold you responsible for the racist…i’m sorry, race realist crap you spew all the time that offends the people here?
b. Why is it you believe that blacks and Africans are responsible for the ills they go through and face because they are black and African and nothing else?
c. Why don’t you hold white people responsible for the ills they’ve done to themselves and other people?
“Perhaps FG is another advocate of the:
— “non-American ‘foreigners’ have no right to comment on this blog-site and if they comment must only praise everything about the US” —
school of non-thought?”
I never told anyone that they can’t criticize the US (or other countries). I just think that several of this blog’s patrons have an unhealthy, sometimes hateful obsession with Americans and American social life. This reached a crescendo with the micro-analysis of the YouTube video made by those two little girls from Florida. If two 15 year-olds living in Britain or France made a comparable video, I wouldn’t give it any attention whatsoever. That’s because I am primarily (though not solely) concerned with what’s going on in the society in which I was born and raised.
on Sun Mar 18th 2012 at 02:22:39 Bliff
You’re new around here, aren’t you? Yeah I am, but more than a match for you, young missy.
you don’t have a clue as to the kind of person I am Let’s see – you think you’re nasty, sassy, think you know more than you do and you actually think that I care.
what do I care about Angelina Jolie and Bono? You missed the point. I don’t care Jolie and Bono either. However, celebrities attract attentionto their causes and that helps the disadvantaged. The point that you missed is the celebrities are unimportant, what they can bring in to help the disadvantagedis what is important. It seems you would let the disadvantage suffer, just to spite the celebrities. Do you understand now.
inferiority of blacks and Africans…believe without question I never stated I believed it without question, like I just woke up one day and it was convenient to me to believe. No, I believe, not in “inferiority”, like you state, but that blacks are less intelligent, more impulsive, and less forward thinking than whites, which causes them to underachieve in a white-based society like the USA. I don’t believe it without question, I have come to see it as a good explanation of blacks’ condition in USA, as opposed to the white racism charges of people like Abagond.
whites …. as saviors of Africans Why do you obsess on this? Whites do what they do to help, other people do what they do to help Africans. Just because there is some publicity in the USA about white peoples efforts, is no reason to get concerned. I would think you would be happy about anyone helping Africans.
we hold you responsible for the realist crap you spew What do you mean by responsible? You can challenge me at anytime on this blog. If you want me to respond, you must write something worth responding to, not just a bunch of personal attacks.
Why is it you believe that blacks and Africans are responsible for the ills they go through and face because they are black and African and nothing else?
As I said before, I believe blacks’ have trouble in USA because of what I said earlier. These are the main reasons.
Why don’t you hold white people responsible for the ills they’ve done to themselves and other people In the last 50 years, whites have been overwhelming helpful to blacks. Few blacks today should be concerned with happened before that, because that is before their time. However, I see many blacks, on this blog and others, who obsess over the past times. I think they’re just trying to scam whites and get extra benefits. Blacks need to let go off past times and be concerned with what is happening in the present and what that means for the future.
you can feel good about yourself for helping the nigras overseas Maybe you would prefer we don’t help the “nigras overseas”, just so the snotty white people don’t feel good about themselves? A great help you are to the disadvantaged.
@vanishingpoint
ever hear of Lauren Gallindo? No, I haven’t and I don’t care about Jolie’s personal life. I am just here to point out that many commenters would rather criticize Jolie, Bono, etc about the publicity they attract, out of jealously, rather than their efforts to help the disadvantaged. Would you would prefer we don’t help, just so the snotty white people don’t feel good about themselves?
on Sun Mar 18th 2012 at 03:15:40 DarqBeauty
How can someone think Africans are inferior then feel out of sorts because we don’t think Africans need white help? These people don’t care about Africans. So why are they pretending indignation. Am I the only one who sees how illogical this argument is? Abagond sure has some interesting visitors.People who think we are inferior, but will spend days and days arguing with those they consider beneath them. o_0??
You confuse me. The Africans can refuse white help at any time. How can you say whites don’t “care about Africans” when we do many things to help. I’m feeling that whites will be criticized by blacks NO MATTER what we do.
I never called YOU personally inferior.
“Reporter Asked Trayvon Martin’s Mom If He Ate Chicken! LAMO. How great is that!?”
That is what you wrote on another post. You are filth. Your diseased mind has been exposed. There is nothing you can say, no sanctimonious stance you can fake. You’ve been exposed by your own words. Don’t address me ever again. Just typing to you creeps me out. You’re a racist with a hard heart. You are irredeemable. I feel sorry for you, but on the other hand, I am deeply disgusted by your very presence. Please. Don’t address me again.
on Sun Mar 18th 2012 at 05:08:26 brothawolf
Bliff,
I won’t try to participate in derailing this thread for your amusement, but you’re just showing how trolls think when it comes to your comments: You basically don’t give a damn who you offend on this blog, do you?
Now back to our conversation:
You say you never stated you believed in black inferiority, but then again, I don’t recall you saying that you’ve questioned or not questioned it either until now when you said that you don’t believe without question.
Here’s what’s so funny. You say you don’t believe in “inferiority” and yet you say that blacks are less intelligent, more impulsive, and less forward thinking than whites which causes us to underachieve in a white-based society like this one. Well, what else do you call it especially compared with your brand or level of so-called intelligence, behavior, and mentality?
You don’t have to say “inferiority” outright if all that what you say you believe in compares one group of people to another based on your own prejudices. If you truly do think blacks are inferior, why not be a (white) man and say it instead of double talking.
If anyone is obsessed with white saviors it’s white people and their media. I’m not happy if all I see are white people as generous, altruistic human beings saving the poor, helpless Africans who can’t save themselves. Why the bloody hell would I be happy to see those images over and over again?
If you’re a white man with intelligence superior to my own, why don’t you tell me what responsible is?
I, Abagond, and most other people have challenged you. Yet, you come up with laughable, offensive, and degrading responses like a typical troll. We’ve written something worth responding to and yet you seem to cower behind your race-realism, fake knowledge of history, narrow-mindedness and other dehumanizing responses.
Why is it you believe that blacks and Africans are responsible for the ills they go through and face because they are black and African and nothing else? As I said before, I believe blacks’ have trouble in USA because of what I said earlier. These are the main reasons.
So, the answer is yes.
See? This is what pisses me off the most. You and your “that’s in the past and it doesn’t matter” crock of bullshit you always type.
And how the f*ck have whites been overwhelming helpful to blacks? Name some true examples–that have actually worked.
Your problem is that you can’t stand to face the truth of the white race’s past let alone the present. No wonder you have a poor knowledge of history. But I bet dollars to donuts that you would get orgasms about Paul Revere’s ride, Ben Franklin’s innovations, and the most important event, how this country was founded.
But Heaven forbid you learning about–and I have to keep this within the subject matter–European colonization of Africa and the West’s–and Europe’s–exploitation of the continent’s rich resources, and the support of the dictators of certain regions. All of which were orchestrated mostly by whites in a subtle method of modern imperialism for greed and power.
This is why I’m tired of seeing the same “white savior of Africa” image over and over again when most/many whites, especially those in power, have corporate interests in the land, and will do ANYTHING, which includes destruction, to take over.
For the record, learn to read directions carefully because I did ask for ‘yes or no’ answers and not paragraphs.
on Sun Mar 18th 2012 at 05:08:33 joshua
What should George Clooney be doing? I’ve seen him interviewed, and he seems to be truly passionate about the causes he gets involved with. Does anyone here know differently?
The map at the start of this thread is bogus. It is titled “African Slave Trade” yet the arrows coded for volume really only show the Atlantic slave trade.
Trickle down is a failure. Feudalism was an example of “trickle down”. The basic problem is that pure capitalism tends to concentrate wealth in few people to the extent that they can manage it. The sayings “it takes money to make money” and “them that have the gold make the rules” are as true now as they ever were. This is even more true in places without decent education systems. The rich can send their kids abroad – what do the poor do?
on Sun Mar 18th 2012 at 07:04:52 anglesanddimensions
neoliberal policies That was India’s first mistake. Should have tried capitalist policies. Works much better…
Lady, I’ll bet you learned your wacko liberal-socialist ways right here in the USA at one of our fine leftist universities. We wouldn’t need any international policies if the poor countries were already doing fine on their own. Capitalism is the GREATEST solution to poverty. Look at Hong Kong, Asian tigers, and China. They are growing due to their adoption of Western (white) capitalist policies.
Because there do not exist any mainstream leftist parties in the US, the American left is the global centrist with a Keynesian approach, practicing a somewhat cushioned capitalism. The political terminology is upside down – the Keynesians are called liberals. If you had the slightest familiarity with politics except what your mainstream ‘Faux’ and CNN are blathering, you would’ve known that neoliberalism is in common parliance what is called the free market policy. Fine specimen of the superior race, you are. And yeah, you lost the bet.
I will not derail the thread going into China’s widespread poverty, labourer repression etc.
I’ve seen American people boast of charity too many times not to think this is the chief reason they donate. I do not say there aren’t white people who care (this is so tiring and we’ve all been through this several times, but you lot are rigidly against any observation of traits prevalent in white people or American people. This helps you deny that environment conditions a person thus denying the necessity to change the environment and attributing everything to ‘genes’, ‘internal structure’ etc. Funnily, you people are constantly making general assuptions about black people, Arab people, Indian people, East Asian people, Muslim people and so on. While not allowing general observation of white Americans and making general observations of many other groups, traits get attributed to race, religion, nationality et al while the white American culture remains ‘no-culture’). Few people, of any ethnicity or nationality, really care. But there’s no point repeating what I’ve made obvious in my previous posts. Not sorry to disappoint you, I think that is exactly why people do this. And this culture of hypocrisy is spread with a purpose which is beyond your comprehension, I’m afraid.
Correction: *The political terminology in America
Just saw the ‘chicken’ comment. Go to Stormfront, that’s where you belong, bliff. I just hope there are no people of color in your neighbourhood.
on Sun Mar 18th 2012 at 07:30:45 abagond
Here is the Ugandan prime minister’s response video to “Kony 2012”. Notice how he sees northern Uganda as something to be proud of rather than something to be pitied or ashamed of:
Jesus Christ, of all people, said that if you do your charity for the world to see then it is not true charity but hypocrisy: you are doing it not out of love and concern but to make yourself SEEM like a good person to others.
on Sun Mar 18th 2012 at 08:01:16 leigh204
Wow, this fellow finds amusement with the chicken comment? Sick! You are so on the money about this pathetic excuse for a human being, DB. The fact that I even acknowledged his lowly presence gives me a feeling of revulsion.
@ Joshua
It does show African slaves going to other parts of the world. If you have hard numbers, rather than wishful thinking, to dispute the indicated volumes for those years (1500-1870) then please share.
Personally I doubt it: there is a huge African Diaspora (160 million people) on the shores of the Western Atlantic. I do not see signs of anything like it elsewhere from the past 10,000 years. The closest thing is the Bantu Expansion but that was within Africa.
In case you do not know, Arab slave traders are a moral fig leaf White Americans like to hide behind. As the map shows it is a pretty slim one.
@ leigh
Yuck, double yuck with a side of crispy fried nastiness. I mean who thinks things like that, let alone says them? smh
That chicken comment was in extremely bad taste, at the least. Therefore I have allowed DB’s and Leigh’s comments to go through.
A few more things you need to realize. The reason why, as you say, I–or rather we are obsessed with the white savior bit is because it’s shoved into our eyes and eyes all the time. We can’t go anywhere without hearing about it from the TV, the radio, or even our co-workers.
But do you hear or see POC going to Africa and doing good deeds there? Hardly. Does this mean POC, including blacks, don’t go to Africa? No. Does this mean they don’t perform good deeds over there. Again, no! But how often do you hear about them as opposed to the white people saving Africa news? You’d be lucky to hear about it at all outside of the Trinity Broadcasting Network, and even then it rarely happens.
The point is that Africans are not helpless. Only someone who learns from the mainstream media or raised by that way would foolishly believe that unquestionably.
I had to deal with two people on Colorlines.com who see white saviors as white saints!! They see this guy Jason Russell as an angel and his movement as something 100% noble. When I placed my two cents into the forum, one kept going on and on about why is this a race issue. The other believed that Africans are really helpless and hopeless. Both saw Kony 2012 as a God send, and despised the fact that questions and criticisms were made as a response. These two would not see what the “fuss” was about no matter what explanations were given. It was like talking to a two cartoon idiots.
I should post the link to the video about Jason’s bender. Then again, they may consider it as a leftist plot, anything not to see the shadows behind their “white knight”.
@ Bliff, etc
Given the bad relationship that whites have had with Africa – slavery, colonialism, neocolonialism, etc – any thinking person is going to question the motives of whites who want to “help”.
Whites in general have way more power in the world than blacks. That the prime minister of Uganda felt the need to defend his country from a YouTube video and found himself writing to the likes of Justin Bieber and Lady Gaga shows that imbalance. It shows how dangerous “well-meaning” whites can be.
Tourists spent $560 million in Uganda in 2008.
Invisible Children spent $3.3 million there in 2011.
If Ugandan tourism drops by more than 0.6% due to the “Kony 2012” video making people think Uganda is a dangerous place, then it will do more material harm than good.
Broken Africa is basically the bases for racist propaganda in USA and around the west, mainly. The idea behind it is that because the whole Africa is just a cesspool of hunger, diseases and poverty and failure, no wonder that all the blacks are basically the same all over the world.
Broken Africa is the reason why blacks are below whites and stay there and should stay there. No need for complicated HBD theories nor any other scinetific crap, just point a finger to Africa and say: See? Broken Africa is the patent aswer for all questions about racism. “See+ Look at It yourself!”.
It is also very important, almost essential, to show year after year how the White West rescues africans from africans and most of all, from Africa itself. It is very important to repeat this message in various forms and platforms, overtly and subliminaly, ober and over again, untill it becomes a reality and replaces any other idea of Africa. It is via this repetition that comes the idea that it is natural to send in some relief troops or military into Africa to helpo africans, because they can not helpo themselves.
In this propaganda it is also very important to avoid all images, stories and videos of any sort of normalcy. Delete all information that shows how normal life is in Africa. Deny all the development in Africa. Also, high light the corrupt leaders of Africa as natural beings for Africa and do not even hint that those guys are stealing their countries blind with the help and assistance of white bankers and consults and big companies etc., sometimes with the helpo of white soldiers who may be “advisors” or “security consultants” or even “friendly forces supporting and protecting democracy”.
Put all these together and you once again can do what ever you want or need to do when ever it is in your white western interests. A very good example: somali pirates. International fishing industry has been stealing the fish from the sea and somali fishermen had no more their traditional way to support their families etc. They became pirates. And how this has been presented in the western media??
That is why and how Africa is ad will be broken in the white western media.
on Sun Mar 18th 2012 at 11:40:19 Matari
SatanForce
I see that you’re “trying” to read my posts. Good for you!! LOL
Keep at it. With time and practice your comprehension skills will improve.
In time, your ability to see past the box you’re in may improve.
At any rate, I think (despite your confusion) this point can’t be stressed enough. Israel is not a good role model to emulate! 🙂
What I actually wrote was:
on Sun Mar 18th 2012 at 14:45:56 Nom De Plume
“Which brings me to the 2 ‘little girls’ on their racist rant on another recent thread.”
“Do you have any sympathy for the black and brown little girls these girls were hating on? And you think Abagond wrote that post only for American commenters?”
I caught that comment, too. “FC” referred to the teen racists in Florida as “little girls.” On another thread, destructure seems to believe that Trayvon, who was around the same age, was a grown man because he could grow hair on his face and get a drivers license. Different commenters with the same double standard.
George Clooney is appearing on “Meet The Press” today, no doubt discussing his recent arrest in Sudan.
on Sun Mar 18th 2012 at 16:17:38 Herneith
Let’s see – you think you’re nasty, sassy, think you know more than you do and you actually think that I care.
That sounds like you are describing yourself.
Do you understand now.
No. You’re writing in circles. On the one hand celebrities are unimportant. On the other hand they generate publicity for these photo-ops, I mean charities. If the celebrities are not important, then how do they engender the publicity to get people to ‘donate’ en masse to these charities? Maybe you and your ilk can promote these causes!
No, I believe, not in “inferiority”, like you state, but that blacks are less intelligent, more impulsive, and less forward thinking than whites, which causes them to underachieve in a white-based society like the USA.
What Bliff really means; “I hate ni&&ers, but am to ‘civil’ to use uncivil words. I prefer to baffle people with nonsense! It is more fun and helps me bolster my already low to non-existant self worth. Where would we be without the lowly negro to enhance our sense of worth or to compare ourselves to(of course to our betterment)?
If you want me to respond, you must write something worth responding to, not just a bunch of personal attacks.
Oh and I guess your reply to Leigh was constructive criticism, cretin?
I think they’re just trying to scam whites and get extra benefits.
Where can I sign up for this program genius? I could use the extra benefits and cash to buy a new handbag!
. Blacks need to let go off past times and be concerned with what is happening in the present and what that means for the future.
According to you, Bliff, we are less intelligent so therefore we cannot. Any suggestions?
So why are they pretending indignation. Am I the only one who sees how illogical this argument is?
Nope. I am starting to think they let the lunatics loose on the computers at the mental hospital. They are f—ed in the head, morally bankrupt among other things. It is too bad there is a comments policy here or I would really let this Bliff person know what I think of them. T’wouldn’t be nice and would make one’s ears burn!
on Sun Mar 18th 2012 at 17:03:19 truthbetold
@ Abagond, Leigh, Darq, Brothawolf
There are some folks on this blog, that I won’t mention, who just come here to incite and fan the flames of racial hatred. These individuals have no purpose here. They’re not here to learn or heal or understand a damn thing.
Just ignore them.
You’ll be better off.
I need to let them go stew in their own hate. They give me nothing in return but headaches.
on Sun Mar 18th 2012 at 22:09:20 kittyem
The woman on the first pic appears to be posing. It’s a norm for western jurnos to go to the refugee camps and actively look for the thinnest children to photograph. A former jurno narrated at how his former boss used to reject his work because the children were “not thin enough”
During the Horn of Africa drought last year, a common complaint among the Somali people at the refugee camps was the jurnos who kept asking them to uncover their children so that they can take “good” pictures. It seems the more the ribs that can be counted, then so much the better.
On the Kony 2012 issue, I learned that our hero recently embarked on a public masturbating frenzy. Apparently he is also a coke addict. It just goes to show that whites are still hankering for for negative narrative about Africa and they will reflexively buy into any such nonsense without even questioning who came up with it.
The third picture is from a coffee house in an upmarket Nairobi mall. It is by Noor Khamis for Reuters and appeared in the South African press.
on Mon Mar 19th 2012 at 00:04:58 Doug1
Projection: It was the West that broke Africa.
No it wasn’t. ssAfrica has always been a very lagging part of the world, throughout all history. There was no literacy in African languages until Europeans taught that to them.
Why? Because of the major geographic races with lots of members, ssAfricans are the least intelligent. Other races as distinct as ssAfricans are from the other six or so major geographic races, are even less intelligent on average than ssAfricans, such as the Koisans, Pygmies, and Australian Aborigines. However their numbers have always been relatively few, and also their impact on world history, A. Aborigines partly excepted due to overplayed by leftists white guilt.
The so called stereotype has TONS of truth to it, in other words.
on Mon Mar 19th 2012 at 00:12:47 JC
@Doug, did you not read the article? Yes it is TRUE that Africa has one of the highest poverty rates in the world, but this doesn’t mean all of Africa should be portrayed that way.
That’s how a STEREOTYPE works, by making blanketing assumptions across the board even when there is diversity.
on Mon Mar 19th 2012 at 00:45:19 Bliff
Oh c”mon the “chicken comment was in extremely bad taste”. This whole blog is in bad taste. People attack me personally all the time here. I’ve seen pornographic conversations on this blog about porn movies (Not that there’s anything wrong with that).
In fact,I was only quoting Oyan who stated it first.
It’s TRUE! Blacks are really OVERSENSITIVE to mild things. In fact, I think it’s worse than that. I think you guys feign being insulted just to have something to whine about and shoot back at the whites.
@Doug1
Good one. Nice to see someone else on this blog who actually knows something and has not bought into the Bad White, Good Black mentality.
You’re writing in circles. No I’m not. You’re playing games with the references to the word important. The celebrities are important to the charities because they raise awareness and bring in more money than if the were not involved. The celebrities should be unimportant to observers, like you, because you should be concerned with the charity work, not weather Jolie and Bono are getting any more publicity. You see? A completely contained reason thought, no circular logic.
What Bliff really means; “I hate ni&&ers. Wrong again. I believe what I said because it seems to be a good explanatory principle. Like a scientific theory. There is no hate involved. Just a dispassionate belief. I have no reason to hate black people. Can you prove that I do?
Where can I sign up for this program genius. You probably already have: affirmative action, anti-discrimination laws restricting whites’ actions, Title I, Head Start, many programs for the poor that help blacks disproportionately.
what that means for the future. If you can’t run or walk, then at least limp into the future. Quit whining about the past, and think about your future in this greatest of all countries.
where was the US when the Acholi people…Banyore massacre….Mukula massacre….Uganda People’s Defence Force…. DR Congo’s resources were being plundered?
The rest of the world, including you, apparently think they have some say in where the USA employs its military forces. The USA will employ them where we have an interest. Africa is not really that place. I wasn’t important when we were confronting the USSR, and it’s not so important in the MIdEast.
Contrary to myth, we DON’T jump into every conflict there is. We get blasted by the rest of the world as it is, so why would we jump into meaningless African conflict?
we are obsessed with the white savior bit is because it’s shoved into our eyes and eyes . It is NOT!! You’re just whining. I watch TV too and it’s just not on that much. If you don’t like it turn the channel.
I would really let this Bliff person know what I think of them. I think you already have….in so many words. Frankly, Herneith, I think you’re just ticked because the truth hurts; you know it and I know it.
on Mon Mar 19th 2012 at 01:37:52 Franklin
@ Doug1
Normally, I ignore your because your arguments because they’re flimsy and full of holes. But periodically, just to demonstrate how little you know, (despite all your desperate posturing) I like to prove that you’re an idiot and that you don’t know squat. Here we go again…
“There was no literacy in African languages until Europeans taught that to them.”
Right off the top of my head Ge’ez, Chromatographic Edo Script, Nsibidi, are three African writing systems among a number, that pre-date the arrival of Europeans on the continent. Now I’ll sit here and wait for you to shift goal posts, by attempt to invalidate that fact by saying something ridiculous like “There were no books, so it doesn’t count!”
on Mon Mar 19th 2012 at 02:56:24 DarqBeauty
” Now I’ll sit here and wait for you to shift goal posts, by attempt to invalidate that fact by saying something ridiculous like “There were no books, so it doesn’t count!””
Exactly. They may tell themselves that we are intellectually inferior, but who are the geniuses arguing with people they consider below them day after day? This is one of those regurgitated “facts” that white supremacist like to regurgitate. Even though the reality is vastly different. But hey, they can’t like little things like facts get in the way of their good old fashioned hate.
on Mon Mar 19th 2012 at 02:59:01 brothawolf
It is NOT!! You’re just whining. I watch TV too and it’s just not on that much. If you don’t like it turn the channel.
If you were to read the whole sentence, I mentioned other mediums. I should’ve mentioned movies as that’s a Hollywood narrative to produce at least once a year.
You’re backed into a corner for which you can not escape by using your ramblings.
Also Bliff,
I’ve written a bit about how people like you act in another thread entitled “My Philosophy on Trolls”. I don’t want to derail this topic. So, if you want to continue with your hatred, meet me there.
@doug1:
“ssAfrica has always been a very lagging part of the world, throughout all history.”
Öööh… You do know that your ancestors came from Africa? Like, all humanbeings came from Africa, right?
And since we are now on the subject, what your ancestors were doing when the nubians were building pyramids or those guys in Timbuktu were collecting one of the biggest library in the world, or those guys in present day Zimbabwe were trading with gold and silver and building castles from stone?
You do know that most of the whites who escaped or were sent by force, were slaves or prisoners or just ran out from Europe because they could not make it there, could not even read, right? You know that at that time the english men bathed perhaps once or twice a year, right?
You do know that the parfume industry was created to cover up the rampant diseases in the court of the Sun Kig of France back in the late 1600’s because the smell of rottening felsh, infections, and other of such since they did not have a single toilet in Versailles nor used baths? Never mind that africans had have their parfumes for centuries by then and washed almost daily were ever water was available.
You do know that in 1700’s absolute majority of the white europeans could not read or write? Majority of the white europeans could not read or write in first half of the next century either.
You do know that there were massive famines in Europe in 1800’s?
You do know that it was only in 1800’s that the white europeans realised that it could be a good idea to wash hands before helping at child birth or surgical operations or at all? The japanese, chinese and indiand, arabs and some africans had done it for centuries by that time.
You do know that the Great White Man had no say so in most parts of Africa untill 1800’s? The funniest thing is that they died in there and could not live there because they had no idea how to survive there. The crucial point came when they realised that perhaps we should learn something from the natives, like kinine, the only working medicine against malaria, which by the way, the africans had used and known for centuries by then. And this happened in late 1800’s, not before.
Now I wonder, if africans and Africa had been lagging all trough the history, why on earth the white man did not take over before that? Why white men did not invade Africa before 1800’s? According to you, the place was a mess and lagging already.
Why not the vikings, who went to America and Asia and kicked almost everyones butts, did not just row their boats up the Nile or Kongo and kicked the butts of those black semianimals and steal their ivory and gold? They did it almost anywhere else, like in the White Sea area where they brought the northern ivory, tusks of the walruses. They were trading slaves from Ireland to Caspia Sea, so why not from Africa?
Why the great english sea dogs and explorers did not just occupy that lagging part of the world in 1600’s? Why the french did not do that? Or the dutch? I mean, they invaded and occupied the East India.
And on that note, why the americans, the greatest of the great whites, did not take over the whole continent from those savages in 1800’s? They took their own continent from the natives just like that, so it could not have been morally wrong or even impossible, right?
Ok, why the USA did not invade and take over Africa after WW1 or WW2? I mean, USA was the only super power in 1945. It could have been so easy. Right?
Now, lets see how the mighty USA has been doing in the lagging Africa… Somalia in 1990’s, anyone??
“Contrary to myth, we DON’T jump into every conflict there is.”
China 1945-51.
France 1947.
Marshall Islands 1946-58.
Italy 1947-1980’s.
Greece 1947-49.
Philippines 1945-53.
Korea 1945-53.
Albania 1949-53.
East Europe 1945-56.
Iran 1953.
Guatemala 1953-90’s.
Costa Rica 1950’s, 1970-71.
Middle East 1956-58.
Indonesia 1957-58.
Haiti 1959.
Guyana 1953-64.
Irak 1958-63.
Vietnam 1945-73.
Cambodia 1955-73.
Laos 1957-73.
Thailand 1965-73.
Ecuador 1960-63.
Kongo/Zaire 1960-65, 1977-78.
France 1960’s.
Brazil 1961-64.
Peru 1965.
Dominican 1963-65.
Cuba 1959- present.
Indonesia 1965.
Ghana 1966.
Uruguay 1969-72.
Chile 1964-73.
South Africa 1960’s-80’s.
Bolivia 1964-75.
Australia 1972-75.
Portugal 1972-75.
East Timor 1975-99.
Angola 1975-90’s.
Jamaica 1976.
Nicaragua 1979-80.
Hoduras 1980’s.
Philippines 1970’s-90’s.
Seychelles 1979-81.
South Yemen 1979-84.
Souht Korea 1980.
Tshad 1981-82.
Grenada 1979-83.
Surinam 1982-84.
Libya 1981-89.
Fidji 1987.
Panama 1989.
Afganistan 1979-92.
El Salvador 1980-92.
Haiti 1987-94.
Bulgaria 1990-91.
Somalia 1993.
Irak 1990’s.
Peru 1990’s.
Columbia 1990’s.
Mexico 1990’s.
Yugoslavia 1995-99.
Just few examples of conflicts were US military or CIA has been involved since 1945.
on Mon Mar 19th 2012 at 07:32:29 dee
I recommend everyone to watch this.
Ignorance is caused by, well, ignorance. Apart from American history, American schools spend way too much time only focusing on Europe. As a high school student, all I’ve learned about Africa from school are basically things that contribute to African stereotypes. I blame textbook makers, and schools, for buying these inadequate learning devices. I don’t understand why the good parts of Africa are completely ignored, beyond ancient Egypt and parts of South Africa. Just because someone doesn’t live in a mansion doesn’t mean their life sucks. But at the same time, there are many people who do live in mansions. I don’t understand why this sort of thing continues
@bulanik: No, he did not know, but then again, he does not believe it. He believes he sees on tv, on the right channel that is.
@bulanik: 😀
on Mon Mar 19th 2012 at 11:48:14 leigh204
@sam:
Italy 1947-1980′s.
Guatemala 1953-90′s.
Costa Rica 1950′s, 1970-71.
France 1960′s.
South Africa 1960′s-80′s.
Angola 1975-90′s.
Hoduras 1980′s.
Philippines 1970′s-90′s.
Irak 1990′s.
Peru 1990′s.
Columbia 1990′s.
Mexico 1990′s.
Now that’s what I call a BURN. lol! 😀
on Mon Mar 19th 2012 at 12:05:36 Jack in the Box
So that’s where all my tax money went?
on Mon Mar 19th 2012 at 12:20:09 Matari
I recall seeing the above JS video years ago. SIX MILLION people from third world (non-white) countries are DEAD in the wake of the CIA’s 40 years (at the time that video clip was produced) involvement in the affairs “other” nations
Remember, this video was made way BEFORE the 911 false flag operation invasion that led to the phony War On Terror in Iraq, Afghanistan, Pakistan (and Iran too if these crooks have their way).
The white racial frame propaganda machine prohibits people from seeing who the true, brutally efficient criminals are in America, and those who are dead as a result. Some of us here know that non-white dead (or alive) people don’t cause whites much concern, or sympathy.
Yet, incredulously adding insult to injury, the white racial frame (POV) maintains that blacks are the most violent criminal group in America that deserves incarceration.
The combined number of black violent criminals worldwide can’t begin to match the atrocities of the top 2% of white male criminals – the ones who wear badges, uniforms, white collars, carry brief-cases and have never seen the inside of a prison.
Remember this the next time a troll, or whomever, suggests to you that blacks are the most aggressive, violent and criminal people on earth.
Sam listed a number of conflicts that we were involved in, though I don’t necessarily agree with his list. These are conflicts we apparently wanted to be involved in.
You listed some we did not get involved in, so my original point, we don’t get involved in every conflict, still stands.
So, all US disruptive involvement in Africa is military? If you’re addressing me, please explain why would you even ask me this. I have made no such generalization. I made one comment about how the USA does not get involved in every conflict when you listed some conflicts in Africa you apparently thought we should’ve have got involved in.
on Mon Mar 19th 2012 at 13:31:02 Nom De Plume
“Does this means then, that the real challenge is to find other sources of capital?”
Dr. Moyo recommends encouraging and assisting people to start their own businesses. She says that http://www.kiva.org is a good way to do this, and believes it will prove to be more beneficial over time than funding from NGOs and others.
I know what you mean. I haven’t had any personal involvement with the organization. I just remember Dr. Moyo recommending it during one of her interviews.
on Mon Mar 19th 2012 at 20:46:22 Tyrone
All of us know that our african sistas and brothas have to reconstruct “Mama Africa” on their own accord going forward, but, we can’t allow those who created the mess to wash their hands of what we see taking place in nations such as Somalia, Sudan, Libya, Congo, Uganda, Nigeria, etc. We should bitch and moan about the ish that we see going on. As black people, we should be outraged at so-called black leadership in this country and in africa. George Clooney has to get arrested outside the Sudanese Embassy to bring attention to the genocide in Sudan and South Sudan, WTF? Why the hell are we voting for a bunch of yes men and women who don’t speak up for us anyway? The CBC loves to travel to africa, but can’t open their mouths when the s**t hits the fan. We have a so-called black president in power, and the bs is still taking place…Scary!!!
on Mon Mar 19th 2012 at 23:02:20 V-4
It seems like Dr. Moyo is ignoring the wests involvement over the years in creating instability and poverty, its not “aid” that has created the problem.
In a very real way, its the system she is talking about, capitalism, profitting off of another human beings misery is pretty much the central tenent of capitalism.
I mean, in the US we getting tremendous amounts of aid from China, so she may have a point. If China wasn’t willing to give us money would we have gone to war?
On the other hand; socialistic countries are way more stable than the ones like the US which are more based on a capitalistic economic system. Less criminal, more literate, less depression etc….
And her Ethiopian example; she pointed out the African average for ownership of cell phones was 30% so their must be countries out their that recieve aid that don’t fall under the Ethiopia example, countries that can do both aid and capitalism, why not look to them as examples?
That being said; she points out the problems with the Aids Culture, its messages are negative and ultimately potentially harmful as pointed out with Invisible Children, if they cause tourism to fall even a tiny miniscule amount they have simply done harm and no good.
The Aids culture message negates people wanting to do business or even interact in africa, while at the same time not pointing fingers at the damage our culture as a whole has done to Africa.
on Tue Mar 20th 2012 at 04:17:04 Secular X. Blood
You really should look at Unamusement Park. He has a great flyer on stereotypes (no, really).
There is this thing in statistics called “The Exception that Proves the Rule.” The term is somewhat misleading. A better, albeit less catchy term would be “The Anomaly that Highlights the Tendency.”
Hitler is one of those exceptions. As is Stalin.
Back to the thing about blacks being just as fit to run a country as whites. Are you willing to make the argument that South Africa is better now than it was 30 years ago? What about Namibia?
Human differences exist. Things would go a lot better if we recognized them and compensated for them. We would have saved millions of lives in America and Africa alike if we would not hide behind your liberal curtain.
If you would like me to show you some evidence that racial differences do indeed exist, you are welcome to email me (please resist the urge to troll). My email is secularblood (at) gmail (dot) com.
Unamused’s Blog: http://unamusementpark.com/
on Tue Mar 20th 2012 at 06:56:52 Franklin
Unamused?
Is that the same Unamused who didn’t even know that “The Rule of Thumb” was an idiom, that had his entire blog consistently refuted by the infamously nutty (but accurate) Obsidian (who Unamused banned because he couldn’t handle facts), and who has been thoroughly embarrassed on this very blog?
He’s a joke who “whores out”/shamelessly plugs his worthless blog and brags about traffic, like he’s some sort of posturing 12 year old that desperately needs validation in order to prove to himself “that he’s a big boy now.”
Unamused’s blog is like “The Mad Magazine of Genetics”.
@ Secular
Your approach has been tried and instead of saving lives it has led to the deaths of tens of millions of people, like Jews, blacks, Gypsies and natives on three continents. “Things” only went better for white Christians.
The current racism of ordinary White Americans, a racism much milder than yours, has led to the rise of the Kleptocracy, bringing levels of class inequality even worse than famously kleptocratic Nigeria. But then again, as a Social Darwinist, you are probably proud of that.
http://en.wikipedia.org/wiki/Gini_coefficient
https://abagond.wordpress.com/2012/03/05/democide/
on Thu Mar 22nd 2012 at 04:20:15 Ace
That has got to be the best shut down of a “Africa’s always been horrible” argument that I’ve ever seen.
It’s funny how these same people won’t even go into how messed up Europe was throughout the majority of it’s history…
on Thu Mar 22nd 2012 at 04:32:40 V-4
Satanforce kind of has a point about Wakanda
I mean they bad talked the various modern powers at that meeting but they themselves do fuck all to help out the various countries around them.
Its a monarchy with an incredibly wealthy elite at the top with an incredibly poor bottom layer…..I mean the people at the top are pretty much techno-gods while the people at the bottom live in huts and still use spears to hunt.
Exactly why don’t they share their technology more, not only with other countries but within their own as well?
I don’t think there’s any escaping the class system they have going on if you want social mobility.
on Thu Mar 22nd 2012 at 22:25:43 Matari
“Lets look at Israel. A constitutional created from an international diaspora of varying peoples. They are energy independent, due to nuclear power. They can kick anyone’s ass, conventionally and nuclear – no nation in their vicinity can fuck with them!!! Through lobbying and and strategic alliances, they guaranteed the utmost support of the US . They have created a “start-up nation” , in essence, a national Silicon Valley. And most importantly, they have enslaved and destroyed the nation-state (West Bank, Gaza Strip) that opposed them. Cheap labour forever. Yes, they could be kinder, but fuck that.”
“I know. I know. I find it hard to escape the fact of how smart and conscious I am.”
And IMMORAL, too – which isn’t at all unexpected, given your name.
YOU would align, ally and imitate…
Theft and occupation of sovereign land, racism, hatred, oppression & mistreatment, slavery-like conditions & wages, expansionism, covert operatives/spies interfering in the affairs of sovereign nations, manufacture/buy/export hi-tech weaponry, attack Iran, (or have a proxy do it), control & own the galaxy. White Supremacy – Lite!
Yup … nice role model, indeed! Why not simply model yourself after the United States of America? The big cheese.
– chuckle –
No thanks Donald. I’ll stick with the imperfect, fictional Wakanda. : ))
on Fri Mar 23rd 2012 at 16:47:16 Bliff
@Satanforce
If a Pan-African solution were created, say a 19 nation Sub-Saharan African Federal Republic (SSAFR), it would by simple definition, be a sub-continental superpower, on the level of Brazil, Russia, India, China and yes, the U.S.
You write some of the best posts on this otherwise lame black-centered blog. However, this one left me LMAO. Are you serious? An African super-power? Run by a bunch of countries who can’t even run themselves. Africa is so tribal each country is dysfunctional, unless bailed out by whites, or more likely now, by the Chinese.
I suppose they could use that Western black powerhouse nation that has been independent for over 200 yrs now – Haiti – as a template. Yes, with Haiti’s senior leadership, maybe they could pull it off.
One thing from history when we are talking about how Africa and its history are seen and what really was:
How many of you know how big Christopher Columbus “ship” was? It was a pretty small boat, actually. Some plus 20 meters long if I don’t remember wrong. And how big were the “canoes” used along the Kongo river system from the earliest times? They were 50 to 60 meters long. They carried people and goods all across the “darkest Africa” for centuries before any white dude showed up with his tsuktsuk steam engines to the same waters.
Why not heavier boats? Because the canoes, just like those viking ships, could go trough shallow waters and navigate trough water vegetation, something that those steam engine boats could not do, even though they had nice sound and that advanced technology!
The guys living on the other side of the world in the New Caledonian islands had “canoes” even longer, carrying up 100 guys and their gear.
Ad the ships on the east coast of Africa? Well, they were bigger than any of the cogs in Europe for centuries. They were trading to Arabia and India and beyond. Some historian think all the way up to China. And this happened well before Marco Polo came back with noodles and created the spaghetti.
Also, something to think about: east africans were trading with the romans. They have discovered at least two cities (roman cities according to the white historians but it can be argued whose cities they actually were) on the east. These were trading with romans in Egypt and in Middle East via Red Sea etc.
The romans also recognised african kings and nations, they also fought long and hard wars against some of them, and if you read their texts about these african adversaries you’ll notice that the romans saw them as equal adversaries, enemies taken seriously. They were not less sub human savages than the celts or any other nations or people the romans met and fought with. Actually roman texts are more hostile and racist towards the northern people than the africans. Just read what they say about the people living beyond the germanic tribes.
So perhaps the history of Africa is not what it has been made to look like in recent decades or during last couple of centuries.
@satanf: Sure, but I just wanted to point out the fact that sea going vessels, which some argue were the reason for the expansion of the white european colonisation (and an example of more advanced technical know how of the whites vs black africans etc.) were NOT unique in the way some have seen it. And while we are here, some of the viking ships were pretty big too, from few centuries before those examples of wikipedia.
on Sat Mar 24th 2012 at 15:02:52 SHONDIS
to get arrested outside the Sudanese Embassy to bring attention to the genocide in Sudan and South Sudan, WTF?
YOU ARE MISSING THE POINT!! THE POINT IS NOT TO BELIEVE THE GARBAGE THE MEDIA SAYS IS GOING ON IN AFRICA IN THE FIRST PLACE!!! if you meet someone from sudan, ask them about the genocide and i bet they will say “WHAT GENOCIDE”???
I love the construction/development shown in those videos you posted. It’s in sharp contrast to what the western MSM shows what;s going on in Africa.
That said, there’s something a bit unsettling about the tall apartment buildings – they seem to suggest movement towards higher population densities.
My personal preference – lol – is for a much lower skyline that lends towards a more spread out community contoured and integrated with open spaces.
People, especially children, should be closer and more connected to the land, NATURE and natural open spaces, rather than concrete, steel, and super tall hi-risers.
Perhaps those skyscrapers are the more affordable housing units for the less well to do as oppossed to the beautiful homes being constructed for the upper-middle class?
I love your Malcolm X picutre. I listen to him these days instead of Lil Wayne and I am a Black teen. I wish you can get other Black teens to stop listening to Lil Wayne and start listening to Malcolm X’s message and speeches. He is way more important to Black History and more inspirational.
As for the Broken Africa Sterotype, where did that come from? The last time I studied African history, there were rich civilizations such as the Mali, Songhai etc. Africa was a rich contient with gold and resources. Even though Afirca seems to be poor today, some people from Africa tell me that there are shopping mall and things in Africa. They never show that on the TV and I always wondered why.
Ms.McKenzie,
Thank you. I totally agree with your opinion regarding Malcolm X vs many of today’s “commercial entertainment artists.” I’m certain there are other young people, however few they may be, who also (or will come to) share your view.
Why is Africa almost always shown in a very negative way on TV?
In a word: RACISM.
White Supremacy/Racism (whiteness) – in order to maintain itself – must elevate itself by devaluing/deflating others.
They transmit their supposed superiority and others’ supposed inferiority messages in thousands of different ways that affects everyone – whether they realize it or not.
Whiteness prefers to showcase Africa’s weaknesses and problems while failing to highlight her strengths, vast potential and material wealth/natural resources. Its intent is to own and control all or some of Africa’s vast mineral abundance because of its insatiable greed/need to consume/control everything and anything within its reach or grasp. Whiteness is like a really bad mental, emotional, spiritual sickness that cannot be cured or fixed.
Thank you because I go to school and all they talk about is Africa being poor and not being anything. I always found that strange.
The movie, Hotel Rwanda was shown in my history class and it really made me think that Africa was poor and nothing.
Thank you for the info.
@adeen:
Always when learning history remember that it is told by some one who has his/hers own agenda and opinions. This is true in every history lesson, book, documentary etc. It is very important to learn more, so that one can make more complete picture about any issue at hand.
One very important thing about Africa: it is a huge continent. When western media talks about Africa, it is the same as it would be for Europeans look at USA nothing but a part of whole Americas and treat all of USA and its people like they are just the same as anyone from Chile or Brazil. That is how western media many times treats Africa.
As for Malcolm X, I think he was one of the most important thinkers of the last century. He was not the monolithic zelot the white media has been always presenting him. He corrected his own views if he learned otherwise and got more and more information for himself for his thinking, he was studying everything all the time, and most of all: he saw the big picture and did the analysis. Very dangerous thing.
He saw the whole thing as it was: poverty and disaster of the black ghettoes, crime and narcotics, black criminals working in cahoots with white criminals, who were working for white organised crime, who was working with the local police, federal law enforcement, CIA, with the help and the blessing of the politicians, who were errand boys of the white elite who was really ruling the country.
That made him so dangerous for that whole power network. That is why they decided to kill him one way or another. The same thing happened to Martin Luther King too, after he started to talk openly about that same power stucture. He understud it too and saw it and talked about it. And was killed.
on Sun Mar 25th 2012 at 18:42:05 matari8017
SantaForce
“Stark Industries, in collaboration with Reed Richards, have found a way to cheaply synthesize artificial vibranium, reducing the thprice from 30,000 dollars a gram, to 3 dollars a kilo, This has caused the Wakandan economy to collapse overnight, with riots shaking the capital and calls for the Wakandan king, T’Challa to step down. Chief amongst these calls is Nobel award winning biophysicist Joseph Kenyatta, who i calling for a constitutional monarchy with a new constitution, as well as abandoning Wakanda’s isolationaist stance so that an East African republic may be created. How will T’Challa respond to this?”
He doesn’t have to respond.
But, why not?
Apparently the Universe had other plans for this small, yet powerful African nation.
Haven’t you heard? The synthetic vibranium was discovered to have a couple of latent flaws that were somehow overlooked by the Stark-Richards consortium.
It turns out that these two literal super-geniuses (like you!) in their rush to, one: undermine Wakanda’s sovereignty, wealth, independence and two: to bring their artificial product to market — failed to conduct substantive empirical testing on what has turned out to be an inherently unstable pseudo vibranium.
Put simply, the free valence electrons in the synthetic version could not maintain and sustain its atomic orbit/integrity. Another snafu was the stock-market backlash (CRASH) caused by the fake vibranium resulted in record breaking financial losses, thereby bringing both Stark Enterprises and Richards Corp along with their hordes of financial backers to the brink of bankruptcy and financial ruin.
Subsequently, the resilient Wakandan economy currently enjoys a full recovery, along with an increased demand for vibranium, now at $40K a gram to replace the faulty synthetic product tragically failing on a global scale in electronic consumer, commercial & military industrial components and systems, not to mention the degrading spy/surveillance satellites orbiting the Earth.
T’Challa’s kingdom, prestige, honor and political base are fully restored.
Rumors about his impending marriage to Storm, a senior member of the X-MEN, have been confirmed by Wakandan press releases. An African mutual defense treaty with Wakanda’s neighbors is in its early development stages. All is going very well for the Black Panther, the sage Wakandan monarch and his people.
Tony Stark & Reed Richards are both facing civil litigation class-action law suits that will likely tie them up in court for the next 20 years.
on Sun Mar 25th 2012 at 19:59:32 Adeen Danica Mckenzie
I am starting to realize that History is told by people with an agenda.I am really young, under the age of twenty five.
Ah, but Bliff, I am afraid that the facts beg to differ with you.
Interesting. However, you can easily get high rates of growth starting off of a very low base, which is where Africa is now. You can never just simply extraplote this growth rates into the future. they are unlikely to last.
Africa has always had a lot of potential. There are the vast mineral deposits in the Congo and elsewhere. The Ivory Coast has great cocoa plantations ever since the cocoa tree was imported from South America during the Age of Discovery and Slavery.
However, the problem is the Africans themselves. They were primitive until Europeans came to colonize. Since the Europeans left, Africa has slid backwards, unable to maintain what the Europeans created.
Africa is highly tribal and their nation-states, imposed by the Europeans, barely work. Strong man dicatators have taken over in most states and have imposed socialist bureaucratic governments. Look at what Mugabe did to Zimbabwea. Most of the people are loyal to their tribes, not the state.
The dictators spend much of the country’s wealth on building grandiose capital cities, with modern airports and modern center city areas. Meanwhile, the rest of the country is in shambles. Even Bulanik seems to be fooled by the lavish capital cities, surrounded by much vaster slums.
The Africans themselves produce mainly bureaucracy. Most college educated Africans go into the govenment, where they are expected to provide favors to their extended families. Corruption, by Western standards, is completely embedded into the system.
The Africans themselves are not exactly the sharpest knives in the drawer. Africa has been dominated by Europeans, and now the Chinese are coming in. I know the Chinese have a low opinion of blacks, so it will be interesting how it plays out.
I see no scenario in which any group of African nations rises to superpower status in anyforeseeable future.
Your Wiki link was interesting, and pointed to some current high rates of economic growth. However, even it did not indicate any thing as preposterous as a SuperPower Africa.
on Mon Mar 26th 2012 at 04:58:44 Herneith
Why don’t you go there and help them out? Invest some?
“You can never just simply extraplote this growth rates into the future. they are unlikely to last.”
You mean like in USA? With several depressions and slumps in its record? What was the growth rate in USA last year? Oh, well…
“They were primitive until Europeans came to colonize. Since the Europeans left, Africa has slid backwards, unable to maintain what the Europeans created.”
They were primitive? You mean unlike europeans out of whom majority could not read or write, who usually lived well below the poverty line, who had famines every now and then in 1800’s etc.?
Yes, they have had hard time to maintain such a rate of slavery and opression, but they try, my friend, they try. It is hard, though, without the european know how on opression. It is kind amateurish now but lucky for them, there are european, american and chinese intelligence people, soldiers, sorry advisors, and big businesses helping them to maintain the opression leves at some kind of standard.
“Africa is highly tribal and their nation-states, imposed by the Europeans, barely work.”
You are right and that is why you have all these ethnic conflicts falring up inside those european imposed un-natural states.
“Strong man dicatators have taken over in most states and have imposed socialist bureaucratic governments”.
Name one African country that is socialist. And those strong men have some backing. Example. Just recently the military took over in Mali because the government was not doing enough to deal with the tuareg rebels in north. You know why those tuaregs are fighting? Their land has uranium. Guess who are after that? Yeap…
“The dictators spend much of the country’s wealth on building grandiose capital cities, with modern airports and modern center city areas.”
Noup. The dictators hide most of their nations wealth into secret bank accounts i Switzerland, Lichtenstein and Caribian island banks. As for building modern airports and cities, you mean like USA did in 1950’s and 60’s and 70’s and…
Those bureacracies were created by europeans during colonial times. They were created to control the population and still do. Nepotism was also a handy tool used by the european minority to conquer and divide and they used it from Africa to India. When it is possible to feed your family by working in the bureacracy, that is where you aim to get in. Once in, you are sipposed to do favors for your bosses and help your own clients. That is called clientism, a nice system, which was also the governing system of Rome. And speaking about bureacracies, isn’t it weird that you guys always complain about the Big Government in USA?
As for the corruption, that is pretty funny coming from a guy who lives in a land where dozen banks stole 770 billion dollars from taxpayers with the help of the government. Or where a war was kept on going for the benefit of private companies for ten years. Nice.
That is because you have a bit naive and short view of history. Egypt was a super power for couple thousand years. How long USA has been one? A hundred, 120 yrs? Not that long in history.
That is true, that is why they do not use knives anymore but assault rifles.
“Africa has been dominated by Europeans”
Right, and yet you claim that africans have caused their problems, this despite of your fact that Africa has been dominated by Europe. So which way it is? Did the europeans dominate africans or are the africans the cause of their plight?
“now the Chinese are coming in”
Well, according the recent studies and findings it is possible that chinese merchants have been coming in since 1300’s but who cares.
@ Satanforce
Right off the top of my head, you can also add the Benin Empire (who are severely mis/under-reported), the Axumite Empire, or even Kanem Bornu as another non-primitive examples.
What do you think of the recent Chinese involvement in Africa?
@StanForce, et al
I originally just wanted to comment on SatanForce’s statement about the Africa SuperPower. Contrary to what it may seem, I really have NO INTEREST IN AFRICA. So this will be my last go round on this topic; just so everyone knows, if you respond to this, I won’t be responding back, so save your typing fingers.
You do realise that all those countries are democracies There are still many strongman governments in Africa, whether they are officially called “democracies” or not. I don’t democracy has really taken hold yet in Africa, it’s counter to their tribal mentality.
were primitive until Europeans came to colonize. Most of subSaharan Africa was preliterate before the coming of Europeans. That does not include those areas where Islam was introduced or those along the Nile Valley.
The Ashanti became an empire only after they encountered Europeans and obtained firearms in exchange for slaves and ivory.
Other commenters referred to battles in the 1800’s between Africans and Europeans. This is again, after the coming of the Europeans.
I see little to change in my original comment. That’s it – I’m done with this Africa thread. You can go and talk amongst yourselves, now.
on Mon Mar 26th 2012 at 20:32:26 SomeGuy
Contrary to what it may seem, I really have NO INTEREST IN AFRICA.
Strange that someone would make a hobby of Black folks and not have at least a passing interest in their continent of origin.
Bliff, I don’t think you are taking this hobby seriously!
on Mon Mar 26th 2012 at 21:37:08 teddy1975
Satanforce, the Ashanti, one of the most notorious slave trading peoples in all of Africa, still not entirely forgiven by others, might not be the best counter example to the broken Africa stereotype.
on Mon Mar 26th 2012 at 23:06:06 JT
Anyone else find it wierd that Black people are Bliff’s hobby?
Do you think it is because he identifies with Black people on some level?
on Tue Mar 27th 2012 at 02:06:34 Bliff
@JT
a hobby…not the hobby; really an interest of mine, not my only interest. Would you find it odd that some people have an interest in watching football? Would that mean that’s all they do? Think first next time, JT.
Are you fucking crazy???!!! Use the n-word again, even with asterisks, and I will fucking ban you.
You’re funny, you know Bliff? Research your claims before committing to them.
Akan Script – Asanteman
Nsibi Script
Geez Script -Ethiopia, approx. 500B.C.
Akan uses a Latin script. Europeans devised the script for the Akan language when they arrived. The Akans had the language, the Europeans invented the writing for them.
Nsibidi is a primitive proto-writing symbology from the Nigeria region. It is a primitive set of symbols, not a true language.
Geez Script, has been used in the Ethiopia area, which is the Nile Valley, not subSaharan Africa. The script has Semitic roots, not Negroid roots, in South Arabia. Again, from Semitic, white people.
Who’s funny now, SatanForce?
on Tue Mar 27th 2012 at 13:33:51 sam
You are funny.
Nubians in present day southern Sudan had their own alphabet and writing already in 100 AD, perhaps even before. Your great great great great great great grand parents did not even know how to read or write. At that time their kingdom was well below Sahara. Around 700 Bc their empire consisted whole of Nubia, Kush, from Meroe to the Libanon in middle east. Burns your behind, doesn’t it?
But never mind the alphabets. You do know that other civilizations, like the incas, used totally different kind of symbol system as a means to communicate, that is to “write” without using letters? You did not know that? Oh my oh my…
So, you do not know everything about all?? Tsot tsot…
You are funny part 2.
“the Ethiopia area, which is the Nile Valley”
Back to school, my friend. Take few geography classes first, before some history. Ethiopia is not the Nile valley.
Sorry about that but hey, you are a product of the american school system so I forgive your ignorance on the geography too.
on Tue Mar 27th 2012 at 16:52:59 Matari
Three words to summarize your latest video offerings:
-Happy
-Prosperous
-Thriving
Three existential things the western media is most likely NOT to televise re Africa.
Pease keep up the good works, even if some of us can’t keep up with YOU!
Bulaniik
“This has led to creation of specialized agencies to handle the work of urban housing by acquiring assistance from the World Bank and UN to implement national or city-based housing-related projects. It sounds good, doesn’t it —- but do these initiatives work without the political will and leadership to carry-through on commitments? ”
The mere mention of the World Bank and the UN, for me, conjures up nasty images of western corruption – both financial and political. I don’t like or trust either of these institutions.The solutions to housing the poor, for example imo, should come from innovative grass-root leaders, scholars and thinkers that are FROM the problem areas. We already have a ton of examples why the IMF, WB, WTO and UN solutions don’t/won’t work. Greed, corruption and the desire for control/power/hegemony.
The best outcome is to enable, empower and allow the indigenous populations to solve their own issues. There are some GREAT forward thinking young (and old) African minds already at work, seeking/offering long term plans and solutions for Africa’s people.
BTW, I love the idea of bottle housing! If waste is used to produce and construct useful/beneficial products – everyone wins!
Still you. Right everybody?
Right you are chap! Bliff is a ras hole!
I will interrupt my self-imposed exile for just this brief message.
I am no Africa expert. Apparently, Africa has brought novel ideas to the entire world, besides spear chucking.
There is that noble practice of….female genital mutilation. The one the West couldn’t come up with. Perhaps Bulanik could bring this practice with her from Mother Africa.
on Tue Mar 27th 2012 at 19:10:25 SomeGuy
Nah, some Europeans should just stick to what they know best: Child Abuse, White Sexual Slavery and Ruining National economies. You know, the good stuff!
“There is that noble practice of….female genital mutilation. The one the West couldn’t come up with.”
Ok, buddy, you asked for it. And I assume you mean whites with the term West?
Ok. Lets see. Every one knows what it was like in the medieval times so just to spare some space here and abagonds nerves I bring you the western stuff since 1500’s.
Religious wars from 1500’s up untill 1600’s in the continent and up to 1990’s in Northern Ireland. The religious wars in France in 1500’s claimed up to 200 000 victims, some estimates are even higher. Mutilation was not only typical, it was the usual method of getting rid of the opponents.
30yrs war (1621-48) by the way was the most destructive event to face Europe up till that time and before Napoleons wars, WW1 and WW2. That was destruction on a biblical scale, so much so that northern Germany was reduced form a green agricultural land into a barren desolet waste land populated by flys only, as one soldier once wrote. Normal practises in that war were: skinning, slaughtering, burning, mass lynching, torture on massive scale and some few thousand witch burnings to go along. Swedes (and finns among them) invented a swedish drink. They poured urine and such into someone untill his stomach was totally bloated and after that they jumped up and down on that individuals stomach, untill it bursted open or internally. Nice, huh?
Holy roman inquistion is well known but its counter part Spanish inquisition (which was independent organ working under the Spanish royalty) was much more original. They had a massive spike, three feet high, widening at the base, into which women were lowered so that the spike penetrated their private parts and lowered still untill women were ripped apart. The famous burining at the stake was considered as an act of mercy since it shortened the time spent in the purgatory. So they tried to burn the victims as slowly as possible for the joy of their ideology. And this went on for few hundred years totally among the westeners.
If we move into USA and genital mutilation, when the colorado volunteers massacred the peaceful natives in Sand Creek, they took some souveniers. They made money pouches from the testicle sacks of the dead natives, pinned male genitals into their hats as trophies and also female genitals, they had legs, thigs, breasts and heads on spikes as trophies as well as killed native children. These were shown to a white publuc on a victory parade held later and received a great joy and jubilation among the white population.
And of course, there were the lynchings of the blacks in which genital mutilation was fairly common feature. And these went on at least untill 1930’s in your beloved US of A.
And of course there are other snappy methods of mutilationa and mayhem that those africans never came up: the flame throwers which made their debut at the battle of Verdun in 1916 and poison gas used as weapon, machine gun which helped the britts to mow down thousands of natives in Sudan early 1900’s. Even Winston Churchill who was at present was impressed when they lost only few men and the natives lost thousands in few hours.
And one thing those africans never came up with was that A bomb. Now that is some serious destructive bisnes right there.
@bulanik: For all my knowledge this old custom is very rare in sub Saharan Africa but more common in the southern Sahara area, around Sudan, Tshad, and northern Ethopia and Somalia etc. in the east. I have no knowledge opf this custom among the central african people. I might be wrong.
This cutting Africa into two parts divided by Sahara is funny since Sahara was steppe and savanna until few thousand years ago. Also rivers like Nile and coastal traffic had not stopped going trough or around that area. Timbuktu is a fine example of how much there used to be traffic across the Sahara during centuries.
on Tue Mar 27th 2012 at 20:27:49 B. R.
I refer at times to sub sahara Africa to define a cultural genius that came from there that can be found all over sub sahara Africa, and, is differant from the culture that is in north of the Sahara Africa (although traces of it are in north Africa also, but, there is a deep Arab influence also up there).
Where there are huge cultural differances from tribe to tribe, area to area, there is a cultural expresion that have similar properties that is the gift that sub Sahara Africa has given the world
Talk about the broken Africa concept and how people outside of Africa look at Africans, here is a excerpt from Che Guevara’s diary. wow, it is pretty shallow :
On July 17, 1952, age 24, in his personal diary, Che Guevara wrote[1]: “The blacks, those magnificent examples of the African race who have conserved their racial purity by a lack of affinity with washing, have seen their patch invaded by a different kind of slave: The Portuguese. These two races now share a common experience, fraught with bickering and squabbling. Discrimination, and poverty unite them in a daily battle for survival but their different attitudes to life separate them completely: the black is indolent and fanciful, he spends his money on frivolity and drink; the European comes from a tradition of working and saving which follows him to this corner of America and drives him to get ahead, even independently, of his own individual aspirations
on Wed Mar 28th 2012 at 03:39:54 Bliff
Cool!! I love Western violence. I am so proud of our boys.
on Wed Mar 28th 2012 at 12:29:51 B. R.
I have to confess, one of my biggest dreams is to visit a country in Africa , like Gana, Angola, Kenya, Senegal.
I dont know if I will ever be able to do that, but, I would love to go to one of the modern cities, stay in a nice hotel and be able to see as much music as posible since music and dance is a tremendous live experiance that have a big affect on me. Especialy the state folkloric danca and drummers. Ways to see the traditions and histories.
Id really like to find out the true Africa instead of the media Africa
on Wed Mar 28th 2012 at 23:48:06 Dahoman X
For those curious about african writing systems, there is this book, by Saki Mafundikwa:
http://creativeroots.org/2011/11/afrikan-alphabets-book-by-saki-mafundikwa/
A review of the book (with some pictures):
http://kintespace.com/rasx46.html
Have you ever heard of Aminata Traore? She summed up your many interrogations in one single question: what kind of development do we (Africans) want for of Africa?
In an interview she was asked: “What does it take to give Africans a dignified life?”
Her answer:
In the first place it takes self respect and a belief in our own capabilities. Real development needs the fertile basis of a lively culture that constantly feeds new solutions. (…)
Real development should also be based on a culture that found the right balance with the surrounding environment. Because every culture primarily is a transformation of the earth, the forests and the soil. Economics, ecology and culture are the three pillars that carry a society. From the moment that triangle is balanced, we can build a society that no longer robs people from their own dignity, knowledge and dreams. Then we can make a future for our own people. If we could have defined for ourselves what democracy is made of, we would have found ways to question and sanction our leaders for example. Because when the moral point of view is shared, the powerful are obliged to listen to the powerless.
http://www.mo.be/node/23000
Aminata Traore is particularly critical of the neoliberal policies enforced in Africa during the last 2 decades. More about her ideas here:
http://www.guinguinbali.com/index.php?lang=en&mod=news&task=view_news&cat=3&id=372
on Wed Mar 28th 2012 at 23:56:25 silentreturn
BR, Start saving a little bit now. 🙂
on Thu Mar 29th 2012 at 00:33:45 silentreturn
‘Nsibidi is a primitive proto-writing symbology from the Nigeria region. It is a primitive set of symbols, not a true language.’
By that logic, hieroglyphs and cuneiform is not writing either.
on Thu Mar 29th 2012 at 03:03:41 Bliff
the black is indolent and fanciful, he spends his money on frivolity and drink; the European comes from a tradition of working and saving which follows him to this corner of America and drives him to get ahead, even independently, of his own individual aspirations
Ya see – if duma$$ Che Guevara had the low down on blacks. A race realist like me couln’t said it any better. This is a pretty typical international-wide opnion of blacks.
on Thu Mar 29th 2012 at 03:23:44 SomeGuy
Since you are so fond of quotes, here’s one:
“Universal truth is not measured in mass appeal.”
-Immortal Technique
Truth spoken. Also, the scrotal sacks of native men, and the breasts of native women, would be dried and cured, and used as tobacco pouches and black-powder (for guns) pouches.
White europeans (the French, specifically) are the ones who originally engaged in the practice of scalping – they called it ‘counting coup’.
And what did he (Che Guevara) do? Did he went on bashing blacks, did he went on stating that blacks are less than human, that they do not deserve the same rights as whites, that blacks are not equal with whites? Did he say that black cubans are less cubans than white cubans? Was he burning crosses and killing blacks for fun?
@sepultra:
It was also pretty common practise among the celts to take the heads of their enemies. It was called “taking beards”. This habbit was practised at least till late roman times and perhaps even till later.
Also let us not forget the romans, those civilized white heros of the past: in one 107 days lasting games given by emperor Trajanus some 30 000 people were killed in Colosseum alone. That is fed to the beasts, killed by any other means, and of course, killed by each other. All this for the great amusement of the audience.
on Thu Mar 29th 2012 at 04:51:54 Linda
In 1964, Che Guevara then denounced the United States policy towards their black population, stating:
“Those who kill their own children and discriminate daily against them because of the color of their skin; those who let the murderers of blacks remain free, protecting them, and furthermore punishing the black population because they demand their legitimate rights as free men—how can those who do this consider themselves guardians of freedom worldwide?”
on Thu Mar 29th 2012 at 10:04:23 B. R.
Sorry , Linda, Guevara’s racsim is blatent in his statement about Africans no matter what he states about Americans.
Sam, you do know that some of Guevaras solderscomplained of his racism?
You do know that the Congolease communists kicked Guevara out because he was too radicle in his methods ?
You do know that a bunch of black scholars has condemned Castros Cuba as racist
You do know that Fidel and Guevara executed more poeple than the militarry dictaroships of Cile, Argentin and Brazil put together?
I mean that is an important question for Africa, do you want just any white man coming in…a white man like Guevara ? Who demonstrates without a doubt that he is racist to the core calling Africans frivilous and saying they smell bad but can mouth the right things about what is wrong with America ?
After that passage in his diary, I wouldnt cut Che Guevara any slack what so ever…
In my book he was a meglomaniac
Bulanik…Gueveras trips to Africa were sponsered by the Soviet Union, since they were sponsoring Cuba. They were everybit and more involved with trying to spread their flawed ideaology over the globe as the USA, and Africa was caught right in the middle of both of these ideologies
Seriously, if any person can read what Guevera said about Africans, and still think he was some noble fighter for justice and equality and really have the interests of black people in his heart…i have to question their logic
What do you not understand about ” Africans are frivolous..they dont bathe…”?
If that is the kind of white man you think is fine to look to for inspiration..becaue he can mouth something about the USA who was his sworn enemy, who would like to find their weakness ?
But fundimentaly he looks down on Africans ?
He is a basic racist ?
What is wrong with your logic ?
How interesting, Guevera is no better than Doug 1, Bliss, or any other racist on here who sais disgusting things about black people
and he is ok with you?
It is absolutly plain and clear that Guevera, a blatent racist , is as bad for Africa as any colonial power out there. He is as guilty as any other power that came into Africa to exploit it and start wars…
And that is ok for you ?
So what the USA did in Africa and the colonial powers is what is bad but the Soviet Union sponsering Cuba and people like Guevera to come there and start wars is ok ?
Looking down on Africans while you come in to start wars and destruction to get power of recources for you and your sponsoring country with a flawed ideilogy to begin with is just fine ?
The hypocricy is mind boggling..see I know both sides are dirty
So you give Guevera a pass? After what he puts in his diary…
You arent going to call Guevera what he is …a blatent racist ?
He is no better than what we have heard from Doug ,Bliff, No Slaps the lot of them
on Thu Mar 29th 2012 at 11:25:06 Matari
“Ya see – if duma$$ Che Guevara had the low down on blacks. A race realist like me couln’t said it any better.”
You and your brethren ought to quit with the phony pretense and just come out of the closet. “Race Realist” is purely a PC way of saying REAL RACIST. Racism (and racists) haven’t changed. Only the language/lexicon has.
Also, if Che Guevara is a “duma$$,” comparatively speaking that makes you (and other real racists) extraordinarily stupid/deluded duma$$es. A trait that you persist on continually showing the world. Despite the grievous offense you bring to my nostrils, I fully understand why Abagond permits your stinking presence to foul up the air in here.
Bulanik , this is the Broken Africa thread. I already said they both were dirty…does that rersonate with you at all? Im making posts on other threads, I suggest you read them.
You were inspired enough by Gueveras scripted words , prepared as his propaganda page to defend them brought in by Linda, against his emotional entry into his diary that reveals he is a blatent racist , which seems to mean nothing to you.
You absolutly cannont discuss broken Africa seriously without examining all the sides who were involved breaking it, and , Guevera, a man who personaly brought his flawed idealogy, who reveals himself to be a racist with a very low opinion of Africa,started armed revolutions , death and destruction in Africa, is as guilty as the USA and all the colonising powers to the factors that contribure to the things that are ailing some of the African countries today. He is part of the whole truth about broken Africa
Yet you fail to acknowledge that,and , are attacking me, have mischaractorised me right along the way since the other thread . . You are trying to shift talking about broken Africa into American racism when Guevara personaly was in Africa promoting death and destruction.
One thing you should know. Communism never was interested in racsim and the civil rights for black people
By the way, Im not like any of the people on here who call Obama a socialist or scream “commie” at any inteligent solutions
They dont know what real communists are
I do, I have researched the numbers of people eliminated under the flawed ideaology of communism . There was a real reason to fight communism , but not what the dorks you see screaming “commie” coming in here know anything about
When I talk about communism Im not talking anything like what those chumps are railing about
Actualy, what Im really saying is that, all the conflicts, the colonizers, the powers that invaded for riches , the Gueveras backed by Fidel in Cuba with Soviet support…etc
All these things are what contriburted to the broken Africa stereotye.They were the conflicts that take away the attention from anything good and growing in Africa.That hinder any good growth when they are set into effect.
Because this thread is about the broken Africa stereotype
By the way, relating to Gueveras diary statement, I just am in humble admiration as to what Africans from countries like Gana, Nigera, Kenya, Semagal etc etc have brought to the tavble of civilisation interms of culture , language, foods, etc I could never make a ststement like his nor ever understand it
@BR:
No I don’t but I do know that he was a real hero for millions who fought against western imperialism in the Third world.
No I don’t but I do know that he was too radical for Castro too.
Who are these black scholars? Name few, thank you.
No I do not because that is a lie. Those three dictatorships killed many more thousands than Castro and his ilk ever did.
The diary you so eagerly quote was written when Guevara was a young amn still looking what to do with his life. At that time he was not a communist nor guerilla, nor anything else than a young middle class kid from Argentina driving around the continent with his friend on motorcycles.
Let me get this very clear to you. I don’t like Che or Castro or soviet or any kind of communism. Why? I lived my whole life few miles from the USSR. I can assure you that I know hell of a lot about USSR than you will ever know. And that includes communism, you know, the real deal, Red Army, red ruskies and all that, not the one you read in the books.
As for Africa, this thread is not about BROKEN Africa per sé but the stereotype of it, the one you so eagerly promote here. If you were alert and understud the post you would realise that in reality there is not that Broken Africa you suscribe for. It is a myth promoted by western propaganda and judging from you, it has worked just fine. There is no lost cintinent raped by communist subversives: that is the CIA vision of it.
You claim that Che Guevara, who only visited Africa, and communists are responsible for the stereotype of Broken Africa. I wonder how you get your head around that. It is the western media which has created that myth. Not communist propaganda. If you look at their own myth, Africa is a place were happy balck people hold hands and sing and dance with Lenin smiling at them, and also a continent raped by the mean american tycoon. That was their myth.
Broken Africa is a western idea of a continent that can not handle itself because of its ow people.
http://articles.latimes.com/2010/jan/03/nation/la-na-cuba-blacks3-2010jan03
I hate making you look bad, Sam because I like your heart is in the right place
Would you like me to destroy your other arguments ?
30,000 people were eliminated by Argentina military dictators, 3,000 in Chile, less than 1000 in Brazil
60,000 were executed in Cuba
Ill be happy to referance it, yes you know more about the red army and I know more about you about what happened in South America
Sam , did you read what I said ? You are putting words in my mouth. These conflicts and the exploiting of Africa that we have all talked about, is one of the reasons for the broken Africa stereotype and I said that right above, are you reading ?
Bulanik, I wrote that you were “inspired” to defend Guevara’s words inspite of seeing he is a blatent racist ( dont buy your excuse, Sam).
You are getting on your motorbike and spinning wheels knocking up a lot of dust to try to point out to everyone that I am for some reason not qualified to post about these things or I might be a racist.You are doing that on the other thread…go right ahead, maybe after spinning your wheels enough and kick up enough dust you might find something that sticks…but you are going to have a lot of dust and smoke in your eyes
Sam , quote quote from wikipedia :
According to various reports and investigations 1,200–3,200 people were killed, up to 80,000 were interned, and up to 30,000 were tortured by his regime including women and children.[6][7][8] Under the influence of the free market-oriented
Bulanik, excuse me, Ive been acused of lies by Sam, do I have any right to prove he is dead wrong….about “inspiration” ive answered twice
Sam here is Brazil “According to a government-sponsored truth and reconciliation commission in 2007, by the end of the 21 years of dictatorship there were 339 documented cases of government-sponsored political assassinations or disappearances. More were interrogated, tortured, and jailed ”
The point we are making about Africans and how this relates to all this, Guevara, represents , along with the colonisers, the USA cold war polocies etc, the real reasons Africa had conflicts that gave people stereotypes of Africa is all conflicts and violence…
(gees Sam, millions of people voted for Bush also, whta does tht tell you? Millions and millions of people can make wrongt choices, millions and millions of people hate them both alsoe
http://en.wikipedia.org/wiki/Dirty_War Argentina ,statistics right at the top
Yeah its wikipedia, but, they fall into the statistics Ive seen many times….they could vary , Ive seen more in some reports
check out this history of how many times Cuba has been involved in Africa for dirty wars that also had involvement by the USA and other out of Africa powers
http://en.wikipedia.org/wiki/Military_history_of_Cuba
again, all this really points out how responsible outside forces were at conflicting inside Africa and creating impresions world wide that Africa is nothing but conflicts
You are looking way more into the word “inspired” than I ever intended…
Let me state , I absolutly dont think you or Sam are communists or followers of Che Guevara
Sorry , Linda, Guevara’s racsim is blatent in his statement about Africans no matter what he states about Americans
I truly hold no white man up as an inspiration, least of all Che Guevara…
I am not sure at what point he made his statement about “blacks being indolent and frivolous” (before or after Congo) but it doesn’t matter…
he was dedicated to his cause and he viewed the Congo as another frontier to conquer (just like European adventurers before him) ….he was also told by the Egyptians not to go to the Congo and interfere, but he did it anyway and like his predecessors before him, he thought he could “tame the natives”..he lost that bet.
“BR But fundimentaly he looks down on Africans ?”
Guevara was no different than the average “white” north American or South American, who thinks they are better than anyone with dark skin.
the average person doesn’t reveal their true feelings when it comes to race anyway.
thanks to the internet, my white coworker who sits next to me all day, can safely go onto a blog forum and call black people the N-word, while telling me about her day and her family (true story)
I put up Guevara’s quote about “race in America” as a balance to the previous quote and as you stated, megalomaniacs (pick any country with money and an agenda with military might to back it up) tend to talk out of both sides of their mouths to further their causes….
on Thu Mar 29th 2012 at 17:00:40 Dahoman X
I re-read my previous post and your subsequent reply, and I believe we may have a misunderstanding.
IMHO, I think one doesn’t have to be African oneself to appreciate the seriousness, the complexities, beauty and supreme importance of Africa’s development by Africans.
I did not imply anything like that.
Quite the contrary: I like how your posts develop actual analysis and it’s obvious that, unlike many commenters, you go through the trouble of researching the issues that you write about.
My Aminata Traore reference was just to bring to your attention a woman whose thoughts on development go in the sense of your own reflection.
Bulanic , I am sorry it took me this long to understand what you needed to hear ….my bad…I hope Im not a person who acuses anyone of being commies for making intelligent statements
Sam is my man also,
Linda, I agree, Guevera is the same as any other white man going into Africa and superimpose his values
Bulanik…again I misspelled your name, my error , I am a person who is paid well for a skill I am good at but I am not college educated so I am always making spelling errors
I have followed your posts and I know you are a very articulate informed young lady…
We are just sharing opinions , right ? We may disagree on other things also but at least I want you to know I have a fundimental respect for you and where you are coming from
on Sat Mar 31st 2012 at 12:18:55 sam
Images are power, that is why the System uses them more and more with more and more sophistication. Africa and africans in the images are part of that use of power trough images and visual means.
Africans are smiling and happy only when a white celebrity comes to their village and hands out some relief. Then they dance and clap their hands and sing their tribal songs for the great white saviour. During other times they are just trying to survive famine, wars, mass murders, genocides, aids, flies in their eyes, tuberculosis, crockodiles and hippos, elephants on rampage, robbers, drunken men in armed gangs looting villages at random, warriors from the neighbouring tribe, islamic jihadists, mercenaries paid by angry arabs, couple Al Qaida guys here and there, dictators and strongmen, unhealthy food full of flies and maggots, dirty water, cholera, malaria, huts built from cow manure, smoking stoves and broken sandals. That is, if you believe what you see in western media.
That is why women today see few hundred photoshopped unrealistic images of the woman in magazines, commercials and practically everywhere, every day. Hundred years ago average woman saw perhaps a 100 women during her lifetime, more if she lived in a city but at most few thousand. Today, if you are living in a big city and heavy user of the media, you will see few thousand of such images a day. Why? To make you feel frustrated of yourself so that would trigger a shopping spree. US marketeers found this out already in 1940’s.
on Sat Mar 31st 2012 at 15:24:09 abagond
I did that same sort of Google experiment with Luanda. If you search CNN or the New York Times for images of Luanda, the first pictures that come up are those of its slums. If you search the whole Internet, the first pictures that come up are beautiful pictures of the centre city:
https://abagond.wordpress.com/2010/06/25/how-backward-is-africa/
The term “sub-Saharan Africa” makes my skin crawl. I should probably do a post on it.
on Sat Mar 31st 2012 at 15:45:26 B. R.
Absolutly correct, people react to image….
Im a person who has never been to Africa, and, it is one of those dreams I have…I would love to know where some countries that have powerful drum and dance cultures, have folklorico national drum dance companies , and be able to stay at a nice hotel…and if its on a beach that has some small waves to swimn in….
Any reccomdations from people who live there or know ?
Actualy, Bulanik, you asked me who I dig from Senegal…I love the drum record by Dou Dou Rose, you can hear the roots of Cuban mambo gua gua co, and samba, and funk and jazz…I was into those AFrican folkways records from a long time ago, Fon Ton Fron drumming, Congo ( I have a record now I listen to), Masai, Kikuyu, Gana drumming, Nigeria
You know, Im one of those people who believe very deeply in the genius of sub Sahara Africa, and in that context, I really do beleive you can look there as the place that came certain concepts of culture, music and dance that have a similar developement, the same way as we recognise Europe classical music , it comes from various countries but in a similar context. And those concepts have affected the world in a big way
on Sat Mar 31st 2012 at 16:19:40 Herneith
Try talking to people from the various countries in Africa. You will get myriad information about politics, societies etc. Many would be surprised at the disparities between what they tell you and what the white media tells you. I am speaking in general, society at large, not anyone in particular, therein lies the problem. Sure some of these countries have problems in varying degrees but what country doesn’t? For example; if you are homeless and starving in North America, that makes that society morally bankrupt as it is put forward as a 1st world country(ies). What is their excuse? They should apply all this charitable work to their own country and clean up their own back yards instead of fomenting propaganda against other countries. But then again they would have to admit their wickedness towards their fellow countrymen both currently and historically. I think they concentrate on these countries and their travails to show that blacks inferiority, this appears to be on a continuum when taken in its’ totality, via media etc. Fools like these race realist have taken to using these images to prove blacks inability to run things and clinging to their white privileges. If I were paranoid, I would think there was a conspiracy of a sort to this end. I don’t credit them with enough intelligence for this, they take a ‘Let the chips fall where they may’ approach.
Good point, Herneith
Its hard to find images of Africans that gets into their humanity, and, the value of their culture. Its all suffering and they are in the distance.
It starts becoming ammunition for what ever agenda wants to use it.
I remember seeing a really off the radar documentary of a tribe from northern Uganda, the part that was more affected by violence, with some of the children had been child solders and others had lost loved ones.
The young kids were getting ready to go down to a big city to compete in a cultural music and dance festival. It showed the teachers come in and demonstrate the dances and musics, and, the kids had seperate interviews about their experiances. They went down to the competition and you could see that through their participation and victory in two of the catagories , a tremendous pride and emotion. One girl , who seemed to have the saddest look, came all alive while dancing with the most incredible expresion of joy on her face, she later said when she is dancing, she forgets all her problems…and the drumming and dancing was wonderful
It was just a moving documentary that got deeper into these peoples humanity and struglle and joy through artistic expresion…I was floored…and you just dont get to see that kind of stuff on tv that often
on Sun Apr 1st 2012 at 00:57:52 B. R.
Enough !! Its over, this phony charade about intelligence tests that are controversial anyway belongs in the trash. They dont cover real ways to survice in life like intuition and improvisation. Bell curves, IQ exames, they are useless in judging real genius.
There is more black American genius at the highest level in the world you can find in this youtube , than you could shake a stick at the whole ivy league. These gentleman have raised the bar in what they do to an unbeleivable hight and their work will be studied in 100 years as the defining thinkers of this time , 1965…
I cant listen anymore to white insecure no nothings who dont know how to difine real genius if it was sitting on their nose .
Any one who question black American intelligence or genius, just tell me what these gentlemen are doing here if you can
Sorry, posted this on the wrong thread, my apologies
on Mon Apr 2nd 2012 at 01:18:58 B. R.
Actualy, Im going to tie this in with this thread…with out the cultural concepts that came from certain areas of Africa, this wouldnt have existed….
And, these concepts are never really addressed or talked about with any depth. With any notion how much they have dominated much of the worlds popular music. Any where there is the African diaspora, there are these concepts that entered the popular musics of where African slaves were brought, and absolutly took over the type of beat and dance that each of the countries turned into their popular grooves and dance crazes , of course mixing with the culture of each area they arrived at.
and, the “broken Africa stereo type” has totaly buried any real look at these incredible concepts that have shaped cultures in various places
The humanity and culture are ovelooked to focus more on misery , death and destruction.
All you hear about is death and destruction in the Congo
Ive got an incredible record of folklorico music from the Congo.
Did you know they have a drum that stretches one gut over the bottom head, so the drum buzzes as you hit it….it is the first snare drum. I thought snare drum concepts came from Europe….wrong
When I think of Congo, I think of these musicians and the concepts they are dealing with, I see their humanity and creativity and artistic expression. These wars and conflicts dont define the people there, the culture and art defines them
on Sat Apr 7th 2012 at 08:15:33 Anna
Another side-effect of the stereotype.
– If you happen to be African, live in a Western country, are articulate, educated, has travelled a lot i.e. don’t correspond to most stereotypes people have of African people, it either mean your parents were diplomats or are corrupt politicians who feed off the poorest of their country.
– You can’t and don’t know much about your history, your culture, your continent because let’s face it, you’re too famished to think about knowledge. African people cannot write plausible and objective facts about themselves: they don’t even have schools.
– If you happen to speak any European languages without the (awful and generic) African accent, it means you went to a private French, Belgium, American or British school in your country
– All African people have protuberant abdomen (a Chinese friend from Mauritius told me that after stressing on the fact that she isn’t African – I asked her why her country was a member of the African Union then)
– Do you live with the lions or in the trees? (not kidding, I was asked this question a couple of times, years ago in France – Same thing happened to my Malagasy friend from Indian descent and another West African friend)
– If you have a light skin, it means you must have had a white or an Arab ancestor.
– “Hakuna Matata! Do you speak swahili?” (Huge eyeroll)
I am not saying that Africa isn’t poor. It is indeed and a lot remains to do, first of all by assuring food security. Yet, Africa isn’t only the dying and begging kids, the dishevelled women, the desert, the armed conflicts and…. the safaris.
I think Sahel is the area on the southern edge of the Sahara proper. I think it does not cover more than that.
As for sub-Saharan Africa, the funny thing is that originally it was geographical term: it described the difference between the Sahara region and area north of Sahara (sub tropics) and the areas south of them. the savannah etc., the climate etc.
BUT what has happened is that racists have hijacked this term too as a cultural and racial divide. This is not an accident. This idea, like others such, come from few racist think tanks which replace the meaning of a word and then begin to use it as their own. This is an old trick used by several ideologies in the past, like the Nazis or communists.
on Sat Apr 7th 2012 at 13:29:59 Dahoman X
what has happened is that racists have hijacked this term too as a cultural and racial divide. This is not an accident.
I believe it dates back to the colonial era. Only then did the Sahara (which historically has always been a crossroad) become this somewhat airtight frontier between “white” and “black” Africa.
Notice how this frontier conveniently ceased to exist every time the colonizer summoned the infamous “arab influences” to explain any sign of “civilization” observed in the southern part of the continent…
I just talk about Africa and for me that covers anything south of Mediterannean. From Morocco to Capetown.
@dahoman X:
I think the racist sub Saharan Africa is quite recent term. I am not certain though.
In colonial times they used very handy term the Darkest Africa. Thus they implied an area whithout any light=intelligence and culture=civilization and also the dark skinned inhabitants. Thus white (light) people were bringing light o the darkness when they conquered it. Nice ideological twist.
on Sat Apr 7th 2012 at 14:47:17 Adeen Danica Mckenzie
What made Africa split into non Black Africa, North Africa and land south of the Sahara is Black Africa?. So strange. I just don’t get that at all because I usually think of Africa as an continent where Blacks descended from like how Caucasians descended from Europe.
Yeah the words Sub Saharan Africa makes my skin crawl as well because the term doesn’t make sense to me at all. What in the world is that term supposed to mean except for the fact that it is the south of the Sahara deser?
I agree with you. Yes, Africa is anthing that is south of the Mediterannean to Capetown is Africa to me as well. Glad someone reads my mind.
All people come from Africa. That is the scientifical fact. The present day europeans are decendants of the people who came from Africa tens of thousands of years ago. So there is no humanbeing who has originated elsewhere. If one wants to be a bit cheeky one can say: biologically we are all Africans. That is also the one thing racists try to hide and do their best to discredit. But that is a fact. So there are no caucasians at all. There is only one humanrace on this planet.
Gentically you and I are more closer than a guy from Mali is to a guy from Mozambique. There are bigger genetical differences inside Africa than in all the rest of the world. That is because the rest of us are the decendants from those who left Africa tens of thousands of years ago.
In colonial times they used very handy term the Darkest Africa. Thus they implied an area whithout any light=intelligence and culture=civilization and also the dark skinned inhabitants. Thus white (light) people were bringing light o the darkness when they conquered it.
Yeah, Africa is often referred as “the dark continent”. All those meanings are implied here.
Joseph Conrad’s title “Heart of Darkness”, literally the tale of a journey to the heart of Africa, also comes to mind.
Yes and it is excellent book. And look who is the worst lunatic of them all: white colonel Kurtz. So the heart of darkness is in actuality inside the white mans head: “Horror, the horror!”
I have no knowledge of this but I always suspected that Condrad knew something about Leopolds Congo.
on Sun Apr 8th 2012 at 06:12:48 sam
I do not know if he ever visited Congo himself. In the book the structure is three dimensional: steamboat travel along the Thames “up the river into the heart of darkness”, in the narrative on a steamboat along the Congo River “into to the heart of darkness” and in the minds of the carachters “into the heart of darkness”.
If he did visit Belgian Congo we know where he got his nightmarish storyline but if he did not, he obviously knew something about what was going on in there.
on Sun Apr 8th 2012 at 07:47:37 Dahoman X
According to the wikipedia page Conrad did visit Congo:
Eight and a half years before writing the book, Conrad had gone to serve as the captain of a Congo steamer. On arriving in the Congo, he found his steamer damaged and under repair. He became sick and returned to Europe before serving as captain.
http://en.wikipedia.org/wiki/Heart_of_Darkness
A good read: An Image of Africa: Racism in Conrad’s “Heart of Darkness”, by Chinua Achebe.
http://kirbyk.net/hod/image.of.africa.html
There is a distinct cultural differance between sub Sahara Africa and North Africa.Some one in here had an argument with me a long time ago, I was telling him there is a distinctive cultural way that drums are played and the dances are done , that seperate sub Sahara Africa from North Africa. I proceeded to bring in youtubes from various areas of sub Sahara Africa with very similar concepts in drumming and dancing. Let me make it clear that Im absolutly not saying all the drumming and dancing are the same. Its the basic pollyrhythmic concepts that are the same. The same way we can say Europe evolved harmony and classical music symphonies even though they are from differant countries that speak differant languages but Europe is where they evolved certain harmonic concepts. In that context you can say sub Sahara Africa evolved certain musical concepts.Ill be happy to bring in those youtubes again if anyone has any doubt that you cant quantify certain concepts of culture from sub Sahar Africa
Recently Ive been listening to a cd from Dudu Rose from Senegal. The drumming concepts are distinctive and recognisable. I have a record from the Congo also. It has very distintive charactoristics but the pollyrhythmic call responce is the same as Senegal. I saw an in depth docu of Uganda recently and some children preparing for a music fest with their drumming and dancing, distinct beats and dances but same concepts as the Congo and Senegal. I have youtubes of the same concepts from kids playing in Kenya, I think they are Kikuyu, you can look at Watusi cerimonies, Zulu cerimonies, I can go on and on and bring in examples. Besides Gnawa in Moroco, Id like to see some North African drumming and dancing that uses these same kind of pollyrhythmic , call responce, pelvic thrust, fast shuffle steps. Im sure they exist, but, Im not aware of them, I dont think north Egypt, Algeria, Tunisia, Moroco except for Gnawa, have those concepts as the dominant factor in their musical culture. Maybe Sudan and Ethiopia have some forms of the drumming, for sure you can really hear mixtures of both the Arab concepts and the sub Sahara drum dance concepts.
If someone can bring in a youtube to educate me , it would be welcome
As equaly frightening as outsiders thinking sub Sahara Africa is some horrible place compared to North Africa, would be denying the genius that is from the culture of sub Sahara Africa. That is extremly important to recognise the cultural gifts to the world that black sub Sahara Africa has been responsible for
To deny this genius fits right in with the broken Africa sterotype, especialy the broken black Africa stereotype
on Tue Apr 10th 2012 at 12:13:17 Adeen Danica Mckenzie
@B.R.
I agree. And why did they separate ”North Africa” from Sub Saharan Africa when both places are in Africa? If all the Blacks came from Sub Saharan Africa, how come supermodel Iman is from Somalia and Somalia is NOT in ”Sub Saharan Africa”. Iman is Black! Somalia is in North Central Africa. That Sub Saharan crap that is perpentrated in History and Geography is a lie. I think they split Africa in two to discredit Africa’s role in civilization and History.
No wonder Egypt is in ”North Africa”, because they weren’t ”Blacks” and couldn’t have possibly have built such an empire! I believe some of the Pharoahs were Black, yes but this foolishness has to stop. Blacks have contributed much to civilization and inventions as much as East Indians, Chinese, Europeans and others.
Adeen, Im in full agreement about any attemt to paint any part of Africa as less than or more backwards. And, I think the cultrual aspects Im talking aboiut dont address color in the sence that North Africa has a wide range of color.
I want to make it clear that I am addressing cultural concepts that most certainly came out of black Africans who have differant culturual concepts from Arabs that took over North Africa
And these cultural concepts are distinctive and can be quantified.
In North Africa, I suggest that there is a mixture of these concepts but the Arab concepts are more in effect in North Africa
Any body who knows a little bit about the various drum/dance concepts that dominate the Afro diasporic cultures throughout the Americas, can recognise the roots of those grooves right away in various sub Saharan drum dance cultures and you cant do that with North African musics
Or , please demonstrate it, because I can demonstrate with authority what Im talking about
this is differant from what I will bring in belowhttp://www.youtube.com/watch?v=YMHucmq7yBE
il try to linc the north African style again
this is differanthttp://www.youtube.com/watch?v=CozpRbD5sms
I mean anyone on here can hear the differance, right?
Its not color, its culture…
Also Im not sure about how one minute we are so firm that Africa is a continent of many countries and cultures and the next oh but its all one Africa…
I mean great about ideaologicy thought out intellectual arguments to counter stereotypes and western ignorance about real Africa, but please dont sweep in distnintive cutltrural differances that actualy point out to a genius of cultural value that is quantifiable and distinct from anythng else in the world
here is the gnawa from moroco that I said is more from a groove stanpoint. It is the exception of North Africa
It is obvious that in North Africa because of the Arab conquest that the Arab concepts of music are going to dominate, like I said this is somewhat of a an exception, but you sure can hear a differance from the youtube avove
As I said, Morroco is the country in North Africa that has good examples of the drum principles that come from the south. You have to look at how the dances hook up with the drums to really see the differance with the Morrocon concepts versus say concept you might find in Nigeria. Of course influences were going back and forth. Swahili had Arab influcence. Nigeria has some of the population muslim.
But this what what I consider a more North African feel
on Tue Apr 10th 2012 at 17:02:22 teddy1975
Well, the Sahara was a greater barrier than the Mediterranean Sea, which with ships and all was rather a way things could be transported, even the fauna and flora of Super-Saharan Africa have more in common with southern Europe than with Sub-Saharan Africa. The Islamic conquest really changed the way Europeans saw (North) Africans. Before that, that part of Africa was not seen as intrinsically different from the European parts and islands of the Mediterranean.
Here is the differace
Absolutly, Teddy, that is my point, there are concepts of life and how to aproach life that come from the middle of Africa down towards the south. Was it the Bantu migration ? I dont know or really think so, I think some of these drum dance concpets go back a long long time.
And, I think the fact that you can see the power in the Afro diasporic concepts, and how they absoutly dominate any country that brought slaves from the culture above, the Mali drumming, for example.
It is a power, a genius, it shouldnt be hidden behind other cultures like the Arab cultures, and the mixtures of those concepts,those are fantastic also, really fantastic. But these principles of life , and living, filtered sometimes through drumming /dancing, the inclination to use these drums and dances to turn off the thinking brain and get in touch with the intuition, need to be examined on their own terms for exacty what they represent and represent alone.
Especialy in light of scientific discoveries that prove that is what is happening in our everyday life anyway
It is that reason that I say there are instances that we can look at culture from sub Sahara Africa…I totaly agree that any point of veiw that choose to look at sub Sahara Africa as sub or worse off, or equal to misery is ridiculas. And again, like in the Congo, if you really begin to understand the humanity of the people, the contriburion their culture has made on the world, those stereotypes couldnt kick in
We have to make the culture as a focal part of what is incredible about all of Africa
Ok all of those sentances are not understandable:
And, I think the fact that you can see the power in the Afro diasporic concepts, and how they absoutly dominate any country that brought slaves from the culture above, the Mali drumming, for example (should continue on to say ) is a tremendous example of that power and genuius. Look how they groove the beat into the ground .
I get it now. I am sick of the false sterotypes about Africa and I really want to know the truth about Africa.
on Tue Apr 10th 2012 at 22:04:42 Dahoman X
Abagond already posted about Achebe’s response to Conrad
Abagond actually commented Achebe’s criticism of Conrad, but his post did not include a link to Achebe’s original article which, IMHO, is pertinent to the present thread. This article also further explores the 2 allegories mentioned by Sam: the one regarding the parallel Thames/Congo, and the one about the darkness inside Kurtz’ (the White man’s) heart.
@ Adeen
Somalia is located in East Africa and is considered part of sub Saharan Africa.
For some weird reason, you seem to infer from my post that:
1) I believe there is no difference between Northern and Southern Africa
2) I imply some kind of inferiority of the Southern part
3) I’m trying to hide it by stressing the “Arab” influence
If you actually read this in my comment, please re-read it. It is not what I wrote.
Northern Africa and Southern Africa have their own identities (notice the plural. None is monolithic). Yes, the Northern part, while very diverse, is culturally close to the Arabic Peninsula and the Middle East. I don’t deny that.
If you take a plane from Tunis to Lagos you will be shocked by the contrast and will feel like you stepped from a world to another.
But if you, say, travel by caravan from Tunis on the Mediterranean Sea to Lagos in the Gulf of Benin, you will have a very different experience. The transition will feel very progressive and you won’t be able to define a clear cut frontier between these two parts of the continent.
That’s because, contrary to what people commonly believe (see teddy1975’s post above) the people living along both banks of the Sahara have always interacted and influenced each other. They have never let the Sahara become a barrier. Quite the contrary, actually: during the past millennium it has been the place of the most dynamical trade routes of the continent, and of racial and cultural melting-pot.
And when I say they have interacted, when I say melting-pot, I don’t imply that it has always been kumbaya love between North Africa and Southern Africa, or between so-called “white” and “black” Africans (see the racist exactions currently going on in “liberated” Libya, for instance).
Regarding the polyrhythmic concepts.
I’ll have to trust your expertise on this, as I’m utterly illiterate in the matter.
I can appreciate good music though. I can’t really see your YouTube videos (slow connection here), but I recognize some names. Beside you cited Doudou Ndiaye Rose. Good pick.
on Tue Jul 17th 2012 at 01:46:31 Anomymous
I have more hope for Africa, than Haiti. However one of the main problem is the government and lack of unity, and initiatives. Africans are very divided. They are still too tribal (IMHO). Then there is the never ending political unrest etc….
If the Africans leaders were serious and there wasn’t all this division going on,then it would move forward in a faster fashion.
on Thu Jan 10th 2013 at 06:25:38 munu aka Bantu
I want to put my two cents to counter stereotypes about Africa in general and a few guidelines about how to look at African affairs:
1. As somebody said already, most stereotypes carry some truth with them; the question is, oft, of how can we expurgate them of implicit falsehoods; for example it’s truth that African governments are, in most cases, corrupt, but a) not all of them (I bet that the Botswana Government is one of the world’s most clean in that regard!) and the rest are corrupt in different degrees; b) outside the continent we find also many corrupt governments (in Latin America, South Asia or Eastern Europe, for example) and, therefore it’s false to draw the conclusion that corruption is kind of an African trademark alone;
2. Africa is a very diverse continent as Abagond has pointed out already (possibly the most diverse of them all!); there are many different countries there, and each of them is an unique “human experiment” by itself; you have different ancient histories from different places (from Yoruba kingdoms in one corner to Zulu warriors in another, and many other different narratives in between); you had different colonial powers in different places (English, Spanish, French, Portuguese, German, Belgian, etc) with different impacts (the different “official“ – European – languages” are a lasting testimony of that); you had different colonial settlements in different places (from none or few European settlers in places like Ethiopia, Somalia or Cameron to hundreds of thousands or millions in most Southern Africa countries and Algeria) and therefore you should expect different degrees of “European acculturation” in those places (in Maseru, Lesotho you will find that most native Africans communicate between themselves in a local African idiom most of the time, but in Maputo or Luanda people opt to use Portuguese as their “lingua franca”)
3. The diversity of situations in Africa is also clear in terms of economic development; from small economies as in the Sao Tome e Principe islands to the relatively highly developed economy and infrastructure as in the Republic of South Africa, which consumes more energy per year than highly industrialized countries like Netherlands or Sweden, you find a large spectrum of all different levels of economic development; a curious fact about the perception of long term economic prospects of Africa is that a few years ago the keyword was “afro pessimism” but now some economists start to look at Africa as the next large emerging market after China and India and they cite the present high grow rates in many African countries as an early indication of that; a more sober and balanced view would be to look at African economies as “developing economies” meaning that they are “yet to mature organic systems” that appear now in a yet relatively young phase of their development; as with humans, adulthood will surely follow the young age, but the journey from one point to the other will be a zigzag of advances and setbacks; so it’s life!
4. Diversity is also to be found in the level of economic development inside each African country; you have the striking divide between the urban (more developed and westernized) and the rural (less developed and more traditional); urban settlements show also a divide between their more developed center and their less developed periphery (shanty towns); there are also oft regional differences (for example the southern part of Mozambique is more developed than the northern part; the same can be said about Nigeria); these features characterize all developing countries including the ones in South America and Asia.
5. Each African country is also a diverse place as a consequence of recent history; the borders of most African states – defined by European powers at the begin of the 20th century – encompass a huge variety of ethnic groups (the so called “tribes”); this is sometimes the cause of internal strife and political instability but when properly managed is the foundation upon which a very rich cultural heritage can develop; one of the functions of the state in Africa is to build the nation from the amalgamation of those diverse groups, contrary to 19th century European states which were, for the most part, mono-ethnic; there are, also, some African mono-ethnic states such as Botswana, Lesotho or Swaziland; this kind of diversity implies that most Africans speak at least 2 languages (one African idiom plus the official European idiom…) and oft even 3 (…plus one more African idiom; this is the case in many urban settings where people from different ethnic backgrounds coexist).
6. Last but not least, the reality of African societies is very fluid and what is true now can change tomorrow behind recognition. This is, in fact, what makes many stereotypes not stand to a close scrutiny: the reality they were supposed to describe oft has already changed when you present them! A few examples: a decade ago it was said that most of Africa (except a few countries) had a very low density of telephone lines and this was seen as a major stumbling block against social and economic progress; today, after a rapid penetration of mobile telephone networks, all over Africa, its citizens are reasonably well connected. It is known that libraries and access to books are in short supply in many African societies and that impacts negatively teaching and learning activities. But as I write, we are witnessing a remarkable grow in Internet access (yet to mature) which can open, in the coming years, the access to universal human knowledge (written documents) to a much wider class of African citizens. More, a decade ago you would see a serene traffic atmosphere in the streets of Maputo and other Mozambican cities. Today, after an explosive grow of the number of car owners, during the past decade, we witness major traffic congestion in their urban settlements which are, therefore, forced to expand their limits outwards and densify their road networks. Twenty years ago we had merely 3 institutions of higher learning in Mozambique enrolling a few thousands students, but now we have more than 30 such institutions which graduate thousands of young (and not so young!) people every year. The same trends you can watch in many other African societies. Many such developments are not an end by themselves, but form a basis for future social and economic progress. Finally, I cannot end without mentioning that all those trends are turning into a reality the emergence of a middle class, in not few African societies, which are gradually overcoming the old motto that says that in Africa either you are (very) rich or (very) poor.
munu aka Bantu
At the 80’s I was in Germany to study and soon it became clear to me that most people there had little to no knowledge about Africa, and from that fact followed a lot of false assumptions and misunderstandings about the continent and its people.
Stereotypes thrive in an environment of ignorance. In most cases it is less a question of malice, and more of lack of knowledge of the facts. This is my opinion.
Therefore the best antidote against stereotypes is to put the facts before people so that they can review their perceptions by themselves.
At that time, I wrote letters to my brothers asking them to send to me dozens of postcards with diverse motifs reflecting life in my country. And I showed them to my German colleagues. I can bear witness to the fact that many of them became, after that, more curious about my “heimat” and, not few, changed radically their view of it.
Today it should be easy for anyone to do the same at a lower cost: you can search through the Web and collect photos and video-clips which show how things are in your country. Or you can upload your own items to your blog or site. It is that easy! And if we, as Africans, don’t do that, then we must bear some of the guilt for the current situation where most people living outside Africa rate the continent much lower than it should be!
Not only Whites who never visited the continent but also Asians, American and European Blacks, and even first generation children of Africans in the Diaspora share those misconceptions. Even worse: often you discover that Africans themselves don’t question such stereotypes when they think about other African nations, sometimes even neighbor countries.
We should do better about this and surely we can!
on Thu Jan 10th 2013 at 14:01:43 Kwamla
@ munu aka Bantu
Thank you for your informed and much needed perspective on the changing and ever developing continent we label Africa.
I for one enjoyed these far more enlightend contributions.
on Wed Jan 16th 2013 at 03:31:03 munu aka Bantu
Kwamla
To close my contributions on this topic of “broken Africa stereotype” let’s show some images of the continent.
I will put some links to web-pages with pictures and video-clips about two places from the eastern part of Africa: Nairobi and Maputo. The former is well-known in many quarters as a beautiful urban setting in Africa, kind of a mini New York of sorts, and the later is my birthplace and, as an American visitor once put it, “one of the most underrated tourist destinations in Africa”.
Let’s begin with Maputo:
Video-clip (taken in the central areas of the city)
• http://www.facebook.com/photo.php?v=373682379318444&set=vb.243802292315574&type=2&permPage=1 (this clip gives a glimpse of the cosmopolitan atmosphere in Maputo)
Photos (taken in the centre of the city)
• http://www.skyscrapercity.com/showthread.php?t=1446879&page=4
on Thu Jan 17th 2013 at 21:49:45 abagond
From munu aka Bantu:
… About Nairobi:
· http://www.youtube.com/watch?v=HyNztfyen7Q (this clip looks at middle class Nairobi life)
· http://www.nairaland.com/51356/nairobi-photos-kenya-beautiful-east
I hope this helps people to review their stereotypes about Africa.
Perhaps, the continent is not “so broken”, after all!
Here is the BBC’s top picture of Nairobi on Google Images:
on Thu Jan 17th 2013 at 22:44:57 Jorbia
Well,if Africa is so broken, why are so many Europeans living there? Many Europeans who live in Africa for a while never want to leave. If they can, they will go back there to live, even if it’s after they retire.
My parents have European friends who went to East Africa when they were adults but call Kenya and Tanzania “home.”
on Sat Jul 27th 2013 at 15:48:16 Shefali
Thank you for posting this. This and the comments are so informative.
One thing to think about re. black IQs – even if IQs are lower in the third world, it is known that malnutrition adversely affects IQs, into the third or fourth generation. So solve the issue of hunger, and the IQ problem would also be resolved, IMHO.
on Thu Aug 15th 2013 at 23:30:11 Colorful Exchange with Lefties and Race Addicts (It’s like dances with wolves, only wolves are smarter) | Praetori
[…] tried elsewhere to give, what I think is, a more balanced overview of Africa. See: https://abagond.wordpress.com/2012/03/13/the-broken-africa-stereotype/#comment-156161 If you want to discuss those issues with me, I would suggest you comment at those aforementioned […]
on Tue Sep 17th 2013 at 06:02:29 ACurious Youngin
Sub-Saharan Africa is the most genetically/phenotypically heterozygous continent and the origin of modern Homo Sapiens. Most racists believe that the regions lack of centralization until 1800s show some sort of failure. They first believe in this false Eurocentric myth that civilization arose there indigenously and not imported from the Middle east and think they have the right to criticize other cultures for lack of writing or urban stimulus for technology yet ITSELF did not invent neither of these things. Secondly, racists falsely believe that the determinants of civilization depend on some genetically conditioned intelligence(guess that makes Europe stupid then). The latter view distorts history and makes Civilization seem like it is a phenomenon that only the group based intelligent can accomplish. For starters, there is no such thing as a ” Group” IQ instead intelligence goes by a bell curve with 15 % between “races” and 85 % within these “races”. There is Within population genetic diversity in every Human population and is expressed highest, as said, in Sub-Saharan Africa, so the concept of a “Universal IQ” seems ludicrous. Furthermore, if genetic variation ,according to racists, determine ability in intelligence and innovation solely, if at all, that would mean that Sub-Saharan Africa and recent diaspora have the highest in both extreme outliers, in other words, the ability to make 2X scientific/technological innovations , in terms of quality. However, at the moment that is not observed, meaning their is more to innovation or civilization than genetics which does not play a major factor (at least evidently) in the divergence of the Mother continent from that of the prehistoric diaspora. According to most anthropologists, there were only six areas that had the requirements that others did not that enabled civilization ; a river valley located in a soft fertile region. The belief in “Anthrocentrism” is what fuels racism in the first place, the thought that Man is God therefore can control every aspect of its progress and those behind are the least “fittest” which is untrue. We are subject to are environment no matter how genetically “superior” or competent we may supposedly be. From the six areas, civilization spread to those that were less efficient reaching Northern Europe(400 AD) and Sub Saharan Africa in several eras; Axum/Ethiopia (400 BCE); Islamic SSA (1000 AD); the rest of Africa (1800s AD). In the former two eras, Africa rose to significance such as in Pastoralist but Imperial Axum, a military power equal to Rome or China emerged according to contemporary prophet Mani or during Songhai dynasty where scholars in a salt (or iodine) depreciated but wealthy region were able to be great leaders in Islamic literature ( Mathematics, Astronomy, History,etc.) and Law. In the latter era, however nothing but destruction was brought from slavery to colonialism to modern exploitation nothing but disaster has befallen SSA forming the modern stereotype which was not far from the truth. In modern times, however, this is not accurate as Sub-Saharan Africa has the world’s fastest growing economies and is predicted by economics to reach 29 trillion USD by 2050,larger than USA and Eurozone combined and definitely larger than United states of America and Europe separately. Sub-Saharan Africa would have gotten back in its feet sooner had not 1.4 trillion USD not been transferred illegally largely to the west, that’s more than the ODA that racists complain about being paid. If anything ODA should be seen as the West paying debt to Sub-Saharan Africa like they are to the Peoples Republic of China. So this stereotype of Africa is long overdue and blasted to make racists feel like “at least the Negros are still down” as we enter a multipolar world;no longer “white man’s Burden”. Deny or envy, but Sub Saharan Africa is getting up in the world. Look for example at Luanda in Angola, it has a booming luxurious industry but they never show you that… they’ll never tell you this ^. I don’t blame them, it is the responsibility for an Afro-descendant to know their history, struggles, progress, and future not the American Western Media, their purpose is to distort, degrade, dehumanize, to erase any sense of hope in an African so that all is left is a empty vessel, a Slave…No more.
See: Get Ready for an African boom/CNN
http://www.google.com/imgres?um=1&hl=en&biw=1366&bih=768&tbm=isch&tbnid=GzgEOtFEwhoNXM:&imgrefurl=http://hotelpresidenteluanda.com/presidente/en/hotel/lazer&docid=omRZdruSt2n26M&imgurl=http://hotelpresidenteluanda.com/site_images/contents/contents/225/page/Luanda.jpg%253F1304523299&w=990&h=600&ei=Y-83UtXyOKrC4APAx4DQBg&zoom=1&ved=1t:3588,r:6,s:0,i:97&iact=rc&page=1&tbnh=175&tbnw=254&start=0&ndsp=15&tx=161&ty=155
(https://www.youtube.com/watch?v=R8DjO8FHj3Y)
@Shefali I do believe malnutrition in Sub-Saharan Africa and its diaspora is preventing it from reaching full potential such that micronutrients like Iodine and iron alone can cost 15 IQ points and 14.8 IQ points respectively along with the effects of others micronutrient deficiency as well as rampant poverty. As I said, the diaspora is also going through this with African American mothers giving birth iodine deficient on average since 1900s. That’s 15 IQ points right there and the Flynn effect has been explained based on micronutrient deficiency( Iodine for instance). In the Western world, the introduction of iodine to Whites via lactose dairy products allowed the IQ to rise to 15 IQ points during the 1900s.
see: http://www.businessinsider.com/iodization-effect-on-iq-2013-7
omg i am so sick of the united states i can’t wait to go over ther to africa
on Wed Aug 20th 2014 at 22:23:50 Legion
(http://youtu.be/5utDdxveaJc)
Trotting out “the children” is always a good say to say shut up! I’m very suspicious of Gates here.
Moyo’s response:
http://www.dambisamoyo.com/?post=dr-dambisa-moyo-responds-to-bill-gates-personal-attacks
on Sat Aug 30th 2014 at 19:38:15 Broken Records: Arguments About Race | Marmalade
[…] The Broken Africa stereotype – Africa is a hellhole […]
on Sun Oct 4th 2015 at 14:33:22 EPGAH
How did whites “break the continent”? Did you forget empires like the Oyo, and even the NIGER EMPIRE starting slavery, then Arab slavers, THEN AND ONLY THEN the whites? We tried to rebuild things. Shining cities, safe countries, rule of law, etc.
If you want to say Mugabe is “just a madman”, that would imply he’s the exception. What about Mandela, Zuma, Shaka Zulu, Idi Amin?
If a group keeps having “exceptions”, they stop being the “exception”, and start being the rule.
Sort of like how the Moslem Cult is associated with terrorism, and even the “moderates” are in favor of forcing Sharia Law on anyone naive enough to let them in?
Even when shown a picture of shining white houses in “Africa”, as I was recently shown to try to shut me up, it was NIGERIA, who are up to their old thieving tricks, AND getting money and infrastructure from CHINA!
Why can’t Africa do on its own, without another group building FOR them and FORCING Order on them?
on Sun Oct 4th 2015 at 15:11:33 sharinalr
@EPGAH
tsk tsk tsk. Oyo, Niger, and Arabs did not start slavery. Your precious slavery was in full effect for years. Used by all. Greeks and Romans alike used slavery. Then along came Whites or Americans if you like who needed new slaves. Whites did not try to rebuild things. They destroyed it. They came and stole any and everything they could from Africa. Did that for years. They created laws that benefited them. Destroyed cities that were already there and replaced them with their own. Laid claim to the ones they liked.
“Sort of like how the Moslem Cult is associated with terrorism, and even the “moderates” are in favor of forcing Sharia Law on anyone naive enough to let them in?”—Claims that require proof. So far this is talk of a mad man.
“Even when shown a picture of shining white houses in “Africa”, as I was recently shown to try to shut me up, it was NIGERIA, who are up to their old thieving tricks, AND getting money and infrastructure from CHINA!”—It was not used to shut you up. It was used to make you look like the fool you are. While you are trying to find some nitch to say how bad Africa is, there are several other cities just like it. Not to mention you made yet another claim your a*** seems to be unable to cash. You claimed there were no such cities that made it. Now you want to whine about how they made it. Yet according to YOU making it entails thievery. So why be made because they are taking a page out of the white play book?
“Why can’t Africa do on its own, without another group building FOR them and FORCING Order on them?”—I would ask the same things about white America, but you are a hypocrite so. At any rate China did nothing more than invest. After investments it takes drives and work to run the businesses to build from that point on. So in short they are doing it by themselves. Just like they are doing it by themselves when they come to america and make your young white children look dumb.
on Sun Oct 4th 2015 at 15:31:05 Michael Jon Barker
@ sharinalr.
A shout out to you for having the patience in dealing with EPGAH. Whatever BS he comes up with you have effectively shot it down.
I’m unable to have civil conversations with people like EPGAH.
His world view is no different then Roofs so he comes here to shoot this place up. To him his views are his religion.
on Sun Oct 4th 2015 at 15:32:30 King
“Even when shown a picture of shining white houses in “Africa”, as I was recently shown to try to shut me up, it was NIGERIA, who are up to their old thieving tricks, AND getting money and infrastructure from CHINA
It would be interesting to hear how Nigeria could possibly be “stealing” from the larger and more powerful China?
One might ask why the backward northern barbarians could not do on their own without the Romans building FOR them, assimilating them, and FORCING order upon them. You know… the Visigoths, the Ostrogoths, the Burgundians, the Franks, the Britons, theVandals… in other words, YOU.
on Sun Oct 4th 2015 at 15:39:04 taotesan
@mike4ty4
“ and this is exactly why I have so much discomfort with the idea of a so-called “white African”. How can “whites” be truly called “African” when they, or at least most of them, benefit from educational, wealth and land ownership, and social privileges that have yet to be afforded to the people who have been in Africa for tens or even hundreds of thousands of years longer than their families have ever been, not to mention it is questionable how much cultural assimilation they have undergone?”
This is my take on ‘white Africans’ in the South African context. It is quite long. Apology.
I do not speak as political analyst, but from a personal broad-based perspective.Being veteran grandmaster thieves of land, this latest development of linguistic contortionism is the refinement of their delusion of white superiority complex and greedy-guts syndrome. These people, including the liberals (we did not know it was wrong to hate Black people, we were only taught to) who owns land that is simply not his or hers, if they are such lovely non-racist Africans, they must give us back our land. I am not sure the time when Black people said: “Here, Baas, take our land, we love living in matchboxes. You are so good.” To be called a white ‘African’ (writing this hurts me) ties in, not with any nationalist, patriotic or any romantic notion, but with their unbridled capitalistic rapacity and their perverted ideology that they are God’s chosen people (Afrikaners) so they are entitled to all our land.
In South Africa, we have Black Economic Empowerment, aka BEE, a program (which is failing dismally) to redress the iniquitous economic disparity wrought on the natural inhabitants by centuries of genocide, slavery, cultural annihilation, land dispossession, colonialism, apartheid and neo-colonialism. Now the very beneficiaries of slavery, colonialism and apartheid, want to insist upon South Africans that they are Africans so that they can continue being first in line, as usual. They just have to be OWNERS. They have to own everything, including their victims’ name and land. So, being a white ‘African’ would tie them to the right to lay claim to mineral rights, economic opportunities and to hold on to land claims.
Not so long ago when these people had their very own nirvana, (and they still do, for the most part) they made up the most crude and de-humanising names for African people. Remember, apartheid was supposed to be forever. Every single facet life of a South Black person’s life was/is still dominated and poisoned by white superiority. As a person who is still trying to heal very deep wounds (and trying hard to forget) from apartheid, I remember how my parents were forced to bow their heads to white people, who insisted they be called ‘baas’ or ‘missus’- master and madam in Afrikaans. [Both of them eventually died from a broken heart.]
The ‘master race’ – the European, in their utopia, subjected the natural inhabitants to unspeakable and intolerable cruelty and made sure that we knew that they were Europeans or whites, who were the acme of civilization. The humiliation of the ubiquitous apartheid signs. Almost ALL of our rivers, mountains, seas, plants, animals and place names are European or British named. They called themselves Europeans and whites interchangeably. Google the apartheid signs.
In their ugly madness they have no insight when they nakedly accuse the victims of their oppression as racist, when we refuse to acknowledge them as Africans. The temerity of these ungrateful gate-crashers. They are not Africans. They are white South Africans. Or European descendants / settlers/ invaders/ living in South Africa.
The African name has been most reviled by the same white man and woman who wants to be included as African for capitalistic, neo-colonialist motives, and further perpetuating their economic dominance in the midst of their manufactured poverty. It also kills two birds with one stone: they can claim victimhood (and what loud moaning Charlies they are) and exonerate them from their complicity in apartheid. But they do that anyway.
In South Africa, they create websites exaggerating the number of farm murders and crying foul that a ‘genocide’ has been committed against them. Understand it is the very people who make/made Black people feel like criminals just for being Black. Although we do not have formal slavery, these Afrikaner farmers (owning millions of hectares of stolen African land) treat their workers sadistically and still pay them a pittance, where they have they still have very little recourse to the law. These wannabe ‘Africans’ have now overwhelmingly denied that apartheid was a crime against humanity.
The deafening silence of the European colonialist has not been punctured by even a susurration of admittance or half an apology. Because they are not sorry.
Whites are symbiotes not parasites…Or at least were.
We built and let anyone in WHO WOULD OBEY THE RULES! “You are welcome to join us, but you will not lead!”
What group doesn’t pass laws that benefit themselves?
I asked you that in another thread, plus asking what nonwhite group passes laws like Affirmative Action, that benefit non-self, at self’s expense. Got no answer so far. Is that a claim every white hater’s a*** are unable to cash?
We have a mediocracy now, because it’s what gets rewarded. I’ll be the first to say Ob-America is an Obamination compared to 80s America. But that is a derail, because it’s all about WHITES instead of Blacks, much less Africa.
http://dailycaller.com/2013/05/01/nine-things-youll-learn-from-pews-poll-of-the-worlds-muslims/
If you prefer, rather than linking, I can copy&paste the whole article, rather than a link? Not sure what your policy is on copy&paste plagiarism.
Did you ever use your favorite search engine and look up the Moslem “refugees” trying to cancel Germany’s Octoberfest, because beer&boobs are offensive to them? I use the quotes, because true refugees would NOT be trying to change their hosts, they’d be thankful their hosts are protecting them from whatever they’re fleeing! Maybe not kissing ass, but at LEAST keeping a low profile and causing as little problems as they could?
South Africa (and others) were under Civilized World control. It put an END to tribes and their petty bickering. It put an end to Shaka Zulu’s “knocking”. (One of those genocides everyone forgets because it wasn’t committed by whites).
It was an idyllic scene straight from the Mythical 1950s!
Important detail: WHITES built that, not the savages. THEY DIDN’T MAKE THAT, WE DID! Mugabe’s “palace” is actually an old white farmers’ house that was stolen!
Savages came in, “Only To Work”, then once they were the majority in the whites’ country, they overthrew and destroyed it. How is that from whites’ playbook? Actually, that sounds more like the Mexican Scam!
Whites never wanted, nor even pretended to want, to JOIN savages’ savagery, buy land, kick them aside and build civilization seems to be our historical path.
Just for clarification: When the savages got control, whom did the laws they pass benefit? Particularly BEE, the exact inverse of our Affirmative Action?
In America, Government forces Black MINORITY into undeserved jobs.
In South Africa (Savage control), Government forces Black MAJORITY into undeserved jobs.
See how that works? A certain asymmetry and/or lack of charity there!
America wasn’t the one that got order forced on us. From the 1800s to let’s say 1964, we have been the enforcer of order. It wasn’t Britain or France that put the Barbary Pirates down…It was America. Britain could’ve stopped the Japanese carrier group that did Pearl Harbor. They didn’t because they WANTED America in the fight. Why?
Everyone “hates” us, sure, but when they have a flood, tsunami, earthquake, or riot, it isn’t CHINA they call for help. Why is that? Is that a long-con plan to drain us of our resources? Are we chivalrous or chumps for always helping others, even our enemies (Like Afghanistan) whenever they call?
China didn’t just invest. China (re)built the country, in exchange for resources. Just like whites did! So why are Chinese “Noble” for doing this, but whites are “evil colonialists” for the same thing?
China is building the country in exchange for resources.
China is “helping”.
Whites did the same thing, but whites are the “evil colonialists”.
Eventually, the savages turned on whites, stole and ruined the country.
Do you think China will let the savages pull that same stunt?
Keep in mind our divergent responses to riots in our own country.
America gives savages “Space To Destroy”, China sent a TANK to stop the party!
What do you consider Romans if not white? Were they Black? Arab? Space aliens?
@Michael Jon Barker
Thanks. That is because he is a big joke. Laugh at him and even you will have the patience.
taotesan
By that “logic”, Blacks in America should be called something else, and if they get “too rich” in our country, they should be murdered and their property stolen, just like the savages did–AND STILL DO–to landowners and farmers in South Africa and elsewhere?
“Kill The Boer Kill The Farmer” vs…Hm, we don’t have a “Kill The Savage” movement here in America, do we?
Of course whites would be owners, whites built the country.
Blacks came in only to work. That “pittance” you call it, was WAY more than they could get under their fellow savages. Once again, why come INTO a place if you’re so ill-treated? Find out if the border is just as permeable the opposite direction!
Have you done any searches on what the savages did to the people who built up a better country that they could live in if they could behave?
Did you ever consider Apartheid was to PREVENT exactly what the savages did when they got weapons from Russia and overran our control?
Google “Farmers killed by machete” and take a REAL wild guess why they don’t consider Apartheid a bad thing. Hint: Your deep EMO wounds are nothing compared to what the savages did to the whites, then stole their land/farm/business to add insult to LITERAL injury!
To wit: If you are violent and untrustworthy (Savage), why not keep you away from us?
As to education, look at the fantastic schools and universities whites built even in the areas they set aside for savages. They didn’t HAVE to do that! They could’ve said, “That side is your side, be as Savage As You Wanna Be”
How DID you learn English anyways, if not taught by the Civilized World?
Did you butcher a human, eat his brain, and absorb the knowledge that way? I thought that only worked in videogames!
As to wealth, you’re right, but whites figured out how to make resources into wealth. That’s why “make money” is an American/European idiom that does NOT mean counterfeiting.
As to land ownership, once again, whites brought the CONCEPT of land tenure there. “This Area Is Ours. Period.” not “Oh, we lay claim to this vast strip, but we’ll keep going back and forth along it like a toy train”
Even now, YOU call the land they own “stolen”, and look the other way, if not cheer, when savages brutally murder them and steal what they built and EARNED, right?
Is that not greedy gutting? (Literally!) Are they made to feel like criminals for being Black or for what they did to the people who built the country?
How many decades are you going to keep pretending to be victims? You killed them, you stole the country, what are you going to do with it? Make it crash&burn, then blame the whites, right? Kinda like someone carjacking me, killing me, then wrapping my car around the nearest utility pole, and blaming ME for not teaching them to drive before they killed me, right?
Michael Jon Barker
Right, ROOF is the threat, not Farrakhan, or Noble, or Kambon, or any of the other savages exhorting the extermination of whites, especially cops?
You don’t see how those two are opposite, but not equal? Farrakhan&co would NEVER dirty their hands by killing a white themselves. They enjoy the luxury of the Civilized World too much. All they’re doing is free speech, right?
“You want freedom? You’re gonna have to kill some crackers! You’re gonna have to kill some of their babies!”
Those were the words of Minister King Samir Shabazz, also known as Maurice Heath, the New Black Panther Party’s Philadelphia leader.
Shabazz is the same man the Holder Department of Justice refused to prosecute after he was filmed on Election Day 2008 with Jerry Jackson wearing paramilitary uniforms, carrying a nightstick and blocking a doorway to a polling location to intimidate voters.
Is their hate their religion too?
small person shout at the warden and tell to loosen your straight-jacket
on Sun Oct 4th 2015 at 16:14:06 v8driver
Awkward! I guess there was a bit of antiamerican sentiment in my part uf u scroll back abit but thats under the category of no way to explain that to the kids that live actually near me
on Sun Oct 4th 2015 at 16:14:29 Omnipresent
EPGAH
What do these savages look like?
^him and whilst you are at it insist on better padding
on Sun Oct 4th 2015 at 16:19:10 Uglyblackjohn
@ EPGAH – But the Africans are wrong for taking over an existing culture? Isn’t that their manifest destiny?
Didn’t most white people end up on other continents in an effort to escape oppression by other white people?
As to views as religion, even here on this very site, some Blacks claim that whites are not human, or in this very thread, one claims we who created the country don’t deserve to enjoy it, so which “religion” do you think is more harmful?
“WE SEE THEM AS HUMAN, THEY LOOK LIKE REAL HUMANS BUT THEY ARE NOT, THEY DO NOT HAVE HUE TO BE MAN.”
HUE-MAN? Sounds like a He-Man villain.
v8driver I don’t blame you at all. You want to escape America to escape your ex-wife.
taoetesan
You justify BEE–Government forcing Blacks into undeserved positions–but isn’t that just the savages, now that they’re in control, passing laws to benefit THEM? Where is their generosity, like whites passing Affirmative Action, laws that harm us, and benefit not-us?
Savages are selfish, whites are generous.
“what nonwhite group passes laws like Affirmative Action, that benefit non-self, at self’s expense. Got no answer so far. Is that a claim every white hater’s a*** are unable to cash?”—That is not the question you asked, but I will quote what you did say so you can stop pretending like you are not goal post shifting when you are. Your original response got an answer. You just did not like it. As such AA actually benefits whites. Which is why they are the biggest benefactors/supporters of it. You need to do research on what AA includes. Not just women but those with disabilities as well.
“If you prefer, rather than linking, I can copy&paste the whole article, rather than a link? Not sure what your policy is on copy&paste plagiarism.”—Two problems with your source. 1. It does not prove or support what you claimed above. 2. It managed to show no sample size. 3. It contradicts what you you claim. Ie In most the percentage of Muslim respondents who said they favor Shariah as the law of the land is 20 percent or lower.
“Important detail: WHITES built that, not the savages. THEY DIDN’T MAKE THAT, WE DID! Mugabe’s “palace” is actually an old white farmers’ house that was stolen!”—Sure and I am an Alien. I require proof. Not a mad man ranting. Even with sources you seem to be unable to realize what they say versus what you believe in your mad mind.
“Savages came in, “Only To Work”, then once they were the majority in the whites’ country, they overthrew and destroyed it. How is that from whites’ playbook? “—How can they come in to land that was already theirs? News flash they can’t. So based on your logic the savages are the whites who came in to “work” and steal and when they became the majority they overthrew and destroyed. Copy that to the situation in America and you have successfully described how everyone took a page from the white playbook.
“Everyone “hates” us, sure, but when they have a flood, tsunami, earthquake, or riot, it isn’t CHINA they call for help.”—You might want to talk to some of those people. They don’t beg for America’s help as the media likes to tell. In fact I have ran across a great deal that would like america to stay out simply because America uses it’s “Help” to build strongholds in their countries.
“China didn’t just invest. China (re)built the country, in exchange for resources. Just like whites did! So why are Chinese “Noble” for doing this, but whites are “evil colonialists” for the same thing?”—Whites did not invest in the country. They simply took. Big difference.
@ EPGAH
That is quid pro quo, or as we like to call it, “doing business.” Each party agrees that the other party has something of value to offer. An exchange is driven, and both parties benefit. Neither party is “stealing” as you have so recklessly suggested.
No, I think not. Whites did not sit down with Africans and hammer out a quid pro quo. Whites simply stole the land and resources by annexing them by force. They did the same in India and later, in China. Whites essentially carved up Africa into colonies as they pleased… which I assume is why they were called “evil colonialists.” To the thinking man, this makes perfect sense.
https://qph.is.quoracdn.net/main-qimg-1e0eaaa410d48dc9e428825b11643bad?convert_to_webp=true
Uglyblackjohn
Well, you COULD say whites LEFT if they didn’t like it! Which was my message on one of the other threads. If I DO have a flaw, it’s that I’m too subtle for most people to get the message.
Whites’ flaw is suicidal altruism. Woman and the snake, Frog&scorpion, whatever. But I digress.
But actually, no, most white countries/colonies/whatever you want to call it is because whites, once we had the wherewithal to, are explorers.
Is there really an “edge of the world”? Is the Sound Barrier real? Is the sky really the limit?
If you’re trying to draw an equal sign between conquests, I have to put a big old NO on that one too. Which group made a BETTER, SAFER, MORE LAW-ABIDING country, and which one made Purgatory on Earth?
Or let’s talk about EARNING?
Which one did it all on their own, and which one needed Russian weapons to overthrow civilization? And now needs constant investment from China?
“Which one did it all on their own, and which one needed Russian weapons to overthrow civilization? And now needs constant investment from China?”—America.
For everything he is trying to say about Africa, I realize he is actually talking about America. ROFL
sharinalr
http://www.reuters.com/article/2015/09/21/us-safrica-mugabe-idUSKCN0RL19P20150921
Let’s start with this one?
South Africa ruled that Mugabe has to give back ONE stolen residential property.
I don’t know how jurisdiction works there, that would be like France making Spain return something they stole.
http://www.telegraph.co.uk/active/11442408/Zimbabwes-white-farmers-targeted-for-new-Mugabe-land-grabs.html
MORE stealing from white farmers. I am shocked! Or at least pretending really really hard to be shocked!
News flash: It WASN’T their land, they didn’t have the concept of land tenure. So it’s NOT theirs! Another poster in this thread put up a map of who owned what. Whites–at least British and Dutch–set aside Reservations for the savages. Savages eschewed that and wanted the whites’ part!
If I let you live in my basement, would you kill me and take over the upper floors of my house?
The whites didn’t come there to work, they BUILT THE COUNTRY! It was their work that made the country worth savages immigrating/invading!
What the savages did is something akin to what I believe Mexicans are trying to do to America.
And South Africa is an EXTRA special case, it was too desert, too inhospitable for even the SAVAGES to want to live there!
So if you throw something away, I take it, recondition it into a gleaming (or at least serviceable) prize, you don’t get to say “I want it back, it’s mine.”
They terraformed it into something worth living in, that’s why the savages wanted it. That, or thriving farms and businesses, electric and road infrastructure, things worth stealing.
I’m sorry, building a whole country from scratch is not investing?
It WAS quid pro quo: WE build a country, savages could live there if they wanted a Better Standard of Living, otherwise, they could get out of the way.
But now the savages have their Wish! They are reduced to a paltry minority in their own countries, if not entirely left or dead (Which is “gone” in the metaphysical sense).
Being our Noble EQUALS, why didn’t the savages build or at least maintain a country every bit as shiny as when the whites controlled it? Why did they NEED China to build infrastructure FOR them? Whites already built the infrastructure, what happened to that infrastructure?
Did whites rip it out with their dying breaths?
Did the savages destroy it because it was a reminder of Civilized World control?
Did they just let it decay because they didn’t know how to maintain it?
@epgah, at that point i was considering moving to lesotho/south africa
America has always been independent by nature. In the last 60 years, we undid our isolationism, which is a large part of the end of my parents’ mythical 50s.
Russia has never given us anything but grief. In the 90s, there was an attempt at reconciliation–and we even bailed them out when they collapsed–but even if Gorbachev was 100% sincere and honest, the long-term effect was that it was just for them to get closer to stick a bigger blade in Uncle Sam’s back.
If you want to borrow King’s thing about a give&take, so far, America’s been doing all the Giving, and Russia is not the least of countries doing all the TAKING! Most egregiously, America GAVE up our anti-nuke project in Poland.
If we hadn’t, Iran’s PROMISE (And probable LIE) about not building nukes wouldn’t matter. They would stay peaceful, because if they weren’t, we’d shoot their nukes out of the sky and return fire.
If Russia FELT it was aimed at them, only the hit dog squeals, right?
What might Russia be doing that an anti-nuke system would thwart?
That is not quid pro quo. Look up the word first before you…..nevermind.
“Being our Noble EQUALS, why didn’t the savages build or at least maintain a country every bit as shiny as when the whites controlled it? Why did they NEED China to build infrastructure FOR them?”—They had. This is the part of the story where the whites come in and destroy it.
“America has always been independent by nature.”—False. Even coming to this land “Americans” were dependent on the help of natives. Otherwise they would have died. Years fast forward they became dependent on the funds of other countries. You forget this country is in debt. We are dependent on foreign oil. Should I continue on this dependency?
I don’t see where I mentioned Russia, but…..deflect on. You are good at that.
FYI my comment came before king so not sure how I borrowed anything from him, but great minds do think alike.
EPGAH, Whites did not “build a country” almost anywhere in Africa. What they built were a very few White cities/towns that were used as garrisons, colonizing centers, and hotels for the Whites who came and went. In all cases, the vast majority of the “country” was worse off after colonization then before colonization.
This idea that Whites built up these countries into shining African empires that were then taken over by ungrateful savages and ruined is more the result of you not reading books than reflective of any historical facts on the matter.
v8driver
That would kind of redefine “Out of the Frying Pan, Into The Fire”
(Capitalization?)
Unemployment has gotten worse, and the savages decided it wasn’t bad enough, so they passed BEE laws, so if you’re white and can’t buy your way into Orania, you can forget about it.
Also, savages with machetes are a constant problem, stealing from anyone who DOES make it. I’ve even heard rumors they have started attacking “too successful” blacks now, but that’s probably overblown.
You see all the houses with concrete corners and barbed wire? They’re not a WWII reenactment troop, they’re trying to ward off savages.
On the other hand, if you join a PMC, you can make serious bank protecting civilized from savage! Even some of the richer savages hire “consultants”, not bodyguards. The name-change is to avoid hypocrisy, of course!
Also, savages with machetes are a constant problem, stealing from anyone who DOES make it. I’ve even heard rumors they have started attacking “too successful” blacks now, but that’s probably overblown
Why is it overblown? Further upthread, I asked you what these savages look like. taotesan suggested they look like you but I don’t think you picture them that way.
If I DO have a flaw, it’s that I’m too subtle for most people to get the message.
I am sure you know what I am driving at here but, if you are ‘less subtle’ and actually honest, it will discredit all of your arguments on here and expose you so instead, you misrepresent things but what is underlying is not at all subtle
You said we were just the same as the savages taking help from Russia to overthrow and destroy. “A page from America’s book”, right?
quid pro quo is a TRADE. Doesn’t have to be a FAIR trade, even, it has to be PERCEIVED as a fair trade at the time.
What do others have to offer that is worth the upgrade in Standard of Living they would get by invading any place created by the Civilized World?
Yes, America TRADED food for protection. The savages didn’t give us food because they were feeling generous or some kind of Welfare project, it was because the Wampanoags were attacking them and they saw Salvation in our metal-and-GUNPOWDER weapons!
We beat the bullies down–then they turned on us!
I think I said that in another thread? Or you just weren’t listening.
Our dependence on foreign oil is a CHOICE. Environmental regs have choked off not only oil-drilling but smelting, manufacturing, all dirty industry.
Economy is less important than ecology, and we have the unemployment to prove it, right?
Of course, Obama claims it’s part of a “strategy” to have oil left when terrorists/Mexico/Canada run out. We suffer until they run out…Does this even “seem like a good idea at the time”?
There was a Faction in America’s RECENT history, say the last 10 years, that wanted eco-exemptions for “Drill Baby Drill”. Refresh my memory, were they praised or ridiculed?
“You said we were just the same as the savages taking help from Russia to overthrow and destroy. “A page from America’s book”, right?”—I didn’t mention Russia, so you basically are putting words in my mouth. The only thing I said from your quote was “A page from America’s book.”
“quid pro quo is a TRADE. Doesn’t have to be a FAIR trade, even, it has to be PERCEIVED as a fair trade at the time.”—Here is the definition of quid pro quo “Quid pro quo means an exchange of goods or services, where one transfer is contingent upon the other.” It requires a trade yes, but forcing a lifestyle on someone is not a trade. You have so far been describing a forced lifestyle on people. Not a quid pro quo. https://en.wikipedia.org/wiki/Quid_pro_quo
“Yes, America TRADED food for protection. “—Nope. Another snippet from your false history. They gave you food and taught you how to grow it. Among other things.
“I think I said that in another thread? Or you just weren’t listening.”—You claim to say a lot of things and when it comes to those things being quoted it turns out that is not what you even said. You make stuff up as you go as I did say and can quote time and date when I said it. Plus I can’t hear you through the computer screen.
“Our dependence on foreign oil is a CHOICE.”—If that is the lie you wish to tell yourself. If it was a choice the choose to drill oil on your own land or choose to make cars that don’t rely on it, but America can not fathom a life without oil. Primarily why the business is rolling in the dough. This quote is a prime example of that dependency “We suffer until they run out”. If you were not dependent on something you would not see it as suffering for not using it.
“There was a Faction in America’s RECENT history, say the last 10 years, that wanted eco-exemptions for “Drill Baby Drill”. Refresh my memory, were they praised or ridiculed?”—Don’t know and don’t care as to answer would give you another deflection route.
Why is it overblown? Because savages would NEVER attack their OWN for being too rich. This is about RACE and who BELONGS there, not who got rich and who didn’t, isn’t it?
They are trying to have the whites’ houses, businesses, and lifestyle, without the whites! Killing fellow savages would not advance this goal. They want a WHITE-free country, not a country purged of fellow savages!
Is that or is that not what is *underlying* the overthrow, no matter how nobly or subtly they may couch it?
Why IS it noble for savages to purge whites–EVEN FROM OUR OWN COUNTRIES–but whites purging savages are “madmen”? Even Hungary building a wall to keep savages OUT, rather than purge them, is considered worse than Mao and Hitler put together!
I picture them as Black, grinning evilly, a machete in one hand, and either a gun or a severed head “trophy” from a recent murder in the other.
Lions are actually more valuable than HUMAN lives to the savages. Which is why they were so tightly controlled when the Civilized World ran the place.
They somehow predicted savages would be savage (Definition: Primitive and violent), so they kept them separate to avoid trouble!
I’ve tried being less subtle but my comments keep getting deleted. Hilarious but unproductive.
What do you think I’ve “misrepresented”? I keep getting accused of moving the goalposts and similar, but I don’t see it.
“very few White cities/towns that were used as garrisons, colonizing centers, and hotels”
What do you consider a COUNTRY to be? Are they supposed to coat the whole place in concrete? Maybe Domed Cities with Cursed Earth between them?
America is generally considered a country, but there are large unoccupied areas, and other areas are over-occupied. Are the unoccupied areas NOT America? If so, why don’t illegals settle there and build their own civilization, rather than invade our ALREADY-BUILT CITIES and antagonize us by failing to observe our language and laws?
Furthermore, what determines ownership? Might Makes Right? Sheer Numbers? (Which is actually a variant, but let’s pretend it’s separate.) Borders and Laws? Or the people who BUILD the country, OWN the country?
I’ve read plenty of books about Rhodesia and South Africa, but it just doesn’t do it justice. When I actually was ASSIGNED there, I was shocked at how much worse it was than the books hinted at.
The books I read were
“Tell Me And I Shall Forget”
“Memoirs of a Traitor”
I also read some book I can’t remember the title of about Cargo Cults in Africa, far deadlier than their Asian counterparts.
After whites left, of course it’ll be worse! We raised their expectations! They’ve always HAD disease, starvation, death, and random violence, but now, because of Civilized World food, meds, and law-enforcement, they EXPECT not to! Somehow it becomes the whites’ fault the savages are dying. Our fault for letting them kill us, I guess, instead of developing bulletproof skin and machete-proof necks?
The underlying problem: They want the white lifestyle without the whites making it/making it possible! That’s where the “White Privilege” misconception comes from.
It’s like a child demanding more toys, more candy, believing the parents have or can buy it, and are just selfishly holding out on them. Someone slips the kid a gun, they shoot the parents, then find out the parents weren’t holding out, they really DIDN’T have it to give. And the kid can’t afford to buy more because anyone unscrupulous enough to HIRE a kid would CHEAT it!
In fact, that was almost verbatim the plot of the book about the African Cargo Cults. Whites were messengers from the Gods, sent to give the savages gifts, but when we stopped giving gifts, they thought we were HOLDING out rather than RAN out of gifts to give, so they killed us! Now THAT’S ungrateful!
“I keep getting accused of moving the goalposts and similar, but I don’t see it.”—You also don’t see what half of your sources say, so the idea that you don’t see it is inline with a lot of things you don’t see.
For example you claimed Africa never made it. Then when presented with a Pictures of Africa that has “made it” you change or switch goal posts to say they are thieves or scammers. This is goal post shifting and you have several across several threads.
China is heavily involved in terms of upgrading several countries in africa’s infrastructure, for commercial gain, it’s true but..
I don’t know if you’re being intentionally difficult/obtuse, or just really can’t figure it out.
We don’t FORCE a lifestyle on anyone. They WANT our lifestyle, and consider it unfair if we have ANYTHING they don’t! BUT they don’t want to follow the rules, or even the annoying steps we had to go through to GET to this point of relative wealth. In short, they want us to build it up, they show up “Where’s My Share?” and we just fork it over! Otherwise we’re selfish Privileged scum, right?
Is that or is that not why poor savages keep pouring into white countries, instead of China or fellow savage countries? Indeed, why is illegal immigration from CHINA now outstripping that from MEXICO, our hereditary invader?
China’s a rich country, shouldn’t they be able to take care of their own excess population?
Unless they WANT OUR LIFESTYLE?
“They gave you food and taught you how to grow it. Among other things.”
Yes, but you keep mischaracterizing it as them doing it out of altruism, the Goodness of their Heart, etc. It wasn’t.
They could’ve let us starve, it wasn’t against their BELIEF, as they later tried to DIRECTLY KILL US, it was against their SELF-INTEREST!
IF we die, the Narragansett keep attacking them until THEY die.
Once the Narragansett were gone, we had Outlived our Usefulness, so they tried to kill us DIRECTLY!
*Sad Music* They USED us! *End Sad Music*
Whites may or may not have whined, “But we had a DEAL!”, but in any event, we kicked savage ass.
Did you read the Wikipedia article on King Phillip’s War? Or just Google it, and find a site you DO trust, if you don’t trust Wikipedia for whatever reason?
It’s not just Americans that can’t fathom (Good pun!) a life without oil. Europe, Chinese, Russians, and savages of every country and description have cars too, and I DON’T think any of them run on fairy dust! Even when savages can’t AFFORD a car in their own country, as soon as they invade the Civilized World, they get one? (If people REALLY cared about Global Warming, or Environment Justice or whatever, they’d stop savages from getting cars, but that’s just shy of stopping them from BREEDING in difficulty!)
Petrochemicals are the ONLY way to get AS MUCH energy as you want WHEN you want WHERE you want.
Battery tech has basically plateaued in say the past 10 years? (We can argue exactly HOW LONG it’s stagnated, but it HAS stagnated, can you agree with that?)
So electric cars are inefficient, and more importantly, EXPENSIVE to have batteries on a CAR scale instead of a cellphone or laptop scale.
The Volt is $70,000 STRIPPED! I can buy 3 cars for that!
And batteries don’t MAKE electricity, they STORE it. Where are we going to get the electricity in the first place?
Solar and wind are unreliable and require constant subsidy. Solar cells and windmills are built in CHINA, so that wouldn’t create any jobs FOR AMERICANS! (It doesn’t “count” if it’s not for us, OK?)
The Bum keeps blocking charters of new nuclear reactors or even renewal of old ones.
So all we’ve got left IS fossil fuels.
EPGAH said: I picture them as Black, grinning evilly, a machete in one hand, and either a gun or a severed head “trophy” from a recent murder in the other.
Lions are actually more valuable than HUMAN lives to the savages. Which is why they were so tightly controlled when the Civilized World ran the place.They somehow predicted savages would be savage (Definition: Primitive and violent), so they kept them separate to avoid trouble!
Your outlook on life is primitive and violent so, I think you fit the term savage more than anyone else. I feel like I am reading the post of a child, one that is constantly pointing the finger saying ‘look what he/she/they did’ and just not understanding the context of anything.
I’m waiting for the other shoe to drop. Look at all the concessions China has squeezed out of America for just monetary loans to support our ridiculous “social safety net” spending, from letting spies go to our nuclear and rocketry secrets. How much MORE would they extort if they actually BUILT THE COUNTRY?
Savages have nothing to offer except staying out of the way while someone mines resources that Civilized World needs and China needs for their cheap (and often toxic) knockoffs of our products…Or LABOR. China does not have slavery, they have Laogai, which is arguably worse…
My outlook on life is NOT primitive and violent. I LOVE the Civilized World’s technology, and I think we could’ve done a LOT MORE if we weren’t constantly trying to keep savages either at bay or paid off.
As to post of a child, there are other threads here that seem like just, “Whites have MORE than we do! GIMME GIMME GIMME!”
I consider myself the adult saying, “BEHAVE! Let us EARN more so we can give you more!”
Savages overthrowing our countries is a primitive, violent way of saying, “WE WANT IT NOW!” Actions louder than words, right?
Or burning down cities in America.
As to context, what “context” could possibly justify invading a country, demanding things from it, and murdering the people and destroying it if they don’t get their way?
·They didn’t build any of it.
·If they worked, they were paid for it.
·We tripled their average life expectancy, so they owe US, not vice-versa.
·If they didn’t like it, they could stay out and return to Nasty, Brutish, and Short!
That is my “context”. What “context” could reverse that formula?
PS, the savages HAVE done that to farmers and other WHITE landowners, so I don’t think I’m particularly off in my idea of how savages look/act/wield.
Do a Google Images Search on it.
Maybe you’ll throw up in horror, or maybe you’ll cheer at the savages killing the greedy selfish whites?
But given what they’ve done, doesn’t that make ANY length whites go to to protect ourselves seem absolutely justified or else “Not enough”?
From Apartheid in South Africa–UNFAIR, sure, but NECESSARY, given what the savages did when it stopped–to Hungary and Israel walling themselves off from the violent savages to America…
Hmm, America doesn’t HAVE ANY defenses from the savages since Wilson, do we?
BTW, this article completely leaves out Amy Biehl. Gang-raped and murdered while trying to help the savages. And her parents put up money…for the legal defense of the savages who did it! THAT is seriously bad parenting!
Or the nurses who got raped in Haiti.
Or the doctors who got kidnapped in Somalia so frequently, that Doctors Without Borders quit going there!
What’s the “context” to justify those?
“I don’t know if you’re being intentionally difficult/obtuse, or just really can’t figure it out.”—Nope that is all you. You seem to have a thing for voicing who you are while trying to paint it as someone else.
“We don’t FORCE a lifestyle on anyone. They WANT our lifestyle, and consider it unfair if we have ANYTHING they don’t!”—That is false and history shows that as much. Take the natives for example. They were put in schools and had their names changed, forced to renounce their old ways, and forced to dress the way “whites” wanted them to. Even if we look at today, whites want to force people who come here to speak English and even force English on other countries.
“Is that or is that not why poor savages keep pouring into white countries, instead of China or fellow savage countries?”—History shows that whites pour into other people’s countries. Just because those minorities decide to return to their lands does not mean they are pouring in to a white country. It just means they are returning home.
“Yes, but you keep mischaracterizing it as them doing it out of altruism, the Goodness of their Heart, etc. It wasn’t.”—-Here is another example of goal post shifting. You claimed America was independent. You have a whole aparagraph above raving about it, but Natives decide to help those helpless white Americans and now you want to claim it was not for nothing. A claim you have no proof of other than your idea of “we whites would have done that so they more than likely did it.” In short the first settlers needed them. Their survival was dependent on them. You were debunked again.
“Did you read the Wikipedia article on King Phillip’s War?”—Save the deflection as it still has nothing to do with what you are claiming.
“It’s not just Americans that can’t fathom (Good pun!) a life without oil.”—But we are not talking about other countries. We are talking about dependency. You claimed America was so independent. Now you are making excuse for why it is SO dependent. See the humor. ROFL
If you want lack of context, look at the top of the page here.
Mugabe is proof that blacks are unfit to rule and Hitler is a madman, because of the CONSEQUENCES for their respective genocides.
Whites all banded together to stop Hitler. Even Russia (for a time) was on the side of the Angels!
Blacks, they banded together…UNDER it! They didn’t try to STOP Mugabe, too busy congratulating it for overthrowing and murdering whites in our own country, and even shielding the King of Sudan from prosecution!
@Omnipresent
I think he is a child myself. I have met some dumb adults but this is utter ridiculous.
The savages wanted to live in OUR country, so why shouldn’t they speak OUR language?
Who is returning to THEIR land? If they’re coming into OUR country, it’s obviously not theirs!
English is the Universal Language because English were the Universal Civilizers–before America took up the torch. Everything from science to commerce to Air Traffic Control is in English. If China had civilized the world, rather than merely usurp America’s tech, would you complain as loudly if they expected anyone who wanted to do business with them to learn Chinese?
Indeed, would China be ANYTHING without England upgrading them?
Why DID they renege on the land treaty of Hong Kong?
“In Perpetuity” becoming “99 years” is moving the goalposts…quite a bit!
The “context” being they killed a lot of English people, and turned one English woman into a Nice Belt! That needs to be punished, don’t you think?
You debunked NOTHING
King Phillip’s War is not a deflection. It is exactly what I’m claiming.
King Phillip’s War is the name usually given to the Wampanoags turning on the Pilgrims. We were independent, trading military aid for food. “America’s” first military treaty even BEFORE America was a country!
If they just fed us and we stood around and did NOTHING for it, then yes, I’d say we were dependent leeches. OK? That is the difference.
Our survival was dependent on them, BUT if we didn’t beat their bullies, their survival was null&void too. They were dependent on us!
If whites were as evil as you pretend, why didn’t we kill BOTH groups of savages, TAKE the food, and that’s that?
“murdering whites in our own country”—anymore questions on the level of delusion of this man?
You don’t HAVE to learn English. You don’t even have to get housebroken. But if you do not, there will be things forever denied you, and people will always treat you as less. Assimilating to a better culture, a better mode of behavior, gives you privileges in return.
Privilege is as always, EARNED, not merely BORN!
Rhodesia was a white country.
If you want to claim the English aren’t or weren’t white, it’s not me that has a level of delusion!
“The savages wanted to live in OUR country, so why shouldn’t they speak OUR language?”—False. You are in their country. You should be speaking native tongue. This is not your land. You wanted to come here. No native invited you.
“If they’re coming into OUR country, it’s obviously not theirs!”—False again. You can return to a land that you once lived on. Reread what I said. You seem to have gotten sidetracked.
“If China had civilized the world, rather than merely usurp America’s tech, would you complain as loudly if they expected anyone who wanted to do business with them to learn Chinese”—Can you stop trying to deflect. You are embarrassing yourself terribly. Forcing English on people in other countries doesn’t have to do with just business. Research…research.
“Indeed, would China be ANYTHING without England upgrading them?”—It would as would any country, but it just would not be what you want it to be.
“You debunked NOTHING”—I actually did. Several times I might add. I got such a level of kick and giggles out of how easy it was.
You made claims you never could support. King Philip was not even one of them. You bring in a bunch of irrelevant things hoping that those will beef up your claims. They don’t. Then you switch positions in hope that moving to another will make you seem more right. It doesn’t
If you like I can and likely will make a list of all the claims you made here and were debunked on.
“If they just fed us and we stood around and did NOTHING for it, then yes, I’d say we were dependent leeches. OK? That is the difference.”—There is no stipulation to being dependent on something. The meaning of the word is clear. If you rely on or your life standing is determined by something or someone else then you are dependent. Period.
“Our survival was dependent on them, BUT if we didn’t beat their bullies, their survival was null&void too. They were dependent on us!”—Except those “bullies” were around before you came. How did they deal with them them? The same as they did before you came.
“If whites were as evil as you pretend, why didn’t we kill BOTH groups of savages, TAKE the food, and that’s that?”—Because you still needed the other group to teach you the land beyond the coast.
Except American culture is not a better culture. You only put it on a pedal stool.
“Rhodesia was a white country.”—Countries don’t have color, but if we want to go their it was stolen. That does not make it a white country.
“If you want to claim the English aren’t or weren’t white, it’s not me that has a level of delusion!”—Except I did not claim that and was not going to. I thought you got enough of embarrassing yourself by trying to lay claim to what I think or believe.
@epgah what does epgah stand for? Btw if you wrote anything besides vitriol and hate you’d be an eloquent and persuasive writer
We’re on land they once occupied. They were no more invited than we.
We actually made a country, they didn’t.
Think of 5-year-olds playing in a dirt lot. They don’t build anything (Or at least nothing lasting), they invent nothing, how is it theirs?
Then if a bunch of musclebound behemoths lift them off that dirt lot, and put them outside it, and build a store there, can they barge in and say “We own this store because we used to play in the dirt lot that was here before!”?
I’ve moved 27 times in my 36 years of life. Could I go to any of those previous houses and say, “Hey, I USED to live here, I’m gonna live here again!”?
I don’t think that would fly. The current occupants might make ME fly out a window, but that doesn’t “count”!
No savages are coming here because America used to be theirs. Mexicans used to be kept out by Apache and Comanche, now immortalized in military helicopters. It would be exceptionally ironic if we used those helicopters to keep them out…but we don’t. We have the Bum’s “Virtual Fence” with camera drones so we can WATCH them invade and rape our country, turning it into the same mess their country already is!
Before English, German was the Prime Language, and before that, Latin was. There’s always some Prime Language, everyone “has” to learn if they want the benefits behind it. AND of course, the lesser cultures are always going to whine some variant of “Hey, why can’t we have the benefits without the rest of the culture?”
American culture of WHAT YEAR? If even HALF of what my parents claim is true, then the 50s were better than the 80s, which in turn, are far and away better than the now-time. Technology is better, people, educational system, manners, safety, and other facets are worse. And this is the same country–allegedly–just separate temporally from itself.
Are you the same person as you were 30 years ago? Or even 10?
But if America is not a better culture, how do we still have a better country?
Or at least better than Mexico…Faint Praise, indeed!
And in turn, there are countries south of Mexico that make MEXICO look like a success story. Mexicans complain about Nigerian and Honduran illegals!
That is what you said. BUT King admitted that Europeans carved the mostly-blank land of Africa into COUNTRIES where there weren’t before.
Just like America, Rhodesia was sparse or even blank land before the Civilized World built it into a COUNTRY!
Stealing a country is a modern thing, there has to BE a country there first!
“Breadbasket of Africa”, now can’t even feed itself.
We send seeds, they either eat them or use them to soak up floods. Hilarious, but unproductive.
“What do you consider a COUNTRY to be? Are they supposed to coat the whole place in concrete?”
What are they SUPPOSED to do? Probably not take over other people’s lands without invitation, consent or payment, If it comes down to what they are “supposed” to do in the first place. But if you want to make an argument that part of the payment was “building up the country,” then it can’t just be built up for the White people in the country. Otherwise it’s not helping the people who you are arguing that it benefits for taking their land.
Well, the Europeans seem to keep changing their minds on what constitutes ownership. For example, when dealing with non-Europeans, then “Might Makes Right” is a perfectly acceptable rationale. “Manifest Destiny” in the Americas and the “Scramble for Africa” on the Continent exemplify that reality. However if Hitler invades Poland or France, then it’s no longer an acceptable rationale. Or if Saddam invades Kuwait, or if Putin invades Ukraine. This is what’s known as Moving The Goal Posts (please see sharinalr for details)
“After whites left, of course it’ll be worse! We raised their expectations! They’ve always HAD disease, starvation, death, and random violence, but now, because of Civilized World food, meds, and law-enforcement, they EXPECT not to!”
But then everyone has always had disease, starvation, death, and random violence. Do you watch the news? Do you read history?
These poor souls… such a Savage existence… (SMH)
EPGAH:
demanding things from it
and murdering the people and destroying it if they don’t get their way
This sounds an awful lot to me like what Europeans did for example in America but under no initial resistance from the indigenous people that lived there. The native people helped them – that’s what Thanksgiving is about isn’t it? Later down the line, they Europeans got greedy, took land but wanted more, encroaching on and then invading on what was established indigenous areas.
Guess who the murderers were here?
It’s my initials.
Why do you consider what I write “hate and vitriol”?
Whites are called “Cancer of the planet” on this very site!
Savages talk&sing about exterminating whites–sometimes they DO it, so why is it “hate and vitriol” to want savages to either calm down and behave or get the expletive of your choice out of our countries?
Is it also hate&vitriol when savages invade our countries, murder the people and overthrow them? Or when say, Mexico doesn’t want savages to breach THEIR southern border and cause “economic and cultural disruption”?
When does it stop being “hate and vitriol” and start being a reasonable desire not to be murdered, robbed, or otherwise violated?
Or is that NEVER a reasonable desire?
Speaking of which, have you seen the savages national anthem after they overthrew South Africa?
(http://www.youtube.com/watch?v=fcOXqFQw2hc)
Kill the White, Kill the Boer.
What “context” makes that not “hate&vitriol”?
It wasn’t murder, it was fighting back. After you sell me land, I can do whatever I want with it. It is no longer yours, it is MINE!
If you get “worried” I’m buying too much land, the correct way of stopping me is to stop selling me anymore.
Japanese and Chinese are buying up land in America, from prime grazing land to Rare Earths mines–the ones necessary for Clean Energy technology as well as battery research. Should we kill them as well because the amount of land they’ve bought is “worrisome”?
Should we claim they only buy it for 99 years, instead of forever? (Hong Kong reference) We don’t renenge on land deals, we play fair, even with our enemies.
In any event, the savages CHOSE to attack us, and we CHOSE to fight back rather than bending over. So yes, the savages were the murderers.
If I sell you my house RIGHT NOW, then I kill you for being in “my” house, then I am the murderer. YOU legally have the deed. All your friends would exact vengeance on me, or at the very least, the police would!
Do you get the “context”?
“Under no initial resistance” is a bit of a red herring, BTW.
If you offer me enough for my house, I won’t “resist” selling to you.
If you buy too many houses in my neighborhood, the civilized way would be to organize the rest of the homeowners NOT to sell to you.
What the savages did was round up a posse and try to kill you for the equivalent of buying too many houses in my neighborhood. After the posse killed 1/10 of your family, you calmly shot the whole posse.
Is that a better explanation?
“Don’t think so.”—It is common knowledge now that you don’t think. Let’s take your example. You don’t just come and build a store on land. You pay for it. Seeing as you never paid the natives for their land then you are on stolen land. I doubt the man who puts up the store invented anything, but felt by some right he could just take the land. In the real world the natives were not just playing in sand on their lands. They had homes, crops, a lifestyle.
All your examples fail in these situation because frankly the key term here is paid for it. Something settlers did not do.
“No savages are coming here because America used to be theirs.”—False again. For example Texas used to be Mexicos. I believe some other areas fall into their too. So yea….they are returning home, but this is another straw man. I never said just Mexicans.
“Before English, German was the Prime Language, and before that, Latin was.”—False again. There were many languages, but none of them were prime ones.
“American culture of WHAT YEAR? “—That is irrelevant. The year does not change the heart of the culture.
“Are you the same person as you were 30 years ago? Or even 10?”—Nope, but that has a great deal to do with me pulling myself away from American culture.
“But if America is not a better culture, how do we still have a better country”—But you don’t have a better country. You would be surprised at the lengths your government goes through to ensure you believe that. It indoctrinate its citizens to believe that.
“anymore questions on the level of delusion of this man?”—I never questioned your delusion. I can read your post and let it stand as proof of your delusions.
“That is what you said. “—If that was what I said then you would be quoting it. The fact that you have not says a great deal. At any rate if you want to do a straw man then it would not be the first, but do stop putting words in my mouth.
“Just like America, Rhodesia was sparse or even blank land before the Civilized World built it into a COUNTRY!”—Just like America this would be another false statement with no supporting facts.
“Stealing a country is a modern thing, there has to BE a country there first!”—No it does not. Stealing by definition is taking what is not yours. If the land was not yours then you stole it. Just because you decided to call it a new name does not mean it was never stolen.
@epgah frankly, i’m surprised that this conversation has been going on all day? But the ‘mostly white’ colonislstic forces interrupted africans’ development, dutch east india co. Style, creating the diaspora, etc at the time of their industrial age, it’s been posited here before, idk you keep saying savages, and your reasoning is biased and ‘monolithic’, xenophobic, idk… not friendly either. My wife calls me racial slurs, so what, i mean we’re all grown (mostly) here, i’d assume
“vitriol and hate you’d be an eloquent and persuasive writer.”—I don’t think so unless he is talking to a bunch of individuals who do not do research. The heart of everything he says is a lie. Most of his rantings of paranoid rants of a mad man. Suffering from delusions of grandeur.
My comment is in moderation, but this portion I want to make very clear.
You have made the claim several times now of me saying something that I did not. If that is the tact that you must resort to then what every debate you think you have had with me has been lost several times over.
I DID quote it, I copied and pasted it directly.
https://abagond.wordpress.com/2012/03/13/the-broken-africa-stereotype/#comment-296048
Here’s a direct link to your comment, in case you forgot you said it.
Yes, and mostly nonwhite conquerors “interrupted” Rome’s development.
But the whites just got back up and continued.
And it should be noticed that whites and ONLY whites judged slavery ILLEGAL.
Whether or not we considered it WRONG, we made it ILLEGAL.
As to being biased, calling “White Privilege” a bad thing should be considered “biased” and thrown away. At least if we’re using the dictionary definition of “Privilege”, “Extra benefit or access earned by meritorious behavior”
When and how did that become a four letter word?
There’s a whole thread on how the Irish “mysteriously” became white, but they did so by learning how to behave, instead of insisting on behaving THEIR way in OUR country.
As to monolithic, we’re talking about a “minority” group that celebrates and angsts over being a “minority” group. Noone else suffered as much as they did, from slavery on up, right? If the majority of a group acts like X, and the rest of the group does not punish those who act X or extra X, we have every reason to suspect the group LIKES acting X, right?
Whites punished Hitler, so he was a madman.
Blacks APPLAUDED Mugabe so it was part of their DESIRED behavior, not a madman to their standards.
Is that a good illustration?
As to xenophobic, that would be true if and only if we had no indication of how a given group behaved. But we have whole COUNTRIES their behavior already ruined. Some groups, we’ve let into our country in substantial numbers, we can observe if their behavior “magically” improves from setting foot in our country. So far, I’d say they act the same or worse in our country as they do in their own, wouldn’t you?
Ever seen Star Trek? Dad bought the tapes and we watched one per night when I was a kid. The most extreme perversions of the human form were accepted because they BEHAVED. Things that looked like humans with bad mustaches and eyebrow implants were NOT accepted because they kept ATTACKING US!
Are we not supposed to judge by their behavior in real life?
on Sun Oct 4th 2015 at 22:49:51 mike4ty4
@EPGAH:
Slaughtering tens of millions in wars and genocides, deceiving and defrauding people out of land so that it could be used to extract resources, etc. are not “meritorious behavior”. It’s nation-scale robbery.
What the savages did was round up a posse and try to kill you for the equivalent of buying too many houses in my neighborhood.
Incorrect, since there is a presumption here that the dealings with the NAs were Honest. They weren’t, and employed various forms of deceit (fraud).
We don’t FORCE a lifestyle on anyone. They WANT our lifestyle, and consider it unfair if we have ANYTHING they don’t!
If they “WANTED” it and it didn’t need to be “FORCED”, then there was no need for whites to SLAUGHTER them by the MILLIONS in pursuit of granting it and try their darndest to obliterate their native culture. That was evil: murder, theft, rape, and psychological torture all in one. (Oh yeah and if you don’t think hostilities emerged until the Natives fired the first shots — WRONG. When Columbus first showed up his men took people and RAPED them. “Civilized” all right. Hostilities were established from day 1, by the Whites.)
“I DID quote it, I copied and pasted it directly.”—Aw so you were referring to that quote. But what you wrote is simply copy and paste and can been seen more as plagiarism than quoting me. Quoting it not throwing out a random sentence with no proper credit to the individual.
Here is an example of quoting: According to Roger Sipher, a solution to the perceived crisis of American education is to “Abolish compulsory-attendance laws and allow only those who are committed to getting an education to attend” (para. 3)
Notice the quotation marks around the quoted phrases. https://owl.english.purdue.edu/owl/owlprint/563/
At any rate, what of it? You have said nothing that changes what I said.
@EPGAH,
Also, if “whites” were truly so “civilized” and “sorry” they did all this slavery and were really trying to end it, not only would they have made it “illegal” but they would ALSO not have instituted 90 years of Jim Crow on top and instead would be or have been paying reparations to recompense the communities who were denied wealth after slavery was made “illegal”. (Seems after slavery was made “illegal” whites tried their darndest to keep Blacks as close to slaves as they could without making them actually so — almost as if the outlawing of slavery was a grudging concession instead of a whole-hearted display of “Civilization”.)
@sharina i meant stylistically,obviously we diverge on content, something … idk
I see africa as a succession of power vaccuums from untenable states of being directly traceable to berlin 1888 i believe bolstered by cheap weapons and expedience and ulterior motives, a sad thing really.
mike4ty4
We ARE civilized, which is why we’ve abided by land sale agreements, and not killed the ex-slaves like Moslems often did when they were “done with them”.
Oprah, MJ, Sharpton, Jackson, etc. were not killed so we could take back their property. Indeed one of those is well behind on taxes, IIRC?
Once the slaves were no longer our PROPERTY, by all logic, they should no longer be our PROBLEM right? We’re off the hook for their upkeep and all that? (Except with the Rise of the Welfare State, we are essentially THEIR slaves, but I think we’re supposed to ignore that?)
BUT that assumes the slaves just stopped existing once they stopped being property. They didn’t, they went directly from “property” (HELPING you make a profit) to “rival” (OBSTACLE to you making a profit), and in some cases, outright ENEMY (KILLING you to prevent you making a profit). So self-preservation would lead us to make the obstacle as small as possible and the enemy as safe as possible, right?
Jim Crow Laws varied from State to State, depending on the severity of the perceived threat. Which State do you want to go through?
One of them had literacy tests for voting. Only people who could READ could vote! I think that’s a GREAT idea, needed now!
Why pay reparations to the enemy? Where are the reparations for the chumps who bought slaves, and were abruptly divested of very expensive property? Or is it because they lost the war, they don’t DESERVE reparations?
What if your car or your computer went from being your property to your enemy? Would you pay it or try to destroy it? How much did you pay for your car, and would that amount of money prevent you putting a bullet through/between the headlights?
If only there were some highly allegorical movies about our machine property turning on us. Get Schwarzenegger on the phone, he’d be good for 3-4 of such movies!
on Mon Oct 5th 2015 at 00:13:39 EPGAH
Also remember, when they WERE offered a chance to get “out from under” AND reparations…Most REFUSED!
·Their own land–FREE
·Their own livestock–FREE
·Their own tools–FREE
·Their own effort determines how much they get!
Maybe they thought it was an MLM scal, but depending whose stats you take as Gospel, only 9,000-13,000 took them up on the Deal..OVER 100 YEARS!
(Lincoln to Eisenhower!)
Modern cruise ships carry more than that–plus passengers–every trip!
Maybe they weren’t crazy or desperate enough to leave, and the real ungrateful complaining wouldn’t begin until the 1960s?
Maybe they knew it would be overthrown as soon as America yanked the Marines that acted as Border Patrol for them?
Maybe if more had gone, they would not have been overthrown?
Look up Liberia in whatever info engine you like, tell me if I’m lying?
on Mon Oct 5th 2015 at 00:18:48 v8driver
one time, when i was in the homeless shelter in easton, pa? i met a marine sniper, he shot the opposition leader in liberia
on Mon Oct 5th 2015 at 00:51:00 abagond
@ EPGAH: Comment deleted for use of moderated language.
on Mon Oct 5th 2015 at 00:52:00 sharinalr
I met the Epic Beard Man before he was Epic, and the American Sniper before he was murdered, does that count?
Just goes to show africa and the middle east has been a chessboard for centuries
And south/southeast asia
EPGAH is banned for plagiarism.
I’m sure i’ve caused some grief here, but that was a little unsettling, plus it was like 2 weeks of discussion in 8 hours? Unreal.
on Mon Oct 5th 2015 at 16:46:17 villagewriter
@taotesan
“To be called a white ‘African’ (writing this hurts me) ties in, not with any nationalist, patriotic or any romantic notion, but with their unbridled capitalistic rapacity and their perverted ideology that they are God’s chosen people (Afrikaners) so they are entitled to all our land.”
When I read about “god’s chosen people” (Afrikaners) I had a good laugh. I am sorry but I do not trust them. They could plant a nuclear weapon in South Africa or even assassinate your president. Their kind of racism is so fresh and pure that it makes American racism look like Godly love.
on Mon Oct 5th 2015 at 19:55:24 Michael Barker
@ Mirkwood
It’s your blog, you shouldn’t have to come here for approval.
What you have in common with him is that the both of you deny white supremecy but for different reasons.
If you kept him around on your blog and debated him it might help you see things differently here and as they truley are. You have been here a while but have resisted changing your world view.
on Tue Oct 6th 2015 at 05:34:19 abagond
@ Lord of Mirkwood
I would stick to my comment policy, though you might want to think about what changes you should have going forward.
He would still be here if he was not caught plagiarizing. To me trolls are part of the cost of doing business. Sometimes they can be put to good use as useful idiots.
Most trolls wind up using sock puppets, so I would keep my eye out for that.
on Tue Oct 6th 2015 at 13:11:21 Uglyblackjohn
Dang it!!! I finally get around to finding his reply and he’s gone?
The thing that he fails to understand is that most white immigration WAS done because white people wanted to get away from other white people.
That most of ‘his’ country’s wars: both World Wars, the Cold War, the Civil War, the Mexican-American War (Spain is European and white – he agrees), the War of 1812, the Revolutionary War and the Seven Year War – were fought against OTHER WHITE PEOPLE.
So much for being a civilized people.
(And yes, it was fun having him around.)
on Tue Oct 6th 2015 at 19:24:22 sharinalr
EPGAH’s screen name was very familiar and then I realized I debated him prior on some youtube comment section.
on Wed Oct 7th 2015 at 01:32:45 Fan ...
“I’ve decided not to ban him,…”
Well, it’s not like you have a large group of posters there, and commenters – for some people – are hard to come by, so I can understand you being far less discriminating… Besides, I didn’t see you disagreeing with a lot of its mess before IT was banned.
I suspect that you may not have enjoyed ITS presence here because IT was stealing away much of the attention you were formerly getting. lol
“If you refuse to do so, then I know you’re not seriously interested in what my political leanings are ….”
You’re kidding, right?? (Nice try … lol)
Even the walking dead KNOW what your politics are… which is why to a very large degree you stand OUT here. Much of what you, if not all you do here, is talk about the donkeys and the elephants. That’s why people like me don’t take you very seriously. You infinitely dodge the root issues, even when it’s politely explained to you.
“I am tired of trying to justify myself to everybody here 24/7, but I will keep at it.”
No one is buying your justifications because they are found bogus and irrelevant to what OUR day to day experiences are. If you wish to be taken seriously and not ignored (or used for entertainment) you need to come in here through a door of OUR shared circumstance. The door you approached and entered in here (your circumstance) just ain’t working!
on Wed Oct 7th 2015 at 15:01:36 taotesan
@villagewriter
I was going to write a sober response to your comment, but this popped into my mind and ran away with me. (Still trying to write, but feeling a little brain-dead at the moment.)
No, I do not ride zebras. It is a surprise to any African that zebras could be ridden, but I do have pet lion, Nelson, whom I walk with to my child’s school every day. I go about my day to day life in a loin cloth, with my breasts bared. Who is this Levi, Tommy Hilfiger and Donna Karan? I wrote this article, in African, had it translated into English by a special seer, in feather pen, in long hand, in my village , on papyrus and sent it cross-Atlantic by carrier pigeon. I do not know how to read. I have never heard of Shakespeare, Jackie Collins, Brendan Behan or Noam Chomsky. When trying to contact a relative long distance, I walk for miles and ululate in special code. What is this thing called a cell phone? My stomach is still digesting the GMO maize meal so generously donated by the USA, with mopane worms and chicken feet. I do not know what a quiche Lorraine, fettuccini carbonara or Nigiri is. When we listen to music, a goat must be slaughtered, and its hide cured and made into a djembe drum and we dance and ululate around the fireplace. I have never heard of Tchaikovsky, Whitney Houston, Eminem, Tupac or Bono.
I must tell you I have never had the AIDS. I am afraid of needles. I know this is too much information and you probably would not believe me, but my private parts are intact. What is this Princess Diana and Prince Albert piercings? When I have that thing Europeans call influenza, (not affluenza) I boil special herbs in water from the river that USA dumps their toxic waste. It tastes horrible. What is antibiotics? I do not have the Ebola either. Mzanzi or South Africa is closer to Antarctica than to Sierra Leone and Guinea. It’s about 9000 km. Sierra Leone is closer to New York (7063 km) than Cape Town. My sister tells me there are white people in America who have the Ebola.
In my hut, I use special cow-dung. I do not know magic white light. I have no idea how to re-heat a pizza, or how to load a washing machine. I have never heard of Mies van der rohe or Buckminster Fuller. Before my daughter goes to school, she walks barefoot in the dark, to collect firewood. I also rise early to collect water for bathing and drinking water. But I heard a lot about this TV, you know, the big box where the people who talk funny in the English tongue, live. My brother tells me that that ladies with long blond hair like to kiss a lot and like the sex with different men. He also says that the people, even the women with the sun-hair and no skin colour and white-white teeth like shooting people a lot. They have better guns than the Russian AK-47s and Kalashnikovs. . I do not like guns. My brother’s wife wants a weave like the Black ladies in the TV. You can buy a weave from the Chinese corner shop. Me, I am just a wash and leave. I also hear in America white fat people are dying from malnutrition.
When I travelled to the USA, I crossed the Atlantic Ocean in a dhow and then hitched a ride, monkey grip on Boeing 747.
I know there is a Black President in America, but my brother,he tells me that there is going to be another Black president, who is very, very rich, just like our president, but he is white and has a carpet on his head, just like our president who has a shower on his head.
My brother says orange is the new black.
(https://www.youtube.com/watch?v=2FPrJxTvgdQ)
Very funny clip by fellow Mzansinite, Trevor Noah.
@LOM
Those are not the root issues. Those are YOUR root issues. When we attempt to discuss anything with you you happily dismiss it.
on Sat Sep 10th 2016 at 10:05:00 TheHipHopRecords (@TheHipHopRecord)
How many countries in Africa can you name ?
http://www.sporcle.com/games/g/africa
Quick little fun game.
I got 27 out 54. Can anyone beat that ? I don’t think so
Don’t cheat though. Unless you want to check spelling
on Sat Sep 10th 2016 at 13:20:30 Kartoffel
Ha, I love these Quizes. got 50/54 but I do them all the time. I couldn’t remember the english spelling of four countries. Also this test doesn’t forcde you to match country and its name, for example I never now which one of the islands is which.
on Sat Sep 10th 2016 at 16:54:41 gro jo
How is Mugabe like Hitler? You swallowed the propaganda all the while pretending to debunk it.
Africa is broken, how could it not be after more than five hundred years of near genocidal exploitation? The real question is how to repair the damage done. Only people like Mugabe have the balls to take on the task of repairing the damage.
@Kartoffel – 50 our 54 ? Are you serious ? What ones did you miss ? Anyone who get’s over 40 is a Jedi on African geography. I’ve never known anyone to get 50; That’s a Jedi master.
The average score is around 22. I’d say about 10% get over thirty, 5% over 40 and as I say (if your telling the truth) no-one has got to 50.
I knew my score of 27 would not be a stern test, the ‘I don’t think so’comment was tongue in cheek but that’s what I got. Best be honest
@Lord of Mirkwood – 38 is still way above average and like you I missed out on some incredible ones, that I can’t believe.
on Sat Sep 10th 2016 at 19:55:58 taotesan
I can tell who is a white American in my area without hearing them talk.
on Sat Sep 10th 2016 at 20:11:45 Mary Burrell
@taotesan: Can you recommend a book about the history of Africa I know this can be quite dodgy?
While trying to find decent reference books about the continent of Africa I have learned many books are written by whites who view Africa with a white lens and they are not objective. What I am learning is the language used in these reference books, for example “darkest Africa or black Africa. There is something very unsettling about that type of language. I want to make smart choices when I purchase reference books any suggestions will be welcome.
@taotesan: I love Trevor Noah he hilarious thanks for the YouTube share.
@ TheHipHopRecords
As I said it wan’t the first time I did such a quiz. I have no idea how much I scored when I did an Africa nation quiz for the first time. Also I learned all African states by heart as a child.
I couldn’t remember the English spelling of Mauritania, Equitorial Guinea, Sao Tome e Principe, Djibouti and other.
( Sorry, was watching Paralympian bench press)
@ Mary I can’t think off hand the exact titles with authors.
I will come back to you soonest.
Off- hand, I would highly recommend Guyanese Walter Rodney’s seminal work: How Europe Underdeveloped Africa. It is information dense beginning with the European slave trade of Africans to neo colonialism in Africa.
Kwame Nkrumah’ Decolonization.
Timbuktu by Diagne.
I can’t get the the title or author of Ancient Egyptian history. The historian was Caribbean and I think he was assissinated. I had read it a few years ago and the historians name eludes me.
A Comparative Study of South African and American History by Frederickson.
On my shelf and not yet read: Half a yellow Sun by Adichi
Chancellor Williams by The Destruction of Black Civilization
Revolution by Frantz Fanon.
Most of my books are packed away, and just can’t recollect.
Perhaps you could tell me the region and era that you might be interested in.
A good place to start would also be a light introduction through literature.
Nervous Conditions, by Tsitsi Dangaremga, a Zimbabwean.
Maru by Bessie Head, South African (highly recommended)
Naguib Mafouz : Trilogy , Egyptian
Things Fall Apart : Achebe, Nigeria
This will be nice a project for the week, and I will provide some background.
My reply to you is in moderation.
Yes, there are a plethora of books written by white foreigners through a paternalistic lens. Read a few and tossed them out.
Give me a bit of time to provide a precis of and better thought through and systematic recommendations .
I think a start could be is to first ground in Ancient history by Black historians:
I think ‘Stolen Legacy’ by a Guyanese, George Granville James, who was also assassinated like Walter Rodney! is a must read.
Cheikh Anta Diop: ‘African Origin of Civilization’ or any book by him.
(Glad you enjoyed Trevor Noah, Unfortunately, I have watched him so many times, that I can’t even laugh anymore. Briefly met him before he was famous. )
on Sat Sep 10th 2016 at 21:43:20 Solitaire
I only got 28. Out of the remainder, there were maybe half I knew but blanked on (e.g. Chad, Angola, Sierra Leone), but the rest I would have never gotten. I need to brush up on my African geography.
I also showed my age by trying Zaire. 😦
What is the name of the small African country with an American miltary base?
Clue:Which you might hear about in a few months time when the US announces that country needs a regime change or needs to install ‘democracy’
Another clue: China has troops there.
@ taotesan
Djibouti?
You are fast , Abagond. 🙂
Now how about on that overdue post on South Africa?:)
I got 53/54. I missed Seychelles.
@ taosetan
What is the name of the island in the Indian Ocean which Britain has stolen from its inhabitants and had sold it to the United States, which is now populated by Americans with its military base and what is the name of the island in the Indian Ocean which the the inhabitants were relocated and now live in abject poverty?
village writer and michaeljonbarker know the answer.
Here’s a gem: Which are the three African countries, which are diamond rich, had the Marburg virus?
Or one on Trevor Noah.
You can put Mary out of her misery, who has been throwing hints for a while. 🙂
53 out of 54?!?
Damn, Abagond, you are smart.
on Sun Sep 11th 2016 at 06:18:49 Afrofem
“the name of the island in the Indian Ocean which Britain has stolen from its inhabitants and had sold it to the United States, which is now populated by Americans with its military base and what is the name of the island in the Indian Ocean which the the inhabitants were relocated and now live in abject poverty?”
Diego Garcia.
on Sun Sep 11th 2016 at 14:59:05 Mary Burrell
@taotesean:Thank you for those titles I will write them down and check them out. A post on Trevor Noah would be great I think he’s funny and sharp.
on Sun Sep 11th 2016 at 20:15:13 taotesan
@ Mary Burrell
Not to mention. I will provide more later, when I am back home.
Trevor Noah On Black Americans.
I must have watched this about 20 times.
(https://www.youtube.com/watch?v=GgZYCj39M38)
Not just a pretty face. Excellent.
And the Indian Ocean island the Chagossians were relocated to? No pressure.
Since you are so smart on African geography and all, perhaps another post on Africa from your pen is in order.
The Chagossian diaspora resides on three islands:
▷the Seychelles (east of Kenya/Tanzania) in the Indian Ocean
▷Mauritius east of Madagascar in the Indian Ocean
▷the UK in the Atlantic Ocean
I hope this is not a spoiler, but I saw an excellent 2015 article about the Chagossians in the Independent, a UK based newspaper/news site:
http://www.independent.co.uk/news/uk/home-news/the-chagossians-the-indian-ocean-islanders-exiled-from-their-home-and-struggling-to-make-ends-meet-10169107.html
on Mon Sep 12th 2016 at 21:11:55 taotesan
You are sharp.
( I could not get on to your link, yet).
(http://johnpilger.com/videos/stealing-a-nation)
John Pilger was the investigative journalist who brought it to the world’d attention.
And resw, it is through the Queen of England’s seal, that this crime is allowed to continue.
And do Americans know about one of the most outrageous crimes of the 20st century?
“Today, the main island of Diego Garcia is America’s largest military base in the world, outside the US. There are more than 4,000 troops, two bomber runways, thirty warships and a satellite spy station. The Pentagon calls it an “indispensable platform” for policing the world. It was used as a launch pad for the invasions of both Afghanistan and Iraq.”
on Tue Sep 13th 2016 at 16:36:40 abagond
LOL. Posts on present-day Africa are hard for me because I know from experience that I sit on the other side of a huge Eurocentric lens. For African history, I have better sources. So, the Songhay Empire, say, is much easier for me to do a post on than South Africa.
That said, on a blog like this, I cannot NOT do posts on South Africa and apartheid. And Zimbabwe too. And, because Mary’s suggestions are almost always good, Trevor Noah.
What are some good websites on news in South Africa?
on Sun Sep 18th 2016 at 02:32:20 Solitaire
So I took the map of European nations quiz on the same website and did just as dismally, like almost the exact same score.
Granted, Eastern Europe has changed a lot since I was in school — but I got several of those new little nations while completely blanking on Austria.
What’s even worse is that as I was filling in those little nations, I thought to myself, “That’s right, this all used to be part of the Austro-Hungarian empire.” And I still forgot to add Austria!
I did get Hungary, though. I do have a few brain cells left.
At least I did much better on the South America quiz, but then there were only 12 nations, so it’s not anything to brag about.
on Sun Sep 18th 2016 at 05:30:18 jefe
Thank you for that video link. I love Trevor Noah. I even tried to book tickets to see him on my next trip to New York.
After hearing his testimony, it reminds me of a lot that I grew up with too. It was not until I was in college that I shared a hotel room together with both my parents – and that was in Boston, not in the South. I find it inspiring that he can make a joke of it now and make others laugh.
on Fri Sep 30th 2016 at 21:09:11 taotesan
I am also an autodidact like you. I think learning about the History of Africa is so important in the diaspora. I have learnt about my own history(through woven interconnections) by learning about African American History.
Experiencing a fever of moods, amidst tumult here, so apology for replying in my own time.
Here is an addenda to previous recommendations.
“An Account of Egypt”, by Herodotus –
Abagond had written on it:
(https://abagond.wordpress.com/2015/02/20/black-people-according-to-herodotus/)
“ The Black Athena” by Martin Bernal, highly controversial book.
Ivan Van Sertima was born in Guyana.He is a literary critic, a linguist, an anthropologist and has made a name in all three fields.
He has also been honoured as an historian of world repute by being asked to join UNESCO’s International Commission for Rewriting the Scientific and Cultural History of Mankind. A small sampling from a prolific writer:
1 “Blacks in Science: ancient and modern”.
2. “Black Women in Antiquity”.
3.” Egypt Revisited”.
4.” Egypt: Child of Africa”.
5.” Nile Valley Civilizations”.
6. “African Presence in Early Europe”.
7.” African Presence in Early America”.
8. “Great African Thinkers”.
Dr. John Henrik Clarke, was a Pan-Africanist writer, historian, professor, and a pioneer in the creation of Africana studies and professional institutions. Molefi Kete Asante listed Dr. John Henrik Clarke as one of his 100 Greatest African Americans.
1.”Nile Valley Contributions to Civilization: Exploding the Myths ”
2″.Dawn Voyage: The Black African Discovery of America”
3.”Christopher Columbus and the Afrikan Holocaust: Slavery and the Rise of European Capitalism” ,amongst many other books. (I had half-read this on pdf and it is brilliant. I had also read that he was a teacher par excellence.
Toyin Omoyeni Falola is a Nigerian historian and professor of African Studies.
1.”Colonialism and Violence”.
2.”The power of African cultures”.
Chancellor Williams was an African-American sociologist, historian and writer. He is noted for his work on African civilizations prior to encounters with Europeans. his major work is:
1. “The Destruction of Black Civilization”.
Yosef Alfredo Antonio Ben-Jochannan,was an African-American writer and historian. He was considered to be one of the more prominent Afrocentric scholars.
1.”Africa: Mother of Western Civilization (African-American Heritage)”.
“Meanings of Timbuktu” by Shamil Jeppie, Souleymane Bachir Diagne
(http://www.hsrcpress.ac.za/product.php?productid=2216)
I apologize, if you were interested you would not have found it by my previous description.
Joseph Ki-Zerbo was a Burkinabé historian, politician and writer. He was recognized as one of Africa’s foremost thinkers. Ki-Zerbo campaigned internationally to make make slavery as a crime against humanity and that Africa should get reparations for it, too.
1. “History of Black Africa” originally written in French.
I have not read anything from a Black South African historian’s pen. However, not quite historical, but urgently, one of the most important books, is Steve Biko’s: “I Write What I Like.”
If you might be interested in South African history, there is an online history written by both Black and white authors.
(http://www.sahistory.org.za/)
It has been a while that I have been to my local library. Most of the books I had read a long time ago on History/Archeaology/ Anthropology of Southern and West Africa were authored by white academics.
Correction: “Toward the African Revolution” By Frantz Fanon
I had also read “Black Skin,White Masks” and “The Wretched of the Earth”, both hard to read, but worth the effort.
I would add: “Precolonial Black Africa” by Cheikh Anta Diop, who was an historian, anthropologist, physicist and politician who studied the human race’s origins and pre-colonial African culture. He was a towering intellectual.
Some I have read, half-read and quite a few are on my wish-list, if I had the time and money (and attention span).
I would love to own Unesco General History of Africa” volumes 1-V111.
Entirely at your convenience and schedule, could you let me know if it was at all helpful and what you book/s you had decided on and your take on them?
No rush.
You might want to dip into a few of these online news wbsites. Honestly, I am the last person to vouch for any newspaper, as I have tremendous feeling that I am lied to and the news seems obscured to demonize Black people as the only corrupt ones, that criminality is essentially a Black enterprise and white plutocracy does not exist, even though there are excellent Black editors such as Justice Malala and previously Ferial Haffejee (I grew up with her) of the “Mail And Guardian” – mg.co.za. Most of the news is still dominated by whites.
I go through spells when I cannot bear to read or watch the news for a long while.
That being said,I would recommend
(http://mg.co.za/) with usually excellent editorials &
(http://www.sowetanlive.co.za/) which is regional.
The rest:
(http://www.iol.co.za/)
(http://www.timeslive.co.za/)
(http://www.news24.com/)
I have added City Press:
[(http://mg.co.za/)
(http://www.sowetanlive.co.za/)
(http://city-press.news24.com/) ] as top recommendations.
(http://www.news24.com/SouthAfrica)
I have a comment for you in moderation.
And corrections in moderation.
on Sat Oct 1st 2016 at 21:37:58 abagond
on Sun Oct 2nd 2016 at 01:04:28 abagond
Do you have any opinions about “Cry, the Beloved Country” (1948) by Alan Paton or “The Covenant” (1980) by James Michener?
on Sun Oct 2nd 2016 at 03:26:19 michaeljonbarker
@Taotasen
I am curious of your opinion of the newly elected major of Johnnasburg, Herman Mashaba. I understand he is a self made millionaire from developing hair products called “Black Like You”.
Is South Africa post aparthied a better climate for Black entrepreneurship ?
on Sun Oct 2nd 2016 at 17:57:06 taotesan
Thank you for asking for my input.
By brain is percolating, and stomach queasy scanning all the rave reviews and critiques of “Cry, The Beloved Country” that has won Alan Paton critical acclaim and is probably the widest read book on South Africa.
I have not read the book and am way too jaundiced to write a balanced critique on a dead white man’s paternalistic juvenile dehumanization of Black people. The white liberal is the one who tells us how to respond to his kick.
For now, I had picked up that book was a ‘poetic and nuanced lyricism” of a quixotic look into pre-apartheid South Africa.
Interestingly, Alan Paton’s widow had scurried back to England, after Nelson Mandela was the first (Black) democratically elected President. She complained South Africa was too violent. When one of the most evil systems was about to be codified, she and her late husband opted to stay put.
I will come back to you tomorrow with some kind of synthesis, Abagond.
Are you reading it at the moment or have seen the film with James Earl Jones
and Charles S. Dutton?
If you do, if I may offer that you read Steve Biko’s ‘I Write What I Like’ as a perfect counterpoint to white liberalism in South Africa.
“The Covenant” was banned in South Africa during apartheid. That in itself should not carry the have to read, because it was verboten. It was merely banned because Michener had wrote about apartheid in his particular style. I have not read “The Covenant” either.
Although, through blurbs, it starts with the San migration, it has a lens through Afrikaners and their history, hundreds of pages long. You will come out dirty. That the tome ends in 1980, when the country was in political turmoil, I do not think justifies reading 900 pages.
If there are any questions or suggestions, I could e-mail you.
(You are catching me out as my reading of late has been from the pen of African American and Caribbean writers).
” it reminds me of a lot that I grew up with too. It was not until I was in college that I shared a hotel room together with both my parents – and that was in Boston, not in the South”
I do not share your stance on Kiwi’s antipathy towards Black people.
That said, I am tremendously saddened to read your story with your mother and father.
I have read a bit about Jim Crow South, but were there codified laws like the ‘immorality act’ , ‘mixed marriages act’ as in South Africa, that legally made such unions illegal, punishable to the full-extent of the law?
In some way, if my child was born during Jim Crow or apartheid, tragedy such as yours, Trevor Noah and Bessie Head would have been befallen my small family.
He is extremely clever, if you know what I mean, to embody magnanimity and self-deprecation showing up the absolute absurdity behind personal tragedy. One can laugh, go mad, like Bessie Head, or die of a broken heart like my half-brother.
I misspelled Taotesan’s name. My apologies
on Mon Oct 3rd 2016 at 00:46:14 Mary Burrell
@taotesan: I thank you for your wonderful suggestions I have decided to go with the UNESCO General History of Africa Volumes. However I will definitely explore some of the other books you suggested. Many thanks sister.🤓🤓
on Mon Oct 3rd 2016 at 04:35:05 abagond
I have copies of both books and am wondering if they are worth reading.
on Mon Oct 3rd 2016 at 21:16:40 taotesan
@ michaeljonbarker :Not a problem at all, will reply later.
As a person that subscribes to Black consciousness, I cannot recommend” ‘Cry, The Beloved Country” the liberals handbook, in good conscience. If you do, use James Baldwin’s understanding of white innocence, and Biko’s appraisal of the white liberal to thoroughly appreciate the project of white South Africans instant self exoneration of crimes against humanity, whilst successfully demonizing the Black (criminals) victims, casting themselves (whites) as civilizing saviours and victims of pinned privilege. This book is one of those.
Of all the reviews, not one Black voice was amongst the praise.
I can’t read anything written by white South Africans without thick cynical cataracts. Strained to yet give good recommendations, because most books are still published white authors.
Wow. Thanks. I was afraid of that.
Quite long, dismiss if necessary.
From studynotes and reviews: (that you won’t find on goodreads)
My obtuse understanding of interweaving Alan Paton’s life and that of the ‘white antagonist’, fleshed out an the white protagonist, this is a beautifully written book about the skin deep understanding of the liberal. Paton, concedes that the South African Black is broken by cultural decimation, through enforced labour, and land loss, through the white exploitation. The landowner Jarvis/ Paton, cannot go below the skin of genocide and slavery and recent recipients of African land, to see that they themselves are the criminals and invaders.
Instead they are come with ersatz Christianity as means of reconciling the irreconcilable. The landowner offering cheap benevolent philosophy to the victim is small change, a pro-active balm against an intuitive sense that white people deserved to be killed for their crimes. The same Christianity that has made the landless, beasts of burden, docile, preaches to the Black man to love his oppressor. There is no sense of irony through Paton, that Jarvis that he is a settler, an invader, but some-one tied to the land, as echoed in Alan Paton living on acres and acres of land, displacing the Native and relying on him for mining, and domestic servitude, and the indentured servitude of subcontinental Indians(in Kwa Zulu Natal).
Got carried away.
That the book was published before 1948, just when virulent Nazi-inspired racism codified under Afrikaner apartheid, was put in place, his vision of South Africa , though quixotic, yet Paton himself and his white ‘protaganists’ never found apartheid repugnant enough to up and leave in disgust to their mother country, merely offering a critique of the status quo, on the racist uncles of Afrikanerdom.
The Afrikaners gave the British and Jewish liberals shade to tolerate the worst abominations. Merely , by describing the abominations and offering advice to the Native about his own liberation through a foreign ‘civilizing’ Christianity betrays the paternalism of the white saviour, without really doing anything, except to dispense maudlin, schmaltzy forgiveness, in a flipped script, that is not theirs to forgive. The liberal colonist gets to keep the land and the minerals, his own religion, obscene wealth hypocritical dependence on cheap labour and the saved façade of goodly ‘anti-racism’, power, exemption from psychological torture, and arrogance to lecture the Indigine, dispensing ‘philanthropy’ through civilizing the already dismembered,disenfranchised and dispossessed.
Any white man killing any black person would have gotten off scot- free. As a matter of fact less than a handful over the last century and a bit has been jailed for killing, stealing, raping any Black man and woman. Khumalo is jailed for killing the settlers son, who forgives him. The unnatural bending forced upon Africans to endure the most abnormal circumstances with no way out is out of the criticism of the white man who is the originator of that abnormality. My words not, Paton’s.
Sophisticated white man’s tears where ‘forgiveness’ is not theirs to give. Alan Paton and Jarvis stayed put on land that was stripped from Blacks 1913 Native Land Act. They did not give it up back then, and they still have not given it back now.
on Thu Oct 6th 2016 at 23:02:42 taotesan
Only a pleasure.
@ michaeljonbarker.
Yes, poportunities have indeed opened up for some South Africans across the board. There are now a few millionaires and a middle-class due to entrepreneurship. ( I, myself am had two failed small businesses- one being freshly prepared vegan and vegetarian food ).There was no Black middl-class twenty years ago.
Most however , are situated in the corporate environment. Before, all that talent was consigned as cheap labour. However, many people have good ideas, but the failure rate for entrepreneurship is very high compared to other countries – about 70% due to complex reasons- competition for markets, not having requisite business skills, lack of role model emulation, high interest rates for start-up , lack of infrastructure, lack of finance due to lack of assets, background of terrible education system and an alloy of other reasons.
What I am more concerned about is the Black and Coloured membership of the Democratic Aliance. The DA is essentially a Jewish and afrikaner party. Some Blacks do not see that they are being played even with leadership positions the top positions, like mayorship. The top echelons of the party are not Black and has strong ties with Zionism. Its unstated mission is to re-install white rule, applying similar undermining tactics as the Jewish presence in the NAACP.
(http://www.smesouthafrica.co.za/15427/The-state-of-SAs-township-entrepreneurship/)
on Thu Apr 12th 2018 at 09:02:38 satanforce
Hey Abagond – check your e-mail again. Could you help me with that thing I asked you?
on Fri Apr 13th 2018 at 16:56:38 abagond
Satanforce’s comments on this thread have been removed per his request.
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« “Where are you really from?”
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The map of white people
Fri Apr 11th 2014 by abagond
The map of white people was not on the Internet, so I made one. Conversely, it is a map of people of colour.
The map (click on it to enlarge) uses four colours:
dark blue: 75% to 100% white
medium blue: 50% to 75% white
light blue: 25% to 50% white
grey: 0% to 25% white
majority POC: grey and light blue
majority white: medium and dark blue
multiracial: light and medium blue
But who is white? For this map two kinds of people are:
Those who self-identify as white, like in a census.
Those who belong to an ethnic group that is historically Christian or Jewish, with roots in West Eurasia.
That means white Hispanics, Armenians and Lebanese Christians are in, most Africans and Muslims, even Albanians, are out.
In the case of self-identification, note that someone who is considered white in one country might not be considered white in another.
I tried different definitions. This one is clean, easy to use and a good, general approximation.
Notes on each region:
North America: While the rest of the map is based on data from 2006 to 2011, Mexico is based on the last census that asked about race: in 1921! For the US, Hispanics who identify as white are counted as white. Doing otherwise led to paradoxes outside the US. Notice that Canada is not as lily-white as many imagine.
South America: Argentina, the pope’s home country, is extremely white. Its most “diverse” province, Chubut, is close to 90% white.
Most whites in South America, like in North America, live outside the tropics, which run from Havana to Rio. Worldwide most whites live in the temperate zone, 23.5 to 66.5 degrees from the equator:
Europe, North Africa and West Asia: Albania and Kosovo are mostly Muslim so they do not count as white, even though they are in Europe. I did not use “Europe” or “European” in my definition of white because then I would have to define Europe too! Not a battle I wanted or needed to fight.
Siberia: The people in the dark blue region are mainly ethnic Russians. Russia and Kazakhstan keep very good records on ethnicity.
The rest of Africa: The surprise here is South Africa. I thought at least the Cape would be light blue. Whites are less than 25% in every single province. The way they complained you would think they were like a third of the country. It is galling to see this.
The rest of Asia: The dark blue at the top is the tail end of Russia.
Oceania: The North Island of New Zealand is more multiracial than Australia, mostly because of the Maori.
Because Australia, Siberia, Canada and Argentina are large but thinly settled, the map makes it seem like there are more white people than there are.
To correct that, let’s scale each region according to its total population and put the map back together:
Notice that whites are not the main part of the world, but only a sixth of it.
Sources: Mainly the English and Russian Wikipedias (2014), the census of Argentina (2010) and New Zealand (2006) and the graphic that inspired this post (2011).
The map of Black people
Black Canada: a brief history
Peters projection
demographically weighted history
Geographical terms:
on Sun Apr 13th 2014 at 03:24:22 Atillah_kasimeyoglu
This is awesome. I really appreciated the time it took to make this.
I see one glaring problem:
You wrote that you couldn’t count Albanians as white because they were Muslim. This doesn’t make any sense.
There are plenty of white Muslims!
Albanians are of Illyrian background, pre-Indo-European. Bosnians, Chechens, and even some Turks are pretty white looking people. Just curious why you’d erroneously link religion to race.
Otherwise, enjoyable piece.
on Sun Apr 13th 2014 at 03:53:59 qweerdo
Thank you so much for taking the time to do this. So dang informative, especially the part where you put everything to scale at the end.
on Sun Apr 13th 2014 at 04:09:59 jefe
Notice that Canada is not as lily-white as many imagine.
Who on earth imagines that? I suppose the same people who thought “American” meant “white”?
Also, I noticed that quite a few people in Argentina were likely mestizo, but identified as “white”. In any case, Buenos Aires looked a lot more white and European to me than any large city I have ever been to in North America.
on Sun Apr 13th 2014 at 05:17:42 Brothawolf
Fascinating.
As a side note, I suspect the reason why most people thought Canada was “lily-white” is due to media images. Most of time. white Canadians are in front of the camera, not much of anyone else.
Costa Rica is an interesting exception – the only country in the tropical zone that is majority white. But of course, so is Northern Australia.
on Sun Apr 13th 2014 at 09:04:08 Teodor Constantin B
Very weird definition of white. How can you link race to religion? Have you seen albanians? They are white as shit, just like bosniak and lots of Chechen, blond hair with often blue eyes.
Here’s a picture of’em. they are very white. they are whiter than Greeks and Romanians who have a majority of dark hair, darker skin than these guys and I’ve seen algerians who could be taken for white or european. If I go to France or England, there is a big possibility of being called gypsy thieves (as it happened), but these people, especially Bosnian and Albanians are taken for white. Also I have met really dark skin Lebanese christian. This white thing I think it refers to Westerners, that is Anglo Saxon, Scandinavian, Finnish, french, Spanish (Catalan) because easterners and westerners look really different at least for me. and of course the ashkenazi in Israel, the very light skin, blue eyes type are not really jewish by blood.
A question.
Would there even be a map of “white” people, or diverse racial classifications if Africans were not forcibly removed from their native lands, tied up in chains and made to produce free labor elsewhere in many parts of the western world??
Another question.
If Africans are no longer being made to work for free by “whites,” why on Earth are they (especially in the USA) still categorizing themselves as “white?”
Last question.
What real purpose does being “white” serve in today’s current world?
on Sun Apr 13th 2014 at 09:51:19 Kartoffel
That Map also highlights that white settler colonies only “worked” outside of the “old world” (except for Israel). The attemps to populate South Africa, Namibia and Algeria with white people failed.
on Sun Apr 13th 2014 at 11:52:39 lifelearner
This map is great! Definitely points out their narcissism. South Africa has little representation and yet they own most everything regarding political/economic power-SMH
on Sun Apr 13th 2014 at 12:26:10 Bulanik
@ Teodor Constantin B
Very weird definition of white. How can you link race to religion? Have you seen albanians? They are white as sh-t, just like bosniak and lots of Chechen, blond hair with often blue eyes.
Here’s a picture of’em. they are very white. they are whiter than Greeks and Romanians who have a majority of dark hair, darker skin than these guys and I’ve seen algerians who could be taken for white or european.
There ARE some Albanians who look like the children in your link, some Balkan people are pale and blond, but with that one, random photo, you seem to be suggesting that that appearance is “representative”of what Albanians really look like.
But it’s not really the whole picture is it? Some, or many, are very blond, true, but some are unmistakably “dark”. I am amazed you didn’t notice that, too, only their whiteness.
I wonder whether YOUR definition could be weirder than Abagond’s!
Over many, many generations, didn’t some Albanians intermarry with darker Balkan neighsbours, like Serbs, and Greeks? Or is that a fallacy?
What about the Turks in Albania?
Also, I heard that the (Ottoman) Turks had African men in their military, and African women as concubines in their homes, and this could explain why some (*cough*) supposedly “white” people in South East Europe don’t look all that white.
Take a fairly well-known person like Rita Ora, a child of Albanian parents, who is often mistaken for black or at least mixed race: http://shrani.si/f/3q/fc/RppDesI/46469.jpg
Come to think of it, I can think of a few more fairly well-known Albanians who would certainly be considered “dark”, rather than blond.
And, then you mention Chechens, who are also mostly “white as s**t … blond hair with often blue eyes…”
Well. I don’t think all ethnic Russians would agree with you at all, because some have, or had, a tendency to refer to people from the Caucasus region (and southern Russia) as “black”! That’s due to the common “dark” appearance of those people … Is thatperception also “weird”?
Perhaps they Russians perceive them as ASIAN, rather than anything else..?
Of course there are pale skin and light eye and hair colours among these different groups of people, but I have to wonder about your generalisation, because it absolutely depends on who is doing the looking.
@ Abagond: excellent maps!
on Sun Apr 13th 2014 at 12:53:49 v8driver
interesting point: to wit, perhaps the image of ‘white christ’ provides a rallying point like that for ‘white identity’
on Sun Apr 13th 2014 at 15:04:00 Da Jokah
Thanks abagond. I don’t know what whites would do if they didn’t have racist negros to tell them who is and isn’t white. Though I don’t think I can take any map seriously that omits people solely on the basis of religion. By that logic someone could change their race simply by changing their religion.
@dj you can change anything
…like social constructs, and such.
Religion is definitely a social construct, race not so much. But I’m not naive enough to think I could change your beliefs on that any more than I could change someone’s belief on creationism. When you claim race is a social construct you’re actually putting yourself in the creationist camp by denying evolution. Congratulations. You’re a religious nut even if you don’t recognize your belief as religious.
on Sun Apr 13th 2014 at 16:19:02 Chris
Can you explain how Israel is a “white” country? It seems that this is a common misconception. The Ashkenazi Jews who founded the country are still Jews. They’re still descended from an ancient indigenous population that was exiled from Israel. They have some European admixture genetically, but so do African-Americans. They were never counted as truly white in the European imagination, yet when they return to the land where they have ancient roots, people flip the script on them and claim that they were white Europeans all along. Seems to me that the main reason that people single out Israel is the role of Ashkenazi Jews in founding the country. Had they been brown-skinned Sephardic or Mizrahi Jews, the country would be seen as an organic entity with a right to exist.
Otherwise, the map is pretty interesting, and I really dug the note about Australia being sparsely populated but geographically huge, making it seem much more “white” then it is in terms of raw numbers.
I’m also curious about your reasoning on Lebanon. Is it because a good chunk of Lebanese are Christians?
on Sun Apr 13th 2014 at 16:33:28 King
When you claim race is a social construct you’re actually putting yourself in the creationist camp by denying evolution.
Haha! That is about as ridiculous a statement as can be offered. Classic Jokah!
^ Yes, classic derailment. Soon he will be discussing chimps and orangutans (after all, their original habitats are in different continents).
Not at all. If someone is going to deny the evolutionary basis of subspecies by calling it a “social construct” then it’s not much of a leap to deny the evolutionary basis of species by calling it a social construct as well. The difference between the two is merely a matter of degree.
on Sun Apr 13th 2014 at 17:08:30 biff
This is interesting and thought provoking. White populations seem to be in decline in all of these places. Aside from Russia and maybe part of Eastern Europe, the primarily white areas seem to have heavy migration of non-whites.
Re: Argentina, white in BA. Not so much in the countryside, even though they might identify as white, they are not treated quite the same.
Yes Jokah, except that the preponderance of opinions do both biologists and geneticists agree that the phenotypic differences that we see within human beings are not actually different “sub species” but that there is only one categorically defined “species” of human.
Only stupid people (like part-time HBD bloggers) think that humans are divided into subspecies by evolution. NO major university on earth teaches this.
on Sun Apr 13th 2014 at 18:25:36 eco
“The surprise here is South Africa. I thought at least the Cape would be light blue. Whites are less than 25% in every single province. The way they complained you would think they were like a third of the country. It is galling to see this.”
Congratulations! You now understand how Europeans feel about Africans and Asians in Europe.
the phenotypic differences that we see within human beings are not actually different “sub species” but that there is only one categorically defined “species” of human
Yes, the differences between human populations are clinal, not at the level of subspecies which would require actual DNA differences among all of the individuals between the two populations and no interbreeding between the populations, even though it might be possible. No such phenomenon exists in modern human populations.
ie, there is an evolutionary basis for subspecies, but this does not apply to humans. Any attempt to use subspecies arguments for humans is already specious, not to mention inducing that from differences between species.
would like to see the links to the sources that this spurious line of reasoning is being lifted from.
on Sun Apr 13th 2014 at 18:59:13 Legion
The surprise here is South Africa. I thought at least the Cape would be light blue. Whites are less than 25% in every single province. The way they complained you would think they were like a third of the country.
No, one would not necessarily think that white numbers were large. One would think whites consider themselves large in some sense. It’s common for conqueror peoples to control a much larger conquered populace. You have to smash the people you’re invading initially in whatever way you think will be most effective but after you’ve smashed them you don’t necessarily need large numbers of conquerors to keep watch over the conquered. (British in India as an example, but I think this has been common through history.)
What I’m getting at is whites controlled the economic capital during Apartheid, in that sense they were large and important, putting aside the evil of the regime for a moment. Whites are economically entrenched in S.A., they are still control a lot of capital, it would be on that basis that they would complain as though they are ‘large’ by some metric, and they are.
@ eco
I don’t know what you mean. Can you explain it.
*No, one would not necessarily think that they are a third of the country.
was what my first sentence should have been.
White is not strictly biological or genetic. There is a cultural component to it. It is not the same thing as “Caucasian”, which goes all the way to the Ganges. For example:
1. When I put Yasmeen Ghauri, 100% Caucasian, on my list of beautiful white women, commenters told me she was not “white” because her father is from Pakistan. Many adjustments later, I found I could just slip in Lebanese or Armenian women on my list, but nothing more. Kim Kardashian (Armenian American) is herself a grey case.
2. The Arab Trader argument. It implies that Arabs are not white. Arabs are the “they” of “They did it too!”, to prove that WHITES are not uniquely evil. No one has ever advanced a Portuguese or Dutch trader argument.
3. No one in the US sees, say, Ralph Nader, Christa McAuliffe or Steve Jobs as anything but white – all of Arab descent. No perpetual foreigner stereotype for them. Americanized Arabs seem to count as white, at least if they are not Muslim.
4. For years and years I have been reading in The Economist about whether Turkey is European. Cyprus is part of the EU, yet all kinds of excuses were made not to let in Turkey, a sturdy NATO ally that is in much better economic shape than, say, Greece. Or Cyprus. It seems to boil down to their being Muslim.
5. The Western prejudice against Muslims, even among scholars, is well-documented. The whole thing about Obama being a Secret Muslim takes such prejudice for granted. Muslim American civil rights are arguably in a worse state than even Black civil rights. They are racially profiled along with Black, Latino and Native Americans.
So, yeah, Muslims in the main are not “white”. They did not take part in the European Expansion. They have been the VICTIMS of Western imperialism. QUITE UNLIKE Israel.
Israeli Jews are as white as sin. It is one of the CRUEL IRONIES of the past hundred years. At Auschwitz they were NOT white. As rulers of one of the most openly racist regimes on earth, complete with US backing, they are white. They put South African whites to shame and that is damn white. The only way Americans can stomach Israel’s crimes is because they share their racism.
Huh? In what European country are only Africans or Asians allowed to vote and own most of the country’s wealth?
The whole point of “white” is to excuse Western crimes – like slavery, genocide (even now, though those things are largely in the past) and theft (of native land, ongoing inequality and imperialism). In the US it is used to blind voters to their class interests.
So your definition of white is dependent on whether or not you see the people as racists and oppressors? US backing? If you dumped a bunch of Israeli Jews in NYC, people would approach them trying to speak to them in Spanish and NOT because they were taken for Spaniards. The cruel irony is that Zionism was created as a bulwark against European racism and is now considered to be of a piece with it.
@ Chris
You shall know them by their fruits.
Your completly right that religion plays a huge part in the cunstruction of whiteness an europeanness. But I would differentiate between religion in general and the religion of an individual or a relativly small minority. Predominantly muslim societies are precieved as non-white, but a muslim of turkish decent in France might not. Because Albanians and Bosniaks are seen as part of the Balkan people (who in general today are regarded as European), they are also seen as European. With Arabs it’s the other way around.
It just seems that for Abagond, “white” is just a catch all for things he doesn’t like. So people of color can become “white” at the flick of a switch if there are considered to be oppressors. Its like what happened to George Zimmerman’s racial identity, only extrapolated across the entire globe.
@ Kartoffel
Predominantly muslim societies are precieved as non-white, but a muslim of turkish decent in France might not..
An example, please. And, could you explain why this is so, if it really is so.
I appreciate the point of this post, but I’m still wondering about what you said about Siberia — if you are saying the population doesn’t count (?), then neither should Alaska’s. Siberian cities have bigger populations than Alaskan ones and more than most Canadian ones.
Sam made that point, and I think that’s still true.
I should have said “non-european”, not “non-white”. An example for what, the perception of societies or individuals?
On the question why that is. I think it’s down to how we perceive “otherness” and construct our identity. Religion is certainly a very important marker to determine otherness, but it can be “overruled”. So Albania is perceived as “non-european” because of Islam, but as “european” because the whole region is now regarded as mainland Europe.
Even if that were true, reality isn’t determined by a show of hands or by an appeal to authority. But it isn’t true because no such consensus exists. In fact, surveys show that a majority of physical anthropologists acknowledge biological races.
Who should I believe — you or my lying eyes?
on Sun Apr 13th 2014 at 21:35:42 Sharina
I think it is a matter to be looked upon for all society and not just Abagond. All too often a person who looks to be a poc is argued to be white by certain white men only if said person is a law biding citizen. Once a crime is committed is when they are deemed the other. Great example is during the Zimmerman debacle a white man proudly stated …”of course Zimmerman is not white because he got caught. ” I am sure others will see this statement as they please, but it implies to me that had he not then he would be accepted as the honorary white.
Societies and/or individuals.
I’d just like to understand what you mean from your earliest comment.
Societies: In the contemporary concept of Europe the borders of Europe are pretty much the ones between Islam and Christianity/former Christianity, with some muslim and orthodox-christian societies with undecided status.
Individual: A native German who converts to Islam is still regarded as german and european. For example we have the converted muslim radical Pierre Vogel who nationalists have called a lunatic, a traitor or terrorst. But I’ve never heard that he was called non-european or non-white.
That’s what I meant in short: A muslim society/people=not european. A muslim person=might be european.
on Sun Apr 13th 2014 at 22:19:48 The map of white people | Community Village Dai...
[…] The map of white people was not on the Internet, so I made one. Conversely, it is a map of people of colour.The map (click on it to enlarge) uses four colours:dark blue: 75% to 100% whitemedium blue: 50% to 75% whitelight blue: 25% to 50% whitegrey: 0% to 25% whiteSo:majority POC: grey and light bluemajority white: medium and dark bluemultiracial: light and medium blue […]
@kartoffel from what i’ve seen, personally? a man declaring as muslim would be that first. american christian? not so much
Your definition of white is very bizarre.
The “dark” ethnic Albanians are no darker than southern Italians, who are classified as white and colonized a bit of Africa. They’re still very western looking and have been in Europe for a very long time.
Again- I find it a bit amazing that people somehow link religion with a race. This is one of the dumbest, most ignorant ideas I’ve ever heard of. There are many white Muslims. Chechens, Bulgarian Pomaks, Bosnians, Albanians. I enjoyed this map until that fact ruined it.
My god haven’t y’all seen Malcolm X?
Remember the scene where he goes to Meccas and realizes Muslims are of all colors and changes his views on humanity completely ?
But you seem to be saying religious conversion will racialize someone.
It doesn’t work the other way either: if Muslim and renounce their faith, it will not suddenly make them Another Ethnicity that they weren’t in the first place.
Are you serious when you say the borders of Europe are now cut depending on where Christianity ends and Islam begins? As if it were so clear cut! Religion is only one cause of division in Europe.
And, whatever happened to secularism in Europe?
I was under the impression that the separation of Church and State was not a contemporary thing but went back a few hundred years…
However, what I was curious about was this:
…Predominantly muslim societies are precieved as non-{European}, but a muslim of turkish decent in France might not.
You mean compared to Arabs?
What do you mean: I am trying to understand your point.
From what I know of Turks in France, this percepton would not generally be so (beyond the French republican ideal of citzenship).
I gave no definition of “white”, and when I think about, most of the Muslims that I know you would fall over to class as “white”, even though they personally wouldn’t.
I’m quite familiar with pale and dark “whites”, even ones that have intermarried somewhat with Asians (or Africans) over generations.
@ Attilah…I just re-read what you said, and can only conclude that you did really read what I said.
on Mon Apr 14th 2014 at 00:20:28 eco
@Legion
Sure. I think Abagond experienced a feeling a lot of Europeans know very well. It’s being irritated by non-native minority groups who don’t seem to be aware how insignificant they really are, and are responsible for an amount of whining that’s completely disproportional to their deserved role in society.
The obvious difference is that the white South Africans whined about losing power they did not deserve to have to begin with, and Africans and Asians in Europe tend to whine about not being able to gain the power and privileges they do not deserve, because of their numbers and non-native status. By “power and privileges” I mean political representation, wealth, representation in popular culture and the media, religious and cultural freedoms, etc.
Large segments of both, white South Africans and Africans and Asians in Europe, seem to think that for some reason the native population should adjust itself to them and consider the non-native voices as at least as equally important as their own when it comes to national matters.
That’s not the kind of analogy I was making. I see how my previous comment was vague, but I think I explained my point of view in this one.
Haha! Eco are you typing that with a straight face, or is this some kind of elaborate joke?
on Mon Apr 14th 2014 at 03:14:49 Mady Preece
The only reason I had to post on this article as well, is to simply say:
Stop spreading your hatred of white people on the internet.
If we met in person, I am sure you would like me very much; I am extremely friendly funny and attractive (at least I think I am). I am trying to humanize myself, rather then hiding behind a computer screen. So please, do the same and have so god damn faith in humanity.
I guess I’m trolling a bit, because I know this kind of stuff is inflammatory and I intentionally used a few completely unsubtle phrases, but overall I’m serious. I genuinely think native people should be privileged over non-natives. Even over non-native citizens. It seems to me that true, perfect equality is unobtainable and of all possible solutions, that allow geographically distant cultures to coexist peacefully, favoring natives is the least of all evils.
on Mon Apr 14th 2014 at 03:38:21 jefe
What is native people? Descendent of indigenous peoples, the people that got there first?
How do we handle a place like Hawaii? or Mauritius?
What’s more, many of the descendants of the non-native people may be so ethnically or racially complicated that they have no other place to “return” to. Where do the Cape Coloureds in S.A. or the Singaporean Eurasian call home?
on Mon Apr 14th 2014 at 05:58:24 gatobranco1
It is really ilogical to classify Greeks, Bulgarians, Serbians, Armenians and Georgians as “white”, while considering Chechens, Daghestanis, Azeris, Albanians, Kosovars, Bosnians, Turks(of Turkey) as “non white”. All these people and some other, as Kurds, Lebanese and also many Afghans, Iranians, Tajiks, Pamiris etc. are best considered as “darker Europoids”. In Russia they are often called “people of Caucasian appearance” and distinguished both from white Slavs as well as from Mongoloids ar Blacks. Although some of people of these nationalities may look as central Europeans.
In Russia, even some Italian, Spanish and Portuguese people very likely would be considered Caucasian, rather than White or European, especially in the street when nobody knows who they are.
on Mon Apr 14th 2014 at 07:23:45 Legion
You’re only trolling if your insincere. You are serious about this view of yours though. Actually Eco, it’s quite an interesting view (and has quite an air of danger to it).
I genuinely think native people should be privileged over non-natives. Even over non-native citizens.
Well you can think/feel that but it’s not a sound view. Putting aside the issue of fairness, your view simply isn’t sound. It’s a recipe for immigrant criminal underclasses and a vicious circle of incarcerating the “ungrateful” immigrants, because they should be overjoyed to live in a society that locks them into 2nd class status.
I don’t believe that immigrants should be permitted to over turn the cultures of their new home countries through political power plays. Cultural change should take place organically, I think.
It seems to me that true, perfect equality is unobtainable and of all possible solutions, that allow geographically distant cultures to coexist peacefully, favoring natives is the least of all evils.
^That is a statement about protecting something. What is it you want to protect? Culture?
“Arabs” would be very difficult to classify according to race, some of them in Sudan or Mauritania, are definitely black, some as in Lebanon or Syria – most likely white, while North Africans, including Egyptians, are probably of mixed race there are plenty people there who are not white by any criteria, but some may look as Southern Europoids.
An interesting fact is that Hausa speaking black Africans call all white Europeans ‘Bature” which taken etymologically means “Turkish”.
In Russia there are some nuances related to race. A person, who has a Caucasian appearance and, let’s say, partially Georgian ancestors, but who is Russian in language, culture and upbringing, would be considered nevertheless a Slav and European, not a Caucasian by people who know him. He however could be taken as a Caucasian by strangers in the street and even hurled racial insults against him, especially in times when there are tensions between Slavic Russians and “Caucasians”, however these people if becoming aware that he is a Russian, would treat him as Russian and probably even apologize for taking him as Caucasian.
Ethnic Russians with Asiatic admixture(there are quite a few of such especially in Siberia would be mostly also considered as Slav Europeans, especially if the admixture of asiatic features is not too much.
Right, Siberia has more people than Canada and way more than Alaska. I scaled the last map, though, by region, not by country or state. So Canada and Argentina got scaled with their continents. They would each be about the size of Oceania or Siberia if scaled on their own. To scale the map at the country or state level I would need one of those cartogram programs.
Oppression is hardly whites-only. I would not consider Hutus, Arabic-speaking Sudanese, Mao, Mobutu, Pol Pot, Clarence Thomas, Condoleezza Rice or Barack Obama to be “white”.
on Mon Apr 14th 2014 at 12:21:14 Bulanik
Come now, King. 😀
You know eco behaves like that because Poland never succeeded in nabbing any colonial territories, not formally anyway. It never materialized…
(Sniff, sniff.)
on Mon Apr 14th 2014 at 12:42:08 Bobby M
About giving native born citizens more privileges:
While naturalized citizens should have most of the rights of the native born – they (immigrants) should have to change their culture and language to fit in with the country they move to, not the other way around.
Poor Poland 😦 Everyone deserves a colony.
Poland never aspired having colonies overseas. In 16-18, Poland, or more exactly Polish-Lithuanian commonwealth ruled vast territories in the East Europe, comprising modern Lithuania, Belarus and much of Ukraine. However in the end of 18 century weakened Poland was partitioned between three large empires – Russia, Prussia and Austria. It reemerged as souvereign state only in November 1918 only to be again partitioned by Communist Russia and Nazi Germany in 1939. In 1945 it reemerged again this time as a puppet state of the Communist Empire and finally became a truly souvereign state in 1989-1991.
Never aspired?
In the September session of 1937 of the League of Nations, didn’t Poland demand colonies? I also recollect hearing that in the same era, wasn’t there some kind of treaty signed between Liberia and Poland (which favoured Poland), and didn’t Poles try to settle there?
http://www.jstor.org/discover/10.2307/2492615?uid=3738232&uid=2&uid=4&sid=21103660958551
I’ve heard of this of a proposal called the “Colonial Theses of Poland”, which was produced by Polish Ministry of Foreign Affairs, but have not have read it:
http://cosmos.ucc.ie/cs1064/jabowen/IPSC/php/art.php?aid=168422
They also had settlement ambitions in Brazil.
http://www.polishroots.org/Research/History/poles_latinamerica/tabid/241/Default.aspx
on Mon Apr 14th 2014 at 13:55:54 Brothawolf
eco said,
Here we go again. Is it me, or does it seem like whites are scrambling to find any hint of being the victim of reverse racism? Instead of self-reflections, they prefer to have the tables turned, not to learn how it feels like to be the “other”, but to condemn nonwhites.
gatobranco1, we are aware of the history. We’re just ribbing eco because he is making nonsensical statements. Two can play at that game!
Additionally, before I forget: the Senegalese who explained that part about Liberia, also said an area of Gambia was leased by the Polish-Lithuanian Commonwealth at one time, too.
http://en.wikipedia.org/wiki/History_of_The_Gambia
There’s probably a lot more info out there than that…
Probably you have in mind the colonial plans of Jacob the duke of the Duchy of Couland and Semigallia(now part of Latvia), which was in 17 century a vassal state of Polish Lithuanian commonwealth
http://en.wikipedia.org/wiki/Couronian_colonization
In Polish and Liothuanian history these attempt played extremely marginal role. Both Polish and Lithuanian nobles were of continental not of seafaring mentality, they were interested in the lands in East.
As for colonies in period before 1939, not only Poland ranted about colonies, but even in Lithuania, a country with just 2,5 millions of population some people had dreams about establishing a Lithuanian colony in Africa:) A professor of Kaunas university Pakštas even made a travel to Africa in order to look for places where Lithuanians could settle:) He described his impressions in the book “from Kaunas to Kapstadt”(Nuo Kauno iki Kapstadt’o). I have read this book long ago, but I remember the passage where professor described the Portuguese colonizators in Angola with deep admiration for the “civilizational work” which they have made.
Thus colonialism wa really a fashion then:)
No, not at all gatobranco1. It’s not something I “had in mind”.
As King says: we are aware of the history.
Saying “it was the times”, or colonialisation was merely a fashion in the olden days, or “extremely marginal”, is an OPINION — and changes nothing.
on Mon Apr 14th 2014 at 15:58:16 Sharina
Bobby M
Please provide and example of where it is the other way around? Oh and nothing made up please because I am not in the mood to waddle through your imagination.
Nope. Not just you at all.
@ Legion
Well said. Though I agree with economic in that he might be trolling if his goal was to stir the pot, but seeing this is his actual view I am confused as to if it it trolling. Can it be both?
The trolling thing is questionable with Eco. I still can’t take his comments on the “white American music thread” seriously.
“What is native people? Descendent of indigenous peoples, the people that got there first? (…)”
I’m talking about something I consider a general ideal, not a precise rule that should be enforced globally. I have no desire to tell nations, ethnic/cultural groups other than my own how they should live their lives and who they should see as one of their own.
I think of nativity the way I think of race. It’s not a real, material thing. In a lot of ways it’s a social construct. The concept of nativity does break down in many contexts. You are absolutely right about that. BUT! So does race. I’m aware of the limitations of the term “native” as much as I’m aware of the limitations of “race”. I think it’s as reasonable to talk about a land’s native people as it’s reasonable to talk about its black or white population.
@Kiwi
“I’ve found that people who make the ‘Nothing is perfect!’ argument (like for racial equality) don’t really care about equality at all. It’s just a lazy, rhetorical deflection tactic they use to paint any effort at civilization as tautologically futile. Why? Well, I just said. They don’t care.”
It’s not lazy. It’s selfish and cynical. It’s not about not wanting to do the work. It’s about recognizing that if you are a native, a member of a dominating majority, multiculturalism is not going to benefit you. Since it requires mutual compromises you can only lose because of it. So why should you want to do it?
“It’s a recipe for immigrant criminal underclasses and a vicious circle of incarcerating the ‘ungrateful’ immigrants, because they should be overjoyed to live in a society that locks them into 2nd class status. ”
True, but that’s pretty much what’s happening in the supposedly multicultural societies, isn’t it? Somebody is always getting the short end of the stick, some group always needs to be the underclass. I think it’s ultimately a choice between glass and concrete ceilings.
“That is a statement about protecting something. What is it you want to protect? Culture?”
Yeah, that’s accurate, but I’ll phrase it in a more general way – it’s about the groups’ right to self-determination.
You said that “cultural change should take place organically”, I’m taking it further – I think the initiative to change should only come from within. In the case of the native/non-native dynamic, natives are not required to do anything, not required to make any concessions. Why should they be?
Based on that principle I wouldn’t support the white South Africans’ right to vote. They have no right to tell the native people what the natives should do with their country. Unless, of course, the natives decide on their own to expand the non-natives’ rights. I apply that reasoning whenever it makes sense to speak of nativity.
“I still can’t take his comments on the ‘white American music thread’ seriously.”
😀 You mean the stuff about socially conscious rap?
@ legion excuse my typos. This auto-correct is killing me. Should be eco not economic.
on Mon Apr 14th 2014 at 23:49:00 Chris
That’s what I don’t get. If you want to make the argument that the Jews went from Auschwitz to apartheid, I can see the argument. I’m not in total agreement, but I can see your argument. I just don’t get where the white racial categorization comes in. It seems to me that your argument is that:
1. In 1943, the European Jews were subject to racist policies backed by a mighty Western war machine.
2. Today, Israelis are subjecting another people to racist policies backed by a mighty Western war machine.
But, I don’t get what the relationship is between that argument, and race, which I see as an extension of how a person looks. I mean, blacks were oppressed by the West for many years, but now the foremost Western military power is headed by a black man who has taken unprecedented liberties with regard to war powers, allowing himself the right to take out anyone, anywhere for any reason. He also authorized the NSA to scoop up enough information to make George Bush II seethe with envy. But he’s still black. Because he looks black and the USA has a one-drop rule. He didn’t become white when he attained massive institutional power.
As a side note, there is a popular French singer named Enrico Macias. The guy would certainly be considered to be a man of color in the USA. He is a Sephardic Jew who was exiled from his native Algeria upon that nation’s independence in 1962. He was never invited back to Algeria, or to any Arab country, for that matter, because he has always expressed staunch solidarity with the Jewish state over the years. This year he announced that, after having spent half a century in France, he would be moving to Israel full time and taking up citizenship there. I don’t think that at the tender age of 75, his racial identity will change based on his new citizenship.
on Tue Apr 15th 2014 at 00:02:13 Chris
To illustrate my point regarding Macias, here he is in 1973 singing “Hava Nagila” with Charles Aznavour, another great French chansonnier. He’s stylin’ in that purple suit! I put this comment separately, lest it get snagged in moderation. (http://www.youtube.com/watch?v=QTRS3oB4b6s)
on Tue Apr 15th 2014 at 00:39:33 v8driver
who is aipac going to lobby in the usa?
http://www.huffingtonpost.com/bill-lucey/113th-congress-by-the-num_b_2737382.html
“Gender/Ethnicity.
• A record number 100 woman serve in the 113th Congress: 80 in the House, including 3 Delegates, and 20 in the Senate.
• 43 African Americans will serve in the House and 2 in the Senate. This House number includes 2 Delegates.
• A record number 38 Hispanic or Latino members are represented in the 113th Congress: 34 in the House, including 1 Delegate and the Resident Commissioner, and 4 in the Senate.
• 13 members (10 Representatives, 2 Delegates, and 1 Senator) are Asian American or Pacific Islanders.
• 1 American Indian (Native American) serves in the House.”
http://www.pewresearch.org/daily-number/aipac-outspends-other-religion-related-advocacy-groups-in-washington-d-c/
israel was granted a wide autonomy after wwii especially to expand and defend their acquisition over there, they got the dice roll, and they are going with it, man.
and to spell it out if you aren’t with me so far as the song goes, it would tend to suggest a support for a ‘judeo-christian’, american is a christian nation ‘partnership’, thank god they didn’t take out the reactor in iran
i’m still unclear on where abagond comes down on north african/arab/semitic as ‘white’ persuant to the “sub-saharan africa thread,” i guess it would fall under what i understand his preference to 3 race only theory, as previously stated; however north africa and ‘the middle east’ are grey in this picture so i am totally confused on that one.
on Tue Apr 15th 2014 at 04:51:17 abagond
Ideas like “race”, “white”. “black”, “savage”, etc, are largely a side effect of Western imperialism. Whiteness comes from the barrel of a gun. The idea that it comes from physical appearance and biology is a self-serving fairy tale used to make Western crimes seem inevitable, acceptable, part of the natural order of things, to make racial inequality seem “just”. I have read enough ancient Greek history to know that racism and the racist status quo are hardly “natural” or some kind of inevitable outcome, to know that it is excuse-making for those in power.
In 1943 Jews were at the “wrong” side of that gun barrel. Now they are on the other side, going above and beyond the call of duty as hired guns for the US. They have ordered their society in a racist fashion, almost like a mini US where Palestinians play the part of Blacks and Natives rolled into one. They even have the Manifest Destiny thing down: that they have a God-given right to other people’s land, people whom they dehumanize and massacre. On top of all that, Jews are accepted as white in the US.
Archaeologists will see Israel as an extension of North American society, as part of the European Expansion, Why would they not?
@ v8driver
North Africa is grey not so much because of its genetics but because I do not see most Muslims as “white”:
https://abagond.wordpress.com/2014/04/11/the-map-of-white-people/#comment-227425
on Tue Apr 15th 2014 at 05:34:30 gatobranco1
[No, not at all gatobranco1. It’s not something I “had in mind”.
Saying “it was the times”, or colonialisation was merely a fashion in the olden days, or “extremely marginal”, is an OPINION — and changes nothing.]
I just wanted to say that all these attempts at “colonialism” from the side of Polish or Lithuanians or Duchy of Courland or maybe also Czechs, Hungarians or Lichtensteinians(who knows:))) are rather comedy and farce:)) 99.99% of the people in these countries knew nothing about any colonial plans:)
Perhaps the only book that the most Polish knew anything at all about Africa and other far away countries was the book of the author Henryk Sienkiewicz “In Desert and Wilderness”(W pustyni i puszczy) http://en.wikipedia.org/wiki/In_Desert_and_Wilderness about two white children who succeed in escaping during the rebellion of Sudanese Mahdi, and have to pass through unexplored parts of Africa. The book is full of stereotypes about Africans prevalent in the 19 century Europe. Sienkiewicz apparently never visited Africa, he took his “wisdom” from descriptions of French and British colonialists.
As regards Brasil, in the 30ies of 20 century Brasilian government indeed had concerns that some of European nations may use their immigrant communities in Brasil in order to carve up colonies. Poland apparently was one of the states that caused concern for Brasilians, but of course the source of the most concern was Germany and Italy, since these nations had more potential, obviously strived for colonies in other parts of the world and had quite large imigrant communities in Brasil.
Besides that the most of Brasilians were quite unsatisfied that German, Italian, Polish and other immigrants do not want integrate in the Brasilian society, but instead strive at maintaining their own closed communities, their own language and culture, their own schools, press, churches etc. Besides, many of these immigrants even in the second and even third generation did not speak Portuguese or spoke very little, especially in rural areas. In 1937 the President Getulio Vargas adopted stringent laws that closed all immigrant political and cultural organizations and even banished speaking in public other languages than Portuguese. After stepping down of Vargas in 1945 these laws were repealed, however they have intiated swifter assimilation of imigrant communities into Brasilian mainstream.
It is not quite correct say that in 1941-45 Jews were killed by German Nazis because they were viewed as “non-white”. German Nazis had more complex racial hierarchy than just “white-nonwhite”. The highest group was not just “white”, but “Nordic”, Germanic” or Aryan”. Jews obviously were at the lowest rung of the hierarchy, Black African on the second lowest, yet the Slavs – Polish and Russians especially(who are “white” by any standards) – were also viewed as “Untermenschen”(subhumans), not very much better than Jews or Blacks. However Nazis had much higher regards for some other Slavic peoples, such as Slovaks and Croatians, as well as for Turkic and Iranic peoples. Asiatic Japanese were allies of Nazis in the WWII.
As for Israeli Jews after 1948, I think your assessment is largely correct. There indeed is much resemblance in the racist mentality of WASP and Israelis, and this hardly surprising since the racism of both stems from the same source – the Old Testament of the Bible, which is full of the stories of racial exclusion and genocide. Catholic nations read much less of the Bible in former centuries, and if they read it was the most often the New Testament, not the Old. This situation had its reflection in the fact that the racism of Spanish, Portuguese of French, which certainly existed, was nevertheless more attenuated, less exclusionary and segregationist, that that of White Anglos, Dutch Afrikaaners or Israelis. E.g. if I am not mistaken there was no “one drop rule” in French Louisiana, and “quarterons” were often accepted as whites or at least there was no stigma on intermarriage.
on Tue Apr 15th 2014 at 07:34:00 sami parkkonen
@abagond: Very interesting. Two comments:
I wonder why you do not see muslims as “white” when there are hundreds of thousands of “racially” white muslims in Europe. Bosniaks, albanians etc. consider themselves as whites in racial sense. Is your view based on the fact that you do not see arabs as pure whites, regardless what they think about themselves and thus all muslims are not white, or is this american view on the subject? I personally would not class anybody racially based on their religious views or beliefs. There are hundreds of million africans who are christians who are in racial cathegories clearly black and yet if there ever was a “white european” religion it is christianity.
Siberia seems to be a bit of mystery for most of the people. Usually its colonization by the russian is linked on race too but reality is something else. There were white natives in western parts of Siberia millenias before the first russians. Starting from the west of Urals, the people called Ves/Vepsä lived in the east from the White Sea and Lake Ladoga and they were white finnourgic people. The bjarmians who also lived on the west from the Urals were also white etc.
Also the hungarians came from the Urals as late as 800’s and they too are of finnougric stock. They migrated to their present day Hungary in early 800’s and lived nomadic life on the present day Ukraine much of the early part of 800’s. And they too are white as can be.
The northern parts of the present day Russia were also lands of other finnougric people, the Murom, Mari, Meretsh etc. The söavic tribes migrated to that region only from 700’s onwards. So the native population of the western half of the Siberia was white by the usual racial definitions from as long as can be traced.
Also the Saami/Sami people of Lapland are white by the usual racial definitions and yet they are natives of the whole Fennoscandia region.
All of these native peoples of the north east and Siberia were colonized and some even wiped out from existence by the new comers from the west. This happened also in Prussia in medieval times where some of the native people were completely wiped out by the germans and other invaders.
All of which also show that racial definitions are a huge load of BS and, just like you say, based on the economics, exploitation and colonization by white minority.
As seen in here:
@sami parkkonen
I think that you do not orient very well in geography:) The ugrofinnic people people that you have mentioned – Vepsä, Permians, Murom, Mari, Meshchera have never lived in Siberia, they lived in the European part of modern Russia. The Vepsä inhabited areas near the lake Laattokka, for example, are quite close to St. Petersburg and to Finnish border which is quite a way to go from Sibiria:))
Siberia as it is usually defined as land to the east of Urals. I strongly doubt if peoples who lived to the East of Urals – Siberian Tatars, Khanty, Mansi – were “white”.
Concerning Hungarians, the most of modern day Hungarians are not the descendants of Magyar Onogur tribes, but rather of Slavs that Magyars found on arrival and Germans that settled in Hungary later. Perhaps it would be quite difficult tell to which racial group ancient Magyars belonged, the origin of their language – Ugro-Finic or Turkic is also not very clear although many scholar classify them as Ugro-Finic.
As for the population of Sibiria proper, the indigenous people belong to several groups as Samoyed(as Nenets, Enets, Nganasan, Selkup – partly also in European part of Russia as well), Khanty-Mansi(condidered as “ugro-finic” yet theIr language has very little similarity with either Finnish or Hungarian), Turkic(Siberian Tatars, Altai, Tuva, Khakas, Saha Yakut, Dolgan). Mongolic(Buryat), Tungusic(Even, Evenki, Nanai, Oroch, Oroqen) and so-called “Paleoasiatic” not a single group but including several unrelated groups(Chukchi-Koryak, Nivkh, Ket, Yukagir)
I think that racially almost all these groups were Asiatic(Mongoloid).
Most of the population of Siberia today speak Russian and identify as Russians and Slavs. Since there was neither “one drop rule” nor ban on miscegenation in Russia, many of Russians in Siberia have admixture of Asiatic(Mongoloid) blood in their veins. Many indigenous people today are also speakers of Russian, the local languages with the most speakers are Buryat, Saha-Yakut, Khakass, Tuva, Siberian Tatar. Everyone is bilingual in Russian as well.
A question to Abagond
could this gentleman be considered white in the USA?
And how about these girls
(https://www.youtube.com/watch?v=SmdPjhTgPNY)
@ Gato Branco #1
The gentlemen looks kind of Asian, kind of white, but if he spoke with a Texan accent, I might not notice that. The singers look white to me.
BUT I am TERRIBLE at telling whether someone looks white. I used to think these women looked white:
http://images5.fanpop.com/image/photos/27000000/bipasha-bipasha-basu-27092317-400-300.jpg
I see no earth-shaking difference between them and, say, these “white” women:
Or these women, who I am still not sure whether they are “white” or not:
http://www.topnews.in/files/paula-abdul-2.jpg
So it is extremely hard for me to buy this idea of “white” as strictly genetic or just a matter of objective physical appearance. If it were that clear-cut or objective, I should be able to easily tell the difference.
Ann Curry looks like Filipina, definitely not white, Paula Abdul like Latina or Filipino Mestiza, Patricia Ford, Yasmeen Ghauri, Maya Rudolph, Bipasha Basu and Kim Kardashian would appear rather like Iranic(Iranian/Tajik/Afghan) or Caucasoid(Azeri/Georgian/Armenian/Chechen) although they could also be taken as Mediterranian(Italian/Spanish/Greek), but probably not as truly Central Europeans.
Nevertheless none of them(except Ann Curry) would look very out of place in the street of a Russian, Polish, Czech, Hungarian or Lithuanian city
For other ladies whom you call definitely “white” it is difficult to say, but all of them are rather of Mediterranian type, some may also look as Tajik/Iranian. Megan Fox has in this picture eyebrows made up as Tajik ladies do, but otherwise she looks more like Spanish senorita.
You indeed are right that it is not always easy to determine “whiteness” according only to looks, especially for the people who are born in Mediterranian/Middle East/Central Asia however religion(Christian or Muslim) is also a poor criterium, since there are lots of Muslims, especially in Bosnia, Albania, Kosovo and Turkey who look definitely white, even like Central European. Probably the best thing is to accept that not everyone can be neatly and easily classified as white or non-white.
@gatobranco:
Thanks for reply. However your definition of Siberia is, typically, quite limited. As for the finnourgic people, such as the Vepsäläiset and others, they lived way up east.
The area west from Urals is known as West Siberia, but granted, not very widely known fact. Actually, geographically, the whole Finland belongs to the western Siberia, but if we feel to be picky, then the whole land mass east from the White Sea is Siberia.
The hungarians of present day are mixed. naturally, but their original home is in Urals. So the white hungarians originated from Siberia.
I understand that it is very hard to realise that there is whole multitude of white natives anywhere outside the west european area, but so it is. Siberia included.
Yes, in east Siberia the natives are more asian BUT still many of them belong the peoples who speak uralian languages.
Like so
The point here is that dividing world by races is in my mind pretty stupid. Culturally yes, but “racially” it is silly.
@ Sami
I thought of using both linguistics and genetics to define “white”. The trouble is that, either way, Iran, Pakistan and much of India would become part of “white”. That was not the sort of white I had in mind. Linguistics would also leave out Finland and Hungary – or, if I included Uralic languages, I would also have to let in all Indo-European languages, which would again bring in India. Religion fell much closer to the fault lines that defined the sort of people I had in mind. I am not saying it is perfect, but is a better approximation than the alternatives I could think of.
I commented on my thinking on Muslims and whiteness here:
on Tue Apr 15th 2014 at 17:05:28 Bulanik
@ gatobranco1,
Perhaps the only book that the most Polish knew anything at all about Africa and other far away countries was the book of the author Henryk Sienkiewicz “In Desert and Wilderness”(W pustyni i puszczy)
Haha. 😀
I’ve heard of this book as well! 😀 Also “Murzynek Bambo” (“Bamboo, the little black child”), a poem of some charm — but how does this makes any difference to the argument?
You see, as farcical as you think Polish attempts at colonisation were, I’m not sure if your reading of European histories has caused you to consider the links between imagination and ideology… Those harmless, if stereotypical references to darker, foreign people from faraway places, can, at times, utlimately lead to “civilizing missions” by even well-meaning Europeans.
You only have to look at the example of India and the emergence of the British in that country to realize that.
(*Amal Chatterjee’s “Creation of India in the Colonial Imagination” explains the the early colonial ideas about the “exotic East” which later led to “primitive subject nation” perceptions.)
When you said the Poles never aspired to be colonialists, it was clearly not so.
From what Taras Hunczak says about Poland’s colonial ambitions, they weren’t, at one time, as “extremely” marginal about it at all. I had to smile at the irony of this, as Poland and other Eastern Slavs were perceived as “Kolonie” (colonies) by Germany who settled in those territories for centuries…
I don’t mean to say that the facts you provide aren’t insightful.
However, your analysis of “extreme” marginality simply isn’t supported.
A government’s decision to colonize other places is not arrived at from dubious and derivative ideas in children’s books alone.
* http://www.fishpond.com.au/Books/Representations-of-India-1740-1840-Amal-Chatterjee/9781283653176
on Wed Apr 16th 2014 at 04:40:20 gatobranco1
@ sami parkkonen
Your definition of “Western Sibiria” is indeed a novelty, since usually Western Sibiria is defined as the territory between Ural mountains in West and Yenissey river in East
http://en.wikipedia.org/wiki/West_Siberian_Plain
http://en.wikipedia.org/wiki/West_Siberian_economic_region
I think you should give at least some refrences where Norhern part of the European Russia or even Finland is referred to as “Western Siberia”. I have never heard such definition yet.
I have never seen other people on the earth so “racially aware” as North-American White Anglos or WASP, with such obsession on “whiteness”. For the most peoples of Central and Eastern Europe “whiteness” is maybe important however it is ethnical origin that matters the most.
For the most of Muslim peoples the issue whether they are “white” or “non-white” is rather non-issue at all. The most important thing is whether one is Muslim or not. Muslims classify people not according to race, real or presumed, but according to religion.
Many Muslims were pround of their ancestry, whether Arabic, Turkic, Kurdish or Iranian, yet what really mattered to them was the ancestry only from paternal side, not from maternal. Whether their mothers were free Muslim women or slave concubines of African, Asiatic or European origin(Sharia allowed for free Muslim men 4 free spouses and illimited number of concubines), the progeny were free if their father was free and had the same inheritance rights according to Sharia and could inherit father’s property, quite differently to the situation of the children of white slaveholders and their black concubines in the North America.
A very important point is that slavery was not racialized in the Muslim world, their were slaves of almost all races and nations in Muslim lands. Arabic or Swahili slave traders brought black slaves from Africa, while Crimean Tatars sold their Polish, Ukrainian ans Russian captives. Other traders could by bringing slaves from Asiatic countries.
Emancipated slaves were given the same rights under Sharia like free Muslim people and they sometimes could rise very high in the social hierarchy, sometime becoming even viziers and rulers. For example, Egypt was run quite a long time by ex-slave sultans of Turkic Qipchak or Circassian origin.
Because of all that there is much less racial awareness among Muslims, and I suppose that Muslim emigrants asked about race, prefer to answer that they not white and black or asian or something of that kind, but are just “Muslims” or “Turks” or “Arabs” or “Iranians” so creating the impression that “Muslim” is a race.
Indeed if the WASP imagination has constructed several ancestry based races( White, Black, Asian, Pacifical Islander, Native American) and one “race” based on language and culture(Latino) so, according to white Anglos, why it couldn’t be one more “race” based this time on religion? Indeed, an average White Anglo is happy only if he is able to neatly categorize people in “racial” categories. If there are some people who defy such categorization, “whites” feel deep psychological pain and anxiety as if the world were about to collapse:)
even if you have classified Linda Perry as “white” but to me she looks indeed black. It is more visible in a better picture
As for Julia Louis Dreyfus, in this picture she looks very much like Turk or Iranian http://upload.wikimedia.org/wikipedia/commons/d/d3/Julia_Louis-Dreyfus_VF_2012_Shankbone_3.jpg
A little bit about “beauty standards” in dependance of race.
For me who live in a country where many women are blonde, and most of the rest are rather “gray”(neither blonde nor dark) rather than dark haired, the most attractive “white” women for me are exactly those who are dark haired, of Spanish/Latino, South Italian, Turkish or Iranian/Tajik type, not very high in stature and rather thick-set. While the beauty standards of Mediterranian, Arabic and Iranian guys are the exact opposite – they are really crazy about tall blonde girls:)
As for “non-white” the most pretty for me are women from Philippines and Congo. This of course does not mean that I consider the ladies from rest of world as ugly:D
Not only Muslims are difficult to classify in the racial optics of White Anglos. Another “hard nut to crack” are Filipinos. There are plenty discussions of the internet the participants of which try to answer deeply philosophical question – whether Filipinos are Asians, Pacific Islanders or Latinos. Sometimes these are questions of white guys, sometime of Flipino Americans who are puzzled by insistant questions of their white neighbors and colleagues about their “race”.
Indeed they are in geographical Asia, have a smattering of Confucian values, but mostly do not look like typical Asians(Chinese, Korean, Japanese); many of Filipinos indeed look similar to Pacific islanders and are remotly related to them linguistically yet Philippines has never been considered a part of Oceania; Filipinos have many Spanish elements in their culture(as Catolicism, musical traditions, many Spanish borrowings in local languages) as well as Spanish surnames, some, especially Filipino Mestizo, can even look like typical Latinos, yet the absolute majority of them speak no word in Spanish but instead Tagalog, Cebuano, Ilokano and some 100 more languages together with English. Really a puzzle for racial classification:))
Besides that, Filipinos could even be considered black since many have admixture of the blood of Agtas(“Negritos”) who are black beyond doubt although differ from African by their much lower stature
http://en.wikipedia.org/wiki/Negrito
on Wed Apr 16th 2014 at 18:41:49 sami parkkonen
Well, do not take my word. Check this program. It is a finnish documentary series “Finnougric people in Thirty Days”, part 6: The Mordvans and the Komi, who live in Siberia. I guess even you would admit that the Komi live in Siberia proper, the one even you can accept as Siberia. And you can look yourself if the Komi are “black”, “asian” or what ever, or “white”. They are finnougric nation, have lived in Siberia from times immemorial etc.
http://areena.yle.fi/tv/1783782
And yes, Komi is west from the Urals
on Wed Apr 16th 2014 at 21:17:10 Bulanik
@ gatobranco1
…Indeed they are in geographical Asia, have a smattering of Confucian values, but mostly do not look like typical Asians(Chinese, Korean, Japanese)
Just to say, whenever I come to this blog, I always have to remember that “Asia” starts in the Eastern part of the continent, somewhere around China, roughly, very roughly, and Asians are, as you say Chinese, Korean, Japanese, etc. Typical Asians never, NEVER, ever look like this:
http://1.bp.blogspot.com/-LQAFScAGSxk/TyKUkgNQSxI/AAAAAAAAANA/jgmcjwC6gRk/s1600/indian+skin.jpg,
Or like this:
https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcT-aDEIME0xlyDsjWc-8hJbFIKxyprX_5TKpQqbGzE3pGzcHE2f
Or this:
…even though there are well over 1.6 billion of them, right in the middle of Asia.
I do see what you mean, gatobranco — it’s just general observation I am making.
on Thu Apr 17th 2014 at 05:44:38 gatobranco1
Unfortunately, the video does not load but it can be found on you tube as well I’ll see. Kiitos paljon:)
I think I know sufficiently well about finno-ugric people. All they(Komi Zyrian, Komi Permyak, Udmurt, Mari, Erzya, Moksha) except Khanty-Mansi live in the European Russia to the West of Urals, not in Siberia. All finno-ugric people to the West of Urals are white. As for Khanty-Mansi living to the East of Urals, from the pictures I have seen on the net, they appear rather Eurasian but not truly Asiatic/mongoloid. Some even may look white
http://commons.wikimedia.org/wiki/Category:Khanty
http://www.eki.ee/books/redbook/khants.shtml
http://www.eki.ee/books/redbook/mansis.shtml
I have however some doubts whether Khanty and Mansi are truly related to Finns. I have found textbooks of Khanty and Mansi languages on internet. These languages have not a slightest ressemblance with Finnish, but neither they do resemble Hungarian. Finnish and Hungarian does not seem to be related either. There are a dozen Hungarian words which resemble Finnish but there are much more which resemble Turkic or Chuvashian.
Chuvash, a non-ugrofinic people living in European Russia (distantly related to Turkic) are also white. Volga Tatars I tink are also mostly white since most of them are descendant of ancient Bulgars and spoke once a dialact similar to Chuvash before they switched to Qipchaq. Some are of Qipchaq extraction and can have Asiatic features.
Regarding Bulgars there is hypothesis that they once lived in the mountainous area in the Central Asia. Probably the name of the city Falghar(Tajikistan) located on the Turkestan range can be related to the word Bulgar. Later they migrated to the North Caucasus area and from there they went and established north to the Black Sea. In 7 century attacked by Khazars they split into several groups, one of them went to Volga region, another led by Khan Asparukh migratred to South of Danube where they established their own powerful state bud made only minority in it(about 20-30% how it is believed) and later slavicized.
It is difficult to tell what language Bulgars spoke, but probably they were a tribal confederation different tribes of which spoke Turkic or rather proto-Chuvashian, Iranic and remaining maybe Finno-Ugric or Proto-Hungarian languages. However these language(s) are not attested. What remains are only some 200 words in modern Slavic Bulgarian which are believed to be “proto-Bulgarian”.
Anyway it is quite probably that these ancient Bulgars were white, and not mongoloid how it is assumed by some scholars.
concerning the concept Asia.
Geographical Asia – in the East it includes Philippines and the most of Indonesia, but does not includes New-Guinea island, Melanesia, Micronesia or Polinesia which are considered to be part of Oceania. In the West, geographical Asia’s limits are Urals mountains, Caucasus range, Bosphorus straits, Egean Sea, Suez Channel and Red Sea.
Asia as used for the purposes of sports competitions, UN agencies etc. – sometimes it can include parts of Oceania or Australia/NZ, sometimes not. Turkey, Israel, Armenia, Azerbaijan Republic, Georgia are often included into Europe
Asian as “race” in the USA – it includes chiefly representatives of the peoples of the Confucian culture – Chinese, Japanese, Korean and Vietnamese, but also may include all those peoples who have more or less “mongoloid” appearance(narrower eyes etc.), as Thai, Burmese, Cambodians, Mongolians, Tibetans, Central Asian and Siberian Turkic peoples etc. It can inlude Indonesians and Filipinos as well
Asian as “race” in the Great Britain – in the GB Asian it means Indo-Pakistanis.
on Thu Apr 17th 2014 at 07:49:25 Pay it Forward
^^ I have commented several times in the past on this as well.
“Asian” in the US context = East Asian, but is sometimes extended to include the others as listed by gatobranco.
In Britian, however, East Asians are variously known as Chinese, “Oriental” etc., with the group /racial designation of “Asian” going to South Asians, who in the US are typically referred as Indians or “East Indians”, I have also heard “Gandhi Indians” and “Hindus” (actual religious affiliation notwithstanding) by older folk, as well as a least two derogatory identifiers which I will not list here.
In this same vein West and Southwest Asians in the USare not typically referred to as “Asians” either. They are Middle Easterners or “Arabs”
Not using the identifier “Asian” for US-based Indians and other South Asians is not intended as a snub, just as — and I will assume — no snub is intended for British-based East Asians in the regard of typically assigning South Asians, rather than East Asians, the general and more encompassing designation of just plain “Asian”.
Concerning the definition of “who is white” there is some interesting historical cases:
An Indian man(Sikh) who wanted to prove that he is white and thus eligible for naturalization(at the time when the Us law allowed only white and black African persons for naturalization)
http://en.wikipedia.org/wiki/United_States_v._Bhagat_Singh_Thind
Another example a Japanese man who wanted Japanese reclassified as white also for naturalization purposes
http://en.wikipedia.org/wiki/Ozawa_v._United_States
However both claims were rejected at that time(1920ies)
Probably that one of things that perpetrates the racial stereotypes and racial thinking is the use of the concept “race” in thie official censuses of the USA
http://www.census.gov/prod/2001pubs/cenbr01-1.pdf
Interesting enough the census qualifies as “white” people “having origins in any of the original peoples of Europe, the Middle East, or North Africa. It includes people who indicated their race or races as “White” or wrote in entries such as
Irish, German, Italian, Lebanese, Near Easterner, Arab, or Polish.”
Thus according to the USA census, all Muslims of North Africa, Arab countries, Turkey, Iran, Albania, Bosnia, maybe also from some other countries would be qualified as white. Thus it goes against the popular perception of the US white Anglos(reported by Abagond) that “Muslims are not white”.
on Thu Apr 17th 2014 at 17:24:55 abagond
@ Eco: Comment deleted for making personal remarks.
More: I deleted your comments about Bulanik’s Polish friends. You are dragging in her private life to smear her. Not cool. I know you think they are imaginary, but you have no way to prove it, at least not on an English-only forum like this one. You will just have to let it go.
on Thu Apr 17th 2014 at 18:08:04 Sharina
gatobranco1,
Well then the obvious question is are all Muslims of North Africa? If they are not then can you reasonable continue to conclude them as white? Also can white according to USA standards be considered white according to them?
on Thu Apr 17th 2014 at 20:12:12 Bulanik
The commonly-understood concepts Asia and its geography have been discussed a few times on this blog, but I feel there’s a bit more to it in the light of reading the recent exchanges about belonging and ethnicity.
Pay it Forward is correct: it IS generally true that in the UK (not for Ireland, though), the term Asian is understood to refer to South Asians.
If someone is of Chinese or Burmese descent, for example, then it’s their particular nationality that will be the identifier instead of the supposedly generic designation “Asian”.
(Perhaps one reason “Asian” became exclusively associated with East Asians was because it was another, more polite way, of saying Mongoloid, the way “Caucasian” became a polite way of saying White…?)
However, it is also my experience that East Asians and Southeast Asians are ALSO encompassed by the term “Asian” in normal conversations.
It is acceptable to call ALL Asians “Asians”, and no one bats an eyelid:
I used to notice this in conversations between and among different Asian ethnicities in England and Scotland.
Therefore, this wouldn’t be an issue of “snubbing”, or exclusion, at all: both East and South Asians see each other as equally and absolutely Asian!
In the UK at least.
Any awkwardness or misunderstanding only seems to arise among Irish, continental Europeans, Americans and Australians who — and I generalise sweepingly now — appear to refuse to see South Asians as Asian.
“No”, they will say, “Indians aren’t Asians.”
These same individuals will say South Asians are Arabs or Middle Easterners.
I have also seen and heard East Asians (US and Australia) say that South Asians cannot have the Asian “racial” designation and be called Asians because that term belongs to them.
So, at best — at best — the term “Asian” is inconsistent.
There is no pan-Asian identity.
Personally, I don’t think “Asian” it is a good identifier for Indians, Sri Lankans, Indians, etc. Sure, they are certainly Asian, like Koreans are Asian, but “Asian” is far, far too general, and far, far too unqualified whether it’s applied to Sri Lankans just as much as it is to Koreans.
Ethnicity always develops differently in each country, and this causes international comparisons to be excluding and confusing, uselessly so.
I believe more accurate and specific descriptions would be much more useful for the naming of different Asian peoples.
on Thu Apr 17th 2014 at 21:01:56 Linda
Gatobranco1, just because the USA census “says so” — does not make it so.
Since Islam is a religion, then that means it encompasses people of different “races” and Ethnicities — just like Christianity
Even the term “Arab” does not mean “White”…. because many people called “Arabs” in north Africa are mixed-race or can be classified as “black”
I think because “race” is political and a social construct developed by white Europeans/American in order to perpetuate their own Agenda’s–
we are all now stuck with shoes that sometimes don’t fit.
http://newsfeed.time.com/2012/09/07/egyptian-immigrant-wants-to-be-reclassified-as-black/
Mostafa Hefny feels he’s been black his whole life. The U.S. government doesn’t agree.
when Mostafa Hefny immigrated to the United States from Egypt in 1978, he didn’t get a say in that decision.
“The US government [interviewer] said, ‘You are now white,”
White” is defined as “a person having origins in any of the original peoples of Europe, the Middle East, or North Africa” — which is why the U.S. government classifies Hefny as such.
However, the designation for “Black or African American” applies to “a person having origins in any of the black racial groups of Africa.” According to CBS, Hefny says that he is descended from the Nubians, the ancient group of Egyptians from the northern part of Sudan and southern part of Egypt.
Since the 1980s, CBS reports, Henfy has been fighting to have the U.S. government reclassify him as black, which is how he’s always seen himself.”
believe it or not, not every “Arab” north African denies their black African mixed ancestry.
just because the USA census “says so” — does not make it so.
A census has uses, but it’s only a tool, not Definitive and Exhaustive Truth…just an enumeration method grounded in arbitrary and socially constructed principles, and one that must be ever-open to improvement.
on Fri Apr 18th 2014 at 04:53:57 gatobranco1
What is indeed strange for me, is that a goverment oficial imposed on Mustafa Hefny a racial label of his own picking instead allowing M. Hefny to autodefine himself. The important point is here is not whether the official classified M. Hefny “correctly” and “incorrectly”, but the mere fact the the official was so arrogant as to better know the racial affiliation of the person than the person himself.
As far I understand from the now existing census rules, in our days, had M. Hefny autodefined as “Arab”, or “Egyptian” he would still be finally classified as “white” but he would also be free to autodefine as “black” if he wished so.
Since it happened in 1979, maybe it was a hangover from old racist times before the Civil Rights Movement when it was usual to establish person’s “race” against his own expressed will and the race was considered as something “objective”, “physical” rather than “social” or “identitary”. I have also heard stories how immigrant people from Europe were forced by officials to identify as “Caucasians” which of course had no sense for them.
I just wanted to ask – whether such forced identification of person’s race still happens today in States?
The US census currently also recognizes people from Indian subcontinent as Asian
A person having origins in any of the original peoples of the Far East, Southeast Asia, or the Indian Subcontinent, including, for example, Cambodia, China, India, Japan, Korea, Malaysia, Pakistan, the Philippine Islands, Thailand, and Vietnam.
So that in the census, the label “Asian” includes Indian Subcontinent, the Confucian countries, the Indo-Buddhist countries(as Sri Lanka, Thailand, Myanmar, Cambodia) and Austronesian countries(Indonesia, Malaysia, Philippines). It is not clear whether it also includes Mongolia or Central Asian countries as Kazakstan or Russian Siberia, but since persons now are allowed no to autodefine, so probably persons from these countries could autodefine as Asians.
In “geographical Asia” there are several cultural areas with different cultural identity, certainly there is no pan-Asian identity.
If one take “geographical Asia” one can distinguished numerous regional cultural (rather than “racial”) identities:
– Arab Muslim(Syria, Lebanon, Irac, Saudo Arabia, Yemen, Golf States)
– Arab Christian(Lebanon, Syria, including also Egytian Copts, but these not in geographical Asia)
– Israeli Jew(Israel)
– Turkic Muslim (Turkey, Rep. of Azerbaijan, Turkmenistan, Uzbekistan, Kazakhastan, Kirgizstan)
– Iranic Muslim(Iran, Tajikistan, Afghanistan)
– Caucasian Muslim(Circassian, Chechen, Daghestani)
– Caucasian Christian(Armenian, Georgian)
– Indo-Pakistani Muslim(Pakistan, India, Bangladesh)
– Hindu(India, Nepal)
– Indo-Buddhist/Theravadin (Sri Lanka, Thailand, Myanmar, Laos, Cambodia)
– Tibetan Mahayanic Buddhist (Tibet, Mongolia, Buryatia, Kalmykia)
– Russian Slav Orthodox(Siberia)
– Confucian(China, Korea, Vietnam, Japan)
– Muslim Austronesians( Malaysia, Indonesia)
– Catholic Austronesians (Philippines)
There are, of course smaller ethnical groups in many countries who not fit in any of these categories
Although much of what I have wrote seems like religious labels, it is much more cultural than merely religious:
-first, religion strongly affects culture, much more than presumed or imagined “race”;
-secondly Hinduism, Islam, Buddhism is not merely a system of belief, but an integral philosophy establishing a way of life, while Confucianism is not a religion but rather an ethical and philosophical teaching
-thirdly even those persons who are not deeply religious or even not religious at all, the most often they belong to the cultural area they were born, e.g. an atheist born in a Muslim or Hindu country still will be mostly Muslim or Hindu in culture; Many Koreans are Christians yet mostly Confucians in culture.
Concerning the question whether some North Africans are aware of their black ancestry.
In Egypt, it may be true. There are much tensions in Egypt between Upper Egyptians(Saeedi, Nubian) and the more affluent people of the Nile Delta. The former are often stereotypized and marginalized by the latter. Upper Egyptians have darker color of skin, they are poorer, they often do low-paid jobs when they live in Cairo, they have a dialect of Arabic different from the Standard Cairene variety, and different social customs.
On the contrary, Cairo and the Nile Delta always were more affluent, the center of political power and received the most of the migrations of “white” peoples(greeks, romans, arabs, circassians, ottoman turks).
Thus is quite possible that South Egyptians may feel discriminated and this can make them aware of their African roots. It is less likely that Cairo and Delta Egyptians would be mindful of their African heritage, although this is not excluded. The president Gamal Abdel Nasser, for example wanted to become a strong leader not only in the Arabic world, but in the black Africa as well. Did he use any cultural or racial arguments besides purely political? I do not know. Maybe some other knows?
As for Maghrib countries, there are strong ethnical tensions between Maghribi Arabs and Imazighen(Berbers), But as far as I know, Imazighen, who are pre-Arab population there, are not black. Moroccans and Algerians do have, however, admixture of African blood due to the importation of black slaves and contacts with Africa. But I do not know how much they are aware of that.
Much of the elite of these countries are by orgin either Arabs, either (especially in Algeria, Tunis and Libya) descendants of Ottoman janissaries or corsary capitans(Turks or European slaves or refugees by origin). Maghrib countries and their elites also had strong influx of Andalusian Arabs(deported by Spanish from Spain). The latter were mostly arabised Spaniards.
on Fri Apr 18th 2014 at 09:01:04 Linda
“gatobranco1
Gatobranco1, you are quoting alot of westernized versions of “African” history
so I will ask you a question, “was Mansa Musa or Askia Muhammad ” imported black slaves?
you do realize that black Africans lived on the Entire continent of Africa and they did not have to be “imported” as slaves to North Africa in order to “add” to the mixture.
and that the Imazighen(Berbers) are not 1 solitary tribe but they are composed of many different Ethnic tribes based on region.. ie Djerba, Mozabites, Siwa, Riffian (the blonds that every likes to boast about but they do not represent the majority of Berbers), Tauregs, etc
the “Arab” slave trade was not the initial way or the only way that black Africans arrived in North Africa.
http://nilevalleypeoples.blogspot.com/2010/05/blog-post_5025.html
Ancient Local Evolution of African mtDNA Haplogroups in Tunisian Berber Populations
“Until recently, some papers suggested that the distribution of the main L haplogroups in North Africa was mainly due to trans-Saharan slave trade.
However in September 2010, a thorough study about Berber mtDNA by Frigi et al. concluded that most of L haplogroups were much older and introduced by an ancient African gene flow around 20,000 years ago.
( haplogroup L is an indigenous black African gene)
The sub-Saharan contribution to northern Africa, starting from the east would have taken place before the Neolithic. The western African contribution to North Africa should have occurred before the Sahara’s formation (15,000 years BP).”
Meaning, black people were already in North Africa before the Maghrebs (Arabs) or Turks arrived.
This is why I mentioned to Abagond that an “Africa” tab is needed — a lot of misconceptions
Certainly contacts started much before than Muslim slave trade.
Imazighen as it is known belongs to the Afroasiatic family of languages, and 5 from 6 of its branches(Chadic, Imazighen, Kushitic, Omotic, Ancient Egyptian) were always located in Africa. Semitic was intially located in Western Asia, semites came to North Africa and Ethiopia later.
With 5 branches of 6 being in Africa, it is inconceivable that the original homeland of the Afro-Asiatic was somewhere else as in Africa. Probably it was somewhere at the lake Chad or in Sudan, and the initial pra-Afro-Aasiatic were with all probability black.
Having migrated from their homeland, they moved north and there subjected to their rule probably some white(?) populations in Maghrib and Egypt. Through the passage of time the black elite in in the North Africa probabably became “whitened” through the intermarriage with white slave girls. I have read somewhere that Egyptian frescos depict Pharaons like black men, and their wives and concubines as white, I do not know if it is true, but it is highly probable.
Probably that the ancestors of Ancient Egyptians or at least their elite came somewhere from Nubia/Sudan since Ancient Nubian cultures display many similarities with Egypt(as building of pyramides).
Another group proceded from Africa to Western Asia where the gave beginning to the Semitic language group.
Later, contacts with the subsaharan Africa never interrupted, despite the desertification of Sahara, so that in all epochs – Carthaginese, Roman. Vandalic, Byzantine, Arab – North Africans traded with the black Africa, not only in slaves of course and the human contacts certainly were not reduced to slave trade alone.
on Fri Apr 18th 2014 at 15:16:33 Bulanik
@ Linda, from your first link:
Our results reveal that Berber speakers have a foundational biogeographic root in Africa and that deep African lineages have continued to evolve in supra-Saharan Africa.
Excellent stuff! Thank you for both those links.
The standard story always shows blacks as “slaves” and being moved about, or “freighted” like cattle “introduced” into the bloodline. It’s almost portrayed like it’s the Natural Order, or something eternal and universal!
At best, this leads to a poor understanding…
This story of African gene flow is narrow. If that is not bad enough, it’s also told the wrong way round. 😀
Recent research is showing that the direction is properly trans-Saharan, into Southern Europea and also the Levant (or what used to be known as the Levant, or the Eastern Mediterranean).
As a cultural staple, this idea has been quite self-serving.
On the “How white was ancient Greece” thread, it’s pretty apparent how much the idea of a White World has penetrated the way we are all supposed to “see” many West Eurasians, for example and especially the Greeks, through the White Lens:
…The British are invested in the Classics, it is the organizing principle of their white, European intellectual identity. The signature of their civilization, the cornerstone of their education.
The Classics is at the root and “the learned vocabulary of international application.”
https://abagond.wordpress.com/2010/03/28/how-white-was-ancient-greece/#comment-193933. Also:
“…similar to the idea that Arabs were a white people who “became” darker by adulteration of their bloodlines. For Greeks, it implies that more Turks moved into Greek lands than the other way round, and that the Greeks themselves started out as uniformly Nordic, blond and blue eyed!
None of this was ever so.
When did the Greeks cease being a people of the Levant?
When did they achieve European-ness and their historic ties with Eastern world get wiped?
The effect though, is clear, because it has white-washed the Ancient Greeks and allowed the West to appropriate this history and culture as its own: from Neoclassiscism in architecture, to literature, the visual arts, theatre, to music…”
https://abagond.wordpress.com/2010/03/28/how-white-was-ancient-greece/#comment-193990
on Fri Apr 18th 2014 at 16:10:04 Da Jokah
There’s no need to “white wash” greeks, berbers or anyone else. This graph is based on data from from The History and Geography of Human Genes by Cavalli-Sforza, Menozzi and Piazza. One interesting thing you’ll notice is that there are four major races, not three, and that northeastern Asians are as close to Caucasians as to southeast Asians. There’s a tendency to lump all Asians together, but they are genetically very different.
Jokah, you supply a graphy and tell me: “…there are four major races, not three, and that northeastern Asians are as close to Caucasians as to southeast Asians. There’s a tendency to lump all Asians together, but they are genetically very different.”
Your graph has nice, primary colours, but where does it say any of that..?
on Fri Apr 18th 2014 at 18:01:30 v8driver
@bulanik, pretty sure the BBC news makes the “Indian subcontinent” and environs into “South Asia,” I guess that kind of covers Pakistan and Afghanistan too.
http://www.bbc.com/news/world/asia/
…down the bottom of the page…
@ v8, the BBC do that. What about in the US, Australia, etc?
bulanik “Your graph has nice, primary colours, but where does it say any of that..?
You’re the kind of person who would look at a photograph of a blue sky and say. “That’s a pretty picture of a blue sky. But where does it say the sky is blue?”
You’re the kind of person who’d answer the question “why is the sky blue?” by showing a blank piece of paper to all and saying:
“Here is my proof on here”.
(Better to give us more and far, far better information to prove your devastating argument, Jokah…)
on Sat Apr 19th 2014 at 00:25:55 v8driver
Drivers License, etc. will just have height, weight, hair color, eye color,
on each job application,”Equal Opportunity” regulations state the federal government is required to try and collect stats on job applicants…
“3. Ethnicity (Check One):
Hispanic or Latino –a person of Cuban, Mexican, Puerto Rican, South or Central American, or
other Spanish culture or origin, regardless of race.
Not Hispanic or Latino
“4. Race (Check all that apply):
American Indian or Alaska Native –a person having origins in any of the original
peoples of North or South America (including Central America), and who maintains
tribal affiliation or community attachment.
Asian –a person having origins in any of the original peoples of the Far East, Southeast Asia, or the Indian subcontinent, including, for example, Cambodia, China, India, Japan, Korea, Malaysia, Pakistan, the Philippine Islands, Thailand, or Vietnam.
Black or African American –a person having origins in any of the black racial groups of Africa.
Native Hawaiian or Other Pacific Islander –a person having origins in any of the
original peoples of Hawaii, Guam, Samoa, or other Pacific islands.
White –a person having origins in any of the original peoples of Europe, the Middle East, or North Africa”
http://federalgovernmentjobs.us/forms/Optional%20OMB_3046-0046.pdf
@DJ in all fairness, those graphs make no sense without some type of key or legend
on Sat Apr 19th 2014 at 03:21:24 Da Jokah
The graph shows the Fst distance between selected populations. Where Fst is the proportion of the total genetic variance contained in a subpopulation (the S subscript) relative to the total genetic variance (the T subscript). Values can range from 0 to 1. High Fst implies a considerable degree of differentiation among populations. As a reference, the horizontal Fst from Japanese to English is 0,1244, And the vertical Fst between Eskimo and West African is 0,2693. But, honestly, a numerical reference isn’t necessary to see relative relatedness. You can just look at it.
@dj that ish makes my eyes bleed, i feel like i’m back in ap bio class, not for me thanks
Yep. Sorry. 😦
on Sun Apr 20th 2014 at 11:44:30 Sylheti
Hi Abagond,
Thanks for the map. Very useful. There is so much I could say so I’ll say it in stages.
White European Muslims such as Bosnians and Albanians will be considered white by most Europeans, but not by right-wing extremists who consider them “traitors” for following a non Judaeo-Christian faith. Of course Judaeo-Christianity itself originated from the middle east and Christ (pbuh) was a middle-easterner, that of course is ignored or not registered by the right-wing Stormfront types (Albanians and Bosnians are not allowed to have their own stormfront sub-forums as they are not “white”).
However would the average Bosnian or Albanian Muslim (Albania is 40% officially non-Muslim anway i.e. Orthodox/Catholic etc) be subject to the mistreatment that non-whites are exposed to e.g. discrimination in the work place, “Micro-aggressions” (to use your excellent phrase) that non-whites such as blacks and Asians are exposed to. No.
A large part of American and European white racism is based on how comfortable they feel with the white/non-white in question and a lot of that is how visibly different you are, do you stand out as an eyesore. Bosnians and Albanians do not.
In their general social lives unless they practise Orthodox Islam staunchly Bosnians and Albanians will not have major problems and enjoy white privilege the only exceptions will be far-right groups and also on a geo-political level the “problematic” issue of them being Muslim societies to US policymakers.
This is my first comment and I hope I haven’t been too longwinded and maybe I can share some other observations later on.
I myself am Bangladeshi from the Sylhet province (hence my nick) raised in the UK.
Once again an excellent map which can be utilized by others on the internet for reference purposes.
on Sun Apr 20th 2014 at 18:59:56 Guadalupe Victoria
Argentina never had black inhabitants but recently there was an immigration of Africans and Haitians
@ Guadalupe Victoria
Is “never” what you were taught in school, or are you only guessing that ALL the black people you have seen are “recent” immigrants?
I am wondering how come you have never heard of Afro-, Mulato or Zambo Argentines. There is quite a lot of information that you can find online that shows your “never” claim is ABSOLUTELY UNTRUE.
According to historical accounts, Africans first arrived in Argentina in the late 16th century in the region now called the Rio de la Plata, which includes Buenos Aires, primarily to work in agriculture and as domestic servants. By the late 18th century and early 19th century, black Africans were numerous in parts of Argentina, accounting for up to half the population in some provinces, including Santiago del Estero, Catamarca, Salta and Córdoba.
In Buenos Aires, neighborhoods like Monserrat and San Telmo housed many black slaves, some of whom were engaged in craft-making for their masters. Indeed, blacks accounted for an estimated one-third of the city’s population, according to surveys taken in the early 1800s.
San Telmo still has a visible Afro-Argentine population, apparently, along with Merlo and Ciudad Evita cities…Do you believe that the black (or possibly black) people in these places are ALL Haitians and or African immigrants?
Historians generally attribute two major factors to this sudden “mass disappearance” of black Africans from the country – the deadly war against Paraguay from 1865-1870 (in which thousands of blacks fought on the frontlines for the Argentine military) as well as various other wars; and the onset of yellow fever in Buenos Aires in 1871.
The heavy casualties suffered by black Argentines in military combat created a huge gender gap among the African population – a circumstance that appears to have led black women to mate with whites, further diluting the black population. Many other black Argentines fled to neighboring Brazil and Uruguay, which were viewed as somewhat more hospitable to them.
Some commentators say that this was a deliberate policy to create a South American country without blacks in it:
<blockquote…the president of Argentina from 1868 to 1874, Domingo Faustino Sarmiento, sought to wipe out blacks from the country in a policy of covert genocide through extremely repressive policies (including possibly the forced recruitment of Africans into the army and by forcing blacks to remain in neighborhoods where disease would decimate them in the absence of adequate health care).
http://www.ibtimes.com/blackout-how-argentina-eliminated-africans-its-history-conscience-1289381
By 1895, there were reportedly so few blacks left in Argentina that the government did not even bother registering African-descended people in the national census. What does that tell you?
And, where did you think Tango came from?
Answer: The blacks of your country, it seems…
http://www.indyweek.com/indyweek/the-blackness-of-tango/Content?oid=1197334
well i know that in Argentina were mulatos the same as in Uruguay, but they have disappeared long time ago, unlike in Uruguay where you can see many descents from black slaves, what I was just saying is that since many many years ago this is a country of european immigrants, mostly from Italy and Spain, i remember when this new african people started to came and for us it was quite unusual to see black people in the streets,,
@ Guadalupe
But that is NOT what you said. What you said was there were never any.
As though Argentina is a totally white country and always was.
And, what do you think mulattoes are? The black parent is black.
If you wish to find out more, you will find that at one time your country’s population was about 50% black.
I understand that this you believe what you have been taught to believe and see what you want to see, but may I suggest that there more to it than that?
Black Argentina:
http://kwekudee-tripdownmemorylane.blogspot.ie/2012/10/african-descendants-in-argentina-afro.html
An extract from it says:
“The demographic decline of the Afro-Argentines has variously been attributed to miscegenation, disease and warfare … [and] reclassification of black people as white or mestizo…
Indeed, reclassification has its origins in the early eighteenth century, when the Spanish monarchy instituted a system whereby a subject could purchase certificates of legal ‘‘whiteness’’ called gracias al sacar. … death had less to do with the perceived disappearance of Afro-Argentines than such reclassification, frequently as ‘‘triguen˜os,’’ and cultural prejudices.
These contributed to downplaying the contribution of black people to porten˜o culture and overlooking the patriotism and high level of integration of some black porten˜os..”
Here is a bit more about the Afro-Argentinian artform, Tango:
(https://www.youtube.com/watch?v=4vRF_hGR_yU)
There are so many articles that you could fill in the gaps about Afro Argentina.
Take this one — it starts off like this:
The most “European” country of Latin America hides its African origin. Today, 200 years after its founding, it faces the problem of the integration of the excluded and the revision of a monolithic and European discourse.
That one paragraph sums up the racial propaganda, doesn’t it?
Here’s the full article about Argentina’s “bleaching policy”:
http://www.guinguinbali.com/index.php?lang=en&mod=news&task=view_news&cat=10&id=607
According to Miriam Gomes, a professor of literature at the University of Buenos Aires, says historians are somewhat to blame for the stereotypes that are so widespread. She says:
“Argentina’s history books have been partly responsible for misinformation regarding Africans in Argentine society, Argentines say there are no blacks here. If you’re looking for traditional African people with very black skin, you won’t find it. African people in Argentina are of mixed heritage.”
And, are you familiar with the “Soy afroargentino/a” (“I am Afro-Argentina/o) campaign from a while back?
(https://www.youtube.com/watch?v=RD6bjXALw-g)
ok you can go to the documents all u like, but the fact is that in Argentina nowadays there s no black people except for the new immigrants
I understand how shocking this must be for you.
But no matter how indoctrinated you are, and no matter how much denial you live in, this will not change facts about Argentina nowadays like over 5% of Argentines state they have at least 1 black ancestor, and a further 20% state they do not know whether or not they have any black ancestors….
No matter what fantasy you hold dear, it will not change the African genetic contribution carried by at least 10% of the Argentinian population.
Your scientists have found this. Not me.
2 Guadalupe Victoria
It seems impossible that you can know what’s going on in the entire country of Argentina just by looking around, and by recalling your own personal experience.
Argentina may be the most White country in South American, but that does not mean that there was ever a time when NO Blacks were living there. At some point, we all have to rely on the history books (since we can’t be in all places at all times) and those seem to indicate the there were always some Blacks around.
It’s a possibility that Guadalupe Victoria’s perceptions are a natural outcome of long-standing policies which’ve promote her nation as “homogeneously” white.
Perhaps the general population does not see diversity.
Perhaps there is not much sensitivity to it.
Xenophobia among the general population is quite pronounced, if the Argentinian federal government research about that is anything to go by.
It seems that Peruvians and Paraguayans, and Bolivians in particular, are singled out for discrimination in that country.
http://www.lanacion.com.ar/890199-discriminan-por-tener-sobrepeso-y-ser-extranjero
bulanik u r right, this is a racist country, can t deny it, here all latin american countries are seen as inferiror u r right, im not proud of that but is reality
on Mon Apr 21st 2014 at 00:01:28 King
It is something that we have long understood, that the tendrils of White supremacy wrap themselves all around the world. Your country is but one example. But at least you know and admit the truth. Many here in the U.S. tout the idea that racism towards non-whites (particularly Blacks) around the world is a confirmation of White Supremacy rather than a direct result of its worldwide indoctrination.
on Mon Apr 21st 2014 at 00:08:48 Guadalupe Victoria
we descent primarily from Italians and many fascists came here, we also had a great number of German nazi refugees, we are the second country in the world (after USA) with larger jewish population, so it s not to be surprised of the idiosyncracy of Argentinian people
Indeed, the Fascists and the Jews must have quite a time getting along in the New World!
on Mon Apr 21st 2014 at 00:46:13 Linda
Bulanik,
I think what Guadalupe calls “black” is people who almost literally have “black” skin or are dark brown, to them, that is what “African” represents.
You have to remember, trigueno, mixed, mulatto, etc.. are sometimes not seen as “black” in certain South American countries — reverse one drop rule, mixes that African away.
so her perception of “black” is different than countries like the US or UK’s perception of black.
As you are aware, even in the Caribbean, ambiguous “black” people or known mixed-race history turns their identity to “brown”
I know that perception of my identity changed depending on the country –I’ve been called Samoan, Indian, Puerto Rican, etc — I think there are a few other posters who also underwent this identity change once they left the US to go elsewhere.
@linda u made me laugh! when I say that Argentina is white is because we descent from Europeans, when u talk about mulatos and all that stuff is people from the rest of Latin America, hardly in Argentina u find those peoples, they exist here but is an insignificant pecentage, my perception of “black” is exactly the same as people from UK, and for black we understand all those u mentioned ( trigueño, mixed, mulatos, etc), regards
on Mon Apr 21st 2014 at 01:33:06 jefe
Seems like the history books in Argentina have been white-washed too.
seems like u dont know anything about my country and dare to talk having no idea
“Guadalupe Victoria
@linda u made me laugh! when I say that Argentina is white is because we descent from Europeans, when u talk about mulatos and all that stuff is people from the rest of Latin America”
Then why would you be confused about the fact that there are “black” Argentinians that are not recent African immigrants– if you see trigueno and mixed race as “black”?
That means you saw “black” people in Argentina before the arrival of recent black African immigrants. I know “black” Argentines are a smaller percentage than the European immigrant descendants in Argentina but they were still there — how did you manage to miss them?
dear , 97 % of Argentinians descent from European immigrants,Period
Thus, most Argentines are descendants of the 19th and 20th century immigrants, with about 97% of the population being of European, or of partial European descent.[3][4] Arab descent is also significant (mostly of Syrian and Lebanese origin), and the Jewish population is the biggest in all Latin America (7th in the world). Mestizo population in Argentina, unlike in other Latin American countries, is very low, as is the Black population after being decimated by diseases and wars in the 19th century, though since the 1990s a new wave of Black immigration is arriving.
Guadalupe,
Thank you for reciting Wikipedia’s information for me, Dear… but I can read and use Google just as well as you.
I wanted YOUR opinion –words from YOUR standpoint as an Argentinean, who I assume still lives there, about why you seem to not know the difference between your fellow so called “black” Argentinean countrymen versus the African immigrants….
you did make the statement that there were “Never” any black people in Argentina, and as a Latina, I know that is not true.. how come you did not?
i expressed my opinion many times here, its noticeable your ignorance, and if u checked wikipedia whats the point in discussing something that everybody knows except u,?
kiwi Chile is full of indigenous people and Urugauy has a lot of black and mestizos, Argentina is the only country almost totally European in Latin America, dont be so confused please!
Guadalupe, I’m trying to be nice to you but you’re trying my patience b
Express an opinion about what? the fact that your ignorant a’s didn’t know that there were black people in Argentina before Africans and Haitians arrived
I asked you a specific question: “why were you unaware of the fact that there were ALREADY black people in Argentina, since you considered people who were mulata or triguena to be “black”?
I would ask it in Spanish, so you have no excuse as to why you won’t answer a simple question, but the blog owner doesn’t want people to make comments in other languages.
on Mon Apr 21st 2014 at 02:51:20 Sharina
“dear , 97 % of Argentinians descent from European immigrants,Period.”—-tsk tsk tsk. Why is the sudden rush of people quoting sources and not really reading it. Sorry Guadalupe, but according to your source it is not period as your source continues on to say partial European decent.
Well there will certainly be a lot of deleting going on in this thread when Abagond gets back!
Wow did we really have to go there?
No one is exempt from comments going into moderation, so basically you are going off on a paranoid rant. Also it is you who provided a source, did not fully read it past what supported you, and opened yourself for me to point it out. Don’t be mad. Just do better.
That depends on what you are considering an insult. If by her questioning you or by you calling her ignorant? In either case I can provide the links to where it began for you to review and determine where it went sour, but I prefer you do that yourself. At any rate I am out.
Before I go. If an opinion makes you turn into that kind of monster then you need jesus or a d*MN exorcism. None of which I can help you with.
Agreed. There was simply no excuse in the world for what guadalupe said. Even that weak one about being from a racist country.
@ Linda
King, I expect Agagond will delete these, that’s why I intend to have fun while it lasts….
Poor Abagond will need his dustbin and broom.
*By the way Abagond, when you make do your inevitable clean sweep though here, feel free to delete my comments within the “void of Spanish insults” also. Otherwise they will not make sense anyway.
on Mon Apr 21st 2014 at 08:06:55 sami parkkonen
Well, once upon a time even finns were not white enough for USA. Heres a bit from Wikipedia:
“The earliest Finnish immigrants, colonialists who were Swedes in the legal sense and perhaps spoke Swedish, and settled in the Swedish colony, were supposed to have assimilated into the British culture quickly.[12] More recent Finns were on several occasions “racially” discriminated[13] and not seen as white, but “Asian”. The reasons for this were the arguments and theories about the Finns originally being of Mongolian instead of “native” European origin due to the Finnish language belonging to the Uralic and not the Indo-European language family.[14]
On January 4, 1908, a trial was held in Minnesota about whether John Svan and several other Finnish immigrants would become naturalized United States citizens or not, as the process only was for “whites” and “blacks” in general, and district prosecutor John Sweet was of the opinion that Finnish immigrants were Mongols. The judge, William A. Cant, later concluded that the Finnish people may have been Mongolian from the beginning, but that the climate they lived in for a long time, and historical Finnish immigration and assimilation of Germanic tribes (Teutons)—which he considered modern “pure Finns” indistinguishable from—had made the Finnish population one of the whitest (fairest) people in Europe. If the Finns had Mongol ancestry, it was distant and diluted. John Svan and the others were made naturalized US citizens, and from that day on, the law forbid treating Finnish immigrants and Americans of Finnish descent as not white.[15][16]
In the beginning of the 20th century, there was a lot resentment from the local American population towards the Finnish settlers because they were seen as having very different customs, and were slow in learning English. Another reason was that many of them had come from the “red” side of Finland, and thus held socialist political views.”
on Mon Apr 21st 2014 at 09:37:30 v8driver
unfortunately, ms guadalupe, doesn’t get it, in the usa most white people would consider her, per federal guidelines of course, racially defined ‘hispanic’, and of late, ethnicity could be ticked off ‘white’ — i am not sure on the history of that particular development of the byzantine categorization process; however, ya latina, that makes it even more twisted, her little rant here, that’s the kind of thing gets your teeth knocked out talking like that in public, but we’re all safe behind our computer screens right?
on Mon Apr 21st 2014 at 10:27:32 abagond
I deleted every comment by Linda and Guadalupe Victoria from 2:20 onwards and some of Sharina’s too, for use of insulting language and comments not in English. See Kiwi’s comments to get an idea of what went on as it relates to the topic of the post.
on Mon Apr 21st 2014 at 10:41:17 Bulanik
Kiwi said, in reference to Guadalupe’s comments to Linda:
But even then, there would still be no reason to call her “perra”, “negra sucia y rastrera”, “ugly nigg´r”, or “negrita”.
You made your views towards blacks crystal clear when you stated, “if i were black i d killed myself”.
Gracious me. I never thought it would go there after I turned off my laptop…
on Mon Apr 21st 2014 at 10:59:10 Kwamla
Ahh… You’ve taken out all the interesting bits! Now where is the fun in that Abagond? I agree with Kiwi. I’d be interested to know the dirty racial insults a typical white Argentina might feel threatened to use…before it goes in the bin of course!
Agree with you there, Mr Kwamla. 😀
Yes, I understand what you mean! 😀
I saw some of this from my Ecuadorian and Colombian foster children in England. Also, because I have family in Florida, I came to hear and see the Hispanic culture there (mostly Cubano of course) in shops, the hairdressers, restaurants, malls… the latinidad.
I quickly got used to their truly ghastly “racial lens”, and got a sense of their blind-spots, the inferiority around white people, desperateness to be white combined with a violent (self)hatred of African blackness and indigenous-Americana. And then because one of the foster children was part-Chinese, that opened up another dimension…
I’d watch sometimes as the Colombianos they socialized with (Calenos at that, from the Caribbean coast!) would spout out that they were “Italian” if someone white asked them what they were. Oh, funny, funny!
Who did they think they were fooling!
Because, the same white people they told would later say to me: “But those people look definitely bit mixed race and Aztec-y..”
Yes, Aztech-y. Haha.
Even the Argentinians we knew didn’t look like “standard white” all the time/ They looked like a hodge-podge of different Europeans, and I would sometimes hear a “dark” Latina say to an Argentinian:
“Too blonde, you are tooooo dark for so much blonde, it looks funny…”
Answer: “My grandmother was German! I can be extra-blonde if I like!”
Linda, when I say “Caribbean coast”, the individuals I am speaking of were all descended, or partly descended, from families originally from the north of the country.
I know someone who worked and travelled in Latin America a lot, and she asked some local friends in Argentina why countries like Chile, Argentina, and Uruguay tended to be more economically prosperous than neighboring countries like Bolivia, Paraguay, and Peru. They responded along the lines of, “Oh, well that’s easy. We don’t have any indigenous people!”
Hmm, that sounds about right. You will hear this, too:
“Argentina doesn’t have a racism problem, because we don’t have any indigenous or blacks.”
I’m surprised about Argentinians believing that Chile does not lots of indigenous people. But…then again, I am not sure if being informed is a priority among white Argentines, really.
Anyway. Most, but not all, Chileno/a I’ve met are mestizo, even the most “Spaniard-white” looking ones. There was even one apparently white-looking family I met who said they were of recent African descent, too. The mother said that blacks were a minority in Chile, but not as small or insiginificant as publicised, and they had traditionally settled in the far north of the country, at the port of Arica. The Chilean Chinese settled there as well.
(A number of Chilean students, business people, artisst, academics settled in the UK following the Allende/Pinochet political upheavals in Chile, so Chileans are fairly well-known in parts of the UK.)
Talking of “No Racism in Argentina”. South Asians from England that have been to Bueno Aires come back and say how untrue that is!
There was a brief report about a couple of years ago on UK tv.
And, the white Argentina are not that fond of East Asians in their country either, here’s a little graffiti (not too rare, it seems) telling the Chinese to get out: http://2.bp.blogspot.com/_fZWs49bl0EM/Rq-sO1mBWkI/AAAAAAAAAR4/g9lQB816qao/s400/DSC01700.JPG
Taken from this blog:http://www.discoshawn.com/2007/07/there-is-no-racism-in-argentina.html
From reading some of what the South and East Asian visitors say about Argentina on that blog, Guadalupe’s responses to Linda are probably characteristic of many of her countrymen.
Your source said:
the Finnish people may have been Mongolian from the beginning, but that the climate they lived in for a long time, and historical Finnish immigration and assimilation of Germanic tribes (Teutons)—which he considered modern “pure Finns” indistinguishable from—had made the Finnish population one of the whitest (fairest) people in Europe…
When I first encountered Finns (in London) they seemed to 2 kinds: ones who were indistinguishable from the the fairest Swedes and others that I can only describe as blond and blue-eyed East Asians. I wasn’t in a hurry to call them “white people”! 😀
I see what you mean that when you said the Swedes regard (or once regardd) the Finnish people as a Mongol nation!
No wonder the old eurovision song Tsingis Khan was a big hit Finland too 😀
@Sami
Very interesting. Even more so today people seem to be knocking themselves down to claim individuals as white, even though at one time they were not.
on Mon Apr 21st 2014 at 13:49:21 Herneith
http://en.wikipedia.org/wiki/Afro-Argentine#Africans_in_the_Formation_of_Argentina
Okay chum.
Maybe so, but there are plenty of ‘whites’ with African blood in their veins. Perhaps many are aware of this, maybe many aren’t, maybe you are one of these African descended people? In any case due to white supremacy, many descendants subsumed this part of their heritage.
Well this Guadalupe Victoria exchange has been quite instructive.
We began with the statement that there were no Black people in all of Argentina. Or at least, there had not been until very recently in then in very small numbers.
Yet, when the opportunity presented itself, Guadalupe Victoria seemed to have quite a long list of ready-made insults prepared specifically for the very people who (according to her) don’t even exist in her country! Pray tell, who does she use these names on when she’s not on Abagond? And where would she have even heard them enough to have them so readily available?
But then, she did say that a few Africans and Caribbean’s had immigrated to Argentina. But when you look at the numbers in the United states, the Africans and Caribbean self-selecting populations are among the most successful and highly-motivated groups of immigrants in the country, often even outperforming Asians (taken as a single block demographic). So why would she have such degrading names for those kind of people?
This little demonstration gives the lie to the brainless theories floated by Da Jokah and others, that racism is really only a just a reaction to Black dysfunction and pathology. You can clearly see that even in its declared absence, the racism doesn’t miss a beat. 🙂
But, don’t you know that Argentina does not have a racial problem because there are no indigenous and blacks to make one?!
Those people only CREATE racial problems for the good and fun-loving people of Argentina.
on Mon Apr 21st 2014 at 14:17:55 B. R.
“Who does she use these names on when not on Abagond?”
Guadalupe specifically mentioned Uruguayans as “black”.
unlike in Uruguay where you can see many descents from black slaves,
Sharina nobody say anything to Linda who blatantly insulted me? INCREDIBLE
I’ll say something about it; Carry on Linda!
Looks likely that the particular ideology, racist ideology, of the Argentines was put together by Domingo Faustino Sarmiento.
He was behind the deliberate extermination of the country’s black population and continuing denial of Argentina’s non-white roots.
It seems he laid it all down in his book: “Facundo: Civilization and Barbarism”, from what the Wiki article about the book explains, “it’s a blueprint for modernization, and the dichotomy between savagery and civilization was explained. It doesn’t mentioned the black population, but I believe he already had plans to wipe them out without writing about his intentions to do so.
In linking Europe with civilization, and civilization with education, Sarmiento conveyed an admiration of European culture and civilization which at the same time gave him a sense of dissatisfaction with his own culture, motivating him to drive it towards civilization..
http://en.wikipedia.org/wiki/Facundo
This little demonstration gives the lie to the brainless theories floated by Da Jokah and others, that racism is really only a just a reaction to Black dysfunction and pathology. You can clearly see that even in its declared absence, the racism doesn’t miss a beat.”
Very true… because when I pressed for her to tell me her personal reasons as to “why she did not realize that black people already lived in Argentina” since she said Argentina Never had black people until recently — she became upset and Rude.
(loose translation of what Gaudalupe said to me in Spanish, right after I told her commenting in Spanish was against in blog rules)
“ because black people in Argentina were exterminated! You come from a country with dirty black and mestizo people, that’s why you care –Bye b’tch
She could have said anything like, such as “I come from a small village” or “I don’t consider triguena to be “black” — not a stretch to imagine since Argentina had a trigueno public health minister, Ramón Carilio, who looked white but he admitted his African heritage.
http://en.wikipedia.org/wiki/Ram%C3%B3n_Carrillo
I thought she might have been serious until she started quoting Wikipedia and then became rude — she did not know anything about Argentine history (or Argentina itself) until Bulanik told her — so, as usual, we had another typical white racist troll with an agenda trying to stir up hate.
I think Abagond should have left her response to me in Spanish on the board — it truly showed who she was– and how she felt about black, Amerindian, and mestizo/ mixed-race people
Oh trust me, Hernieth, I carried on and lit a bon-fire under her….
I really wanted to do it in Spanish and Patois but then everyone would have missed the show 🙂
I thought the girl was serious and slightly confused, so I thought I was helping her out with my statement to you… whelp, so much for trying to assist, when it’s just a white racist troll on the prowl.
As for racism in Argentina, I have met many Argentine people who were proud of their “white” European lineage of course, but they don’t think Argentina is any more racist than any other white majority country.
Indeed, Argentina white-washed their history, so I would say most people are ignorant of the historical facts concerning black/African people. I’ve heard about their stereotypes and micro-agressions against dark skinned people.
The term “Cabecita negra” means little black head and this is used against people with “dark” skin and black hair ie Indios or anyone who is considered poor from working class neighborhoods.
From what I understand of the situation, in Buenos Aires, there is definitely a love-hate relationship with the people from Brazil, Paraguay, Peru, Bolivia – many people from these countries move to Buenos Aires for jobs —
so I would say, Argentines are xenophobic against foreigners and there is prejudice against “Indios” (Native Americans), mestizos and stereotypes against black people
and funny enough, they also use the term “Gringo” in a derogatory way against north Americans or English speaking white people.
The Argentine people definitely promote the myth that Argentina is a “white” country but the Indians and Black people who lived there before mass immigration in the early 1900’s had to go somewhere —
http://blogs.discovermagazine.com/gnxp/2009/12/how-argentina-became-white/
How Argentina became white
“In contrast to Mexico, which is self-consciously a synthetically a “mestizo” nation which conceives of itself as a cultural and biological synthesis between European and native, I think it is fair to portray Argentineans as a settler society of Europeans in their self-image. As I have said before, this mythos goes a bit too far.
Since Argentina was a mixed-race society before mass immigration, as long as the roots of any given individual goes back to the period before mass immigration than it is likely that they will have some non-European ancestry.
We investigated the bio-geographic ancestry of Argentineans, and quantified their genetic admixture, analyzing 246 unrelated male individuals from eight provinces of three Argentinean regions
Argentineans carried a large fraction of European genetic heritage in their Y-chromosomal (94.1%) and autosomal (78.5%) DNA, but their mitochondrial gene pool is mostly of Native American ancestry (53.7%); instead, African heritage was small in all three genetic systems (<4%).
The median Argentinean probably has enough indigenous ancestry (Native American Indian) to qualify as a Native American tribal member in the United States by the rules of blood quantum (on the order of 20-25%).
As for the African lineages, the proportions are small, but one could envisage scenarios whereby slave women have mixed-race children, and for whatever reason their sons marry out and reproduce to a greater extent than their daughters. This would eliminate African mtDNA from the population, but maintain the total ancestral contribution"
So apparently, the native Indian and African slaves people went into the Argentinean artery and veins.
There is a huge rivalry between Argentina and Brazil, and some Argentinians dont hesitate to use racist terms at Brazilians
The indiginous mix is much more than the Afro diasporic mix in Argentina….much larger
That’s the way it worked in the America’s, Kiwi…. in south, central, and the Caribbean
The Spaniards did not bring their women to the Americas in the beginning and they had no qualms about procreating with Native Indian and African women.
Once European women started arriving, there was a shift in the paradigm of course — but countries like Argentina and Chile did not truly “whiten” up until mass immigration in the early 1900’s.
and to some extent, you will see a similar situation in north America. If you look at the genetic DNA of some African American men, their Y chromosomes will also go back to Europe… .
http://www.ebony.com/life/dr-rick-kittles-breaks-down-dna#.U1WtJM9OXcs
“We also look at the Y chromosome DNA, which is a history of the male lineage in the family. There are DNA patterns that are specific to Africans: For instance, there’s what we call a Y chromosome alu polymorphism [YAP] that is found just in West Africa, and is definitive for West African ancestry.
But the most interesting thing is, when we look at most African-American men, upwards of thirty five percent of their Y chromosomes don’t go back to Africa; but to Europe!“
that was the way of the world during colonial times
on Tue Apr 22nd 2014 at 00:22:44 Bulanik
THANK YOU for that that last link from about the genetics of Argentina.
Very revealing.
But I wonder, did it go far enough?
In making transnational comparisons, I feel that that link made the same error of RACIAL AMNESIA that seems to plague population assessments of Spanish-speaking South America by totally marginalizing and excluding the black populations, whilst rightly highlighting the contribution of indigenous ancestry in those nations.
It seems to take with one hand, and take away with the other.
For instance, this part:
“In contrast to Mexico, which is self-consciously a synthetically a “mestizo” nation which conceives of itself as a cultural and biological synthesis between European and native, I think it is fair to portray Argentineans as a settler society of Europeans in their self-image. As I have said before, this mythos goes a bit too far…”
Mexico has a known black population of 5%. So, it seems they are obviously outside the cultural and biological synthesis! although it’s well-known that Africans were:
–an essential feature of Mexicos early economic growth,
–worked in urban professions,
–developed and cultivated farmland,
–provided skilled labour in the silver mines,
–workedon cattle ranches and sugar plantations,
–created Jarocho music — made famous throug the song “La Bamba” — all AFRICAN in origin.
Plus, recent studies* have also shown African contributions to cuisine, marriage customs, medical practices, architecture, and language (the Mexican f-verb chingar coming from Angola).
And, if the white-washing trend we have observed throughout the Americas is anything to go by, that 5% of the population could be somewhat higher as many white or mestizo Mexicans do not know they are of Afro-Mexican origin, or do not say they are, leading to the trivilization and denial of African contribution to Spanish-speaking America that we are all too familiar with… (http://www.minorityrights.org/?lid=4455&tmpl=printpage)
Linda, contd.
Historian Marco Polo Hernández Cuevas sees it differently, and puts the true figure of Mexicans of African-descent at between 55%-85%. He says:
t’s estimated that over 300,000 enslaved Africans were brought to Mexico during the colonial period, producing millions of offspring. Many of the major leaguers of the Mexican liberation movement were black themselves. The last two top commanders of the movement, José María Morelos and Vicente Guerrero, as well as a significant number of other leaders and troops have now been identified as mulattoes pardos.
Even the Spanish conquistadors brought African heritage with them, as descendants of the Iberians and the Moors of northern Africa who occupied Spain during the medieval era, said Hernández. The modern Spanish language still contains over 4,000 Arabic words.
[Mexicans] are African on [their] Spanish side, and African on [their] African side…as much African… as … Amerindian or European…
The Black Virgin — a representation of Virgin Mary with dark skin common throughout Spain, France and Mexico – is one example of African cultural influences….the battle commemorated by the national holiday of Cinco de Mayo was fought by African Mexican “maroons.”
His book describes how Mexican cultural leaders have rejected this African heritage, choosing instead to “whiten” Mexican literature, film and popular culture from 1920 to 1968, a period described as the “cultural phase of the Mexican Revolution.
* http://losafrolatinos.com/2012/12/09/exploring-mexicos-african-heritage-with-dr-marco-polo-hernandez/
The article said something that got me thinking:
blockquote> As for the African lineages, the proportions are small, but one could envisage scenarios whereby slave women have mixed-race children, and for whatever reason their sons marry out and reproduce to a greater extent than their daughters. This would eliminate African mtDNA from the population, but maintain the total ancestral contribution”
Whatever reason…this I would like to know! 😀
It just goes to show that although research is at least being done, it is nowhere near complete.
What is the reason for this “Directional mating”? I don’t know if that is the right phrase for it, but it leaves me wondering what happened and how come.
Was the reason some kind of pattern of patrilocality, some unexplained migration, a bottleneck of some kind? It’s almost like the work has only started…
To go back to Uruguay (a country hardly ever, ever mentioned anywhere, lol).
In European accounts of Uruguayan society in the 1800s, a typical family structure was a frequency of Spaniish men and Indigenas with large numbers of children.
Yes, Spanish women were scarce, and European immigrants were overwhelmingly male at the start.
That sounds harmless enough, and makes sense. But, a detail is missing — what about the Indigenous men? It’s easy to skip over that.
In the case of Uruguay, the indigenous men (the Charrua) had indeed been killed off in massacres and the surviving women and children enslaved.
http://en.wikipedia.org/wiki/Charr%C3%BAa_people
on Tue Apr 22nd 2014 at 01:20:03 Pay it Forward
“[…] but one could envisage scenarios whereby slave women have mixed-race children, and for whatever reason their sons marry out and reproduce to a greater extent than their daughters. This would eliminate African mtDNA from the population, but maintain the total ancestral contribution […]”
Yes, this is true as mitochondrial DNA is passed only through the mother to ALL her offspring, whereas Y-DNA is passed only from the father but to his MALE children only (daughters obviously do not have have the Y chromosome, and would have to get that type of genetic info through the DNA testing of their father, a full brother, a paternal uncle or grandfather et cetera).
If, then, men who were mixed race / Black on their maternal side were to reproduce to a greater extent than their own mixed race sisters, and if they reproduced only with white women, it is the mtDNA of those white women which will continuously be passed down in far greater numbers through consequent generations.
African genetic heritage, however, might still remain generations later in the autosomal DNA, and might be revealed through DNA testing, even in trace amounts.
For “whatever reason” in this case basically means that the reason for such an occurrence is unimportant for the purposes of said postulation / suppostion.
In the theory of the Mitochondrial Eve their is the belief that there most probably was other possible mtDNA donors, but for whatever possible reason, their mtDNA was not passed down, leaving only mtDNA Eve’s in evidence.
King said this after Guadalupe’s racist comments:
…when the opportunity presented itself, Guadalupe Victoria seemed to have quite a long list of ready-made insults prepared specifically for the very people who (according to her) don’t even exist in her country! Pray tell, who does she use these names on when she’s not on Abagond? And where would she have even heard them enough to have them so readily available?
And you made this observation:
You’re right about the “love-hate” thing, but Guadalupe was nation-specific about Uruguay. Could it be more than economics? After all the population of Uruguay is small and mostly white. A small country, with a small black population. But for all its smallness, it might be particularly irritating for a reason. Like Argentina, Uruguay is not conventionally thought of as part of the African diaspora, in fact, it’s rarely, if ever, mentioned at all, and ignored.
Back in 1925, the year Uruguay celebrated 100 years of becoming a Republic, El Libro del Centenario del Uruguay went so far as to explicitly deny cultural influence from any group outside of Europe, apparently:
“Uruguay is populated by the white race, totally of European origin.”
That sounds just like something an Argentinian would say…
The 2 countries share a fair bit in common, originally both being part of the Viceroy of Rio de la Plata, with Bueno Aires as the capital city and Uruguay, a province. They share linguistic, cultural and economic ties, not just similar European heritage.
But there are important differences that have struck me after I heard a talk by George Reid Andrews on the national culture of Uruguay>>
Linda, contd:
According to him, at one time :
Afro-Uruguayans created the most active (on a per capita basis) black press anywhere in Latin America. Between 1870 and 1950 black journalists and intellectuals published at least 25 newspapers and magazines in Montevideo and other cities. This compares to between 40 and 50 black-oriented periodicals during the same period in Brazil, where the black population is today some 400 times larger than Uruguay’s; and 14 in Cuba (black population twenty times larger than Uruguay’s).
Unlike Argentina, the Uruguayan black population seems to have somehow made its mark on mainstream society one way or another, despite ingrained and widespread anti-black racism in Uruguay. Even under these conditions, the black population were far more literate than their counterparts in Latin America. Who knows, but could they have been comparatively more literate than many white Argentines in comparative social strata at that time?
I don’t whether it’s possible that this makes Afro-Uruguayans appear “uppity” in the eyes of white Argentina.
There is also another difference between Argentina and Uruguay.
George Reid Andrews also says the culture of Afro-Uruguayans has been embraced, body and soul, by the white majority, to the point where “white people get to be black”. Then, as now, they get to immerse themselves in Candombe and Tango, take great pleasure in dressing up and acting out beloved stereotypes about black people’s “nature”, such as natural rhythm, supposed hypersexuality, connection to magic…and, even wear blackface.
It’s so much a part of white Uruguayan national consciousness, he says, that “the white influx into comparsas is now pushing down wages for black drummers”. (comparsa=musical band).
I wonder whether Argentina’s whites long for the privilege of expressing and defining themselves so openly using black artforms?
The author does report that Afro-Uruguayans aren’t best pleased with their racial caricaturisation or what seems like a white obsession with African dance and music as a national expression. It has nothing to undo racial inequality.
However, I can only speculate on how the 2 countries could regard one another.
(From: “Blackness in the White Nation: A History of Afro-Uruguay”)
(http://www.amazon.com/Blackness-White-Nation-History-Afro-Uruguay-ebook/dp/B0042X9O8K/ref=la_B001IODP9K_1_2?s=books&ie=UTF8&qid=1398132806&sr=1-2)
on Tue Apr 22nd 2014 at 05:44:56 gatobranco1
Concerning Argentina, I have once read a Russian publication about that country where it was claimed that in the end of 18 century about 30 percent of the Agerntinian population of the time(less than 1 million people) could have been black. The rest were mostly Spanish-Native American mestizos, only small group were white(criollos) but probably even these had at least some Native American ancestors. So that Argentina before the beginning of the mass migration of Europeans(somewhere about 1860- 1870) was not really different from other countries of the continent.
And by the way, the Argentinian gaucho poem “Martin Fierro” quite often mentions “morenos” which was the name given to black people in Agentina.
How Egyptians looked 2000 BP
http://commons.wikimedia.org/wiki/Category:Fayum_mummy_portraits
on Tue Apr 22nd 2014 at 08:33:16 B. R.
Where I live is a huge destination for Argentinians and people from Uruguay , the Argentinians come in bus loads, and their is a season for the Uruguaians..these are more blue collar people the elites go to Rio….
The Uruguaians always have some phenotype black people among them and the Argentinians rarely have phenotype black people .They both have many people with phenotype indiginous indian looks .The Candombe carnival celibrations in Uruguay, have many black neighborhoods drum corps. Uruguay has way more phenotype Afro descendants than Argentina
A person from Argentina, Buenos Aires , who has some Afro descendancy but is not overly phenotype Afro looking , is a guy like soccar player Tevez…he played in Brazil, and they did a back ground bio report on him and they said he came from a poor neighborhood with a violent reputation , and when they showed shots from there, you could see the people were a little darker than average . still no heavy phenotype Afro representation, but , Afro descendant traits . They even went into the origins of his victory dance after his goals and how it was a dance from that neighborhood.
The Tango was influenced by the Cuban Habanera , and they say from Uruguay as well as Argentina…for sure , Uruguay could have an Afro influence on Tango
But Tango has other influences that are stronger than the Afro influence…many times , the flow is interupted by retards, or stops…very anti groove when that happens. It is one example of many in Latin America , where there is some Afro influence, but it is diminished. There are other anomolies in Gaúcho culture that have Afro referances but mostly done by white people. Something done with two hard balls on a rope that they swing very percusivly in 6/8 Afro sounding cadance, and a rhythm they play on a drum called bumbalagueiro
Brazil is so much more Afro descendant. There are huge amounts of dominant Afro diasporic expresions, actualy varying from big city to big city, like they were a country onto themselves…huge varieties of Afro diasporic beats and dances and huge varieties in how mixtures of people in the Americas played out, if not all the examples…fewer workers from Índia were brought to Brazil, where Guyana to the north has lots of people whose ancestors were brought from India
@ Pay it Forward
I haven’t the foggiest about studies like that, so thank you for shedding light on them.
on Sat Apr 26th 2014 at 02:31:52 TheSocialCentre.WordPress.com
Your white teachings about JudaeanHebrews as white,regardless of self described wanna be Jews is not in syche with genographics!
check genographic nation on Patrilineal JudaeaoGerman mid east roots!
Check out my SocialHandle.WordPress.com on my SocialHumanRace.WordPress.com It is probably Also SocialKin.WordPress.com! You will find the Genographic National Geographic testing shows comparable kinship of JudaeaoGerman,Yiddish Ashkenezim with both Mediterranean JudaeanHebrew,SephardicJews and as comparable with PalestineArabs’ patrilineage! If you want to sharpen up on your Lebanese war material, you might want to check out the Genographics on the Maronites as well as the pages showing each of the countries of the Mid east North African Mediterranean! I advise you to free your mind from the old radical militant affinity to the ArabistEmpireRacist genocidal perps, raping and genocidal destroying of Darfur, Sudan as well as the SudanArab war on South Sudan Blacks, Black lives and Black social culture! That is, as you obsess over the Angloes’ old hat, worn out standard , not new at all, stuff! With the exception of your great 1949 Blues,Rock n Roll first rate music! You need a refresher brother! The term Sudani means Black, while Bidani means white, from the Arabic self described labeling of Arabist Empire conquest, enslaving Africa! Meanwhile PLO definition of Patrilineage, as the defining property, to identify Arab nationality, particularly the PalestineArab centre of ArabEmpire nationalism, places JudaeaoGerman Patrilineage, right smack dab in the centre of PalestineArab common rooted kinship! Last but not least, on the ArabEmpire conquest over JudaeanHebrew,Zion,Israel, the Mediterranean, North African South West Asian, JudaeanHebrew roots, are as PalestineArab rooted, as any PalestineArab Man Woman or child! Meanwhile you do not distinguish between the Zanzibar Black Swahili,Bantu Non Arabs and the minority ArabistAryan mixed ruling apartheid minority! The Zanzibar White Arabists can be as white as Freddy Mercury of the rock group Queen, remember?
PalestineArabs are kin to SudanArabs, a mix of ArabEmpire conquering invaders, over non Arab country! So the Patrilineal roots of Arabist men, Arabized the native first nation, matrilineal pool of JudaeanHebrew and AramaicCanaanite geneologic roots! This same pattern happened all across the ArabistEmpire, conquered Africa and South West Asian, Mediterranean countries! So now, you have First nation AramaicAssyrian-AramaeanSyriac, occupied by Arabizing, ArabistEmpire patrilineage! The same goes for Nubian, Darfur, Beja and Kordofan-Nuba Nile and Saharan Blacks, occupied by ArabistEmpire patrilineage! That is the reason self described White Bidani Arabist Patrilineage, calls them selves white, while their Arabist gulf brothers call them ABEED FOR BLACK SLAVE, FROM THE SAME ROOT WORD AS SERVANT OF ALLAH ABDUL! So you might be interested to learn that MauritanianArabist Bidani whites, also call their Black subordinates, Sudanis and Abeeds! The Fulani Free Blacks, never enslaved, are still third or fouth class due to their not speaking the standard HASSANIA Arabic,te HassaniaArabs trace their patrilineage back to the Arabian peninsula! Fulanis do speak the Koranic Classical Arabic THAT ALL EDUCTAED MUSLIM BLACK NON ARABS SPEAK! But that Islamic scholarly Koranic Arabic does not earn the SudaniFulanis the respect of the demeaning ArabistEmpireApartheid occupiers of Mauritania, any more than Darfur Muslim non Arabs! Instead the Fulanis have been gradually organizing, no thanks to the USA militant radical Black Progressives! Mostly, if at all no help or attention comes from the Jew haters of the militant radical alleged Black nationalist, activism leaders, in positions of influence like your site!
on Sat Jun 21st 2014 at 07:36:56 Mihai
Because jews are white. *retard face*
on Sat Jun 21st 2014 at 16:54:53 Kotkoda (@kotkoda)
What does your map really show??? Your data range from 1921 to 2014 and from more to less reliable sources such as the US census or wikipedia. Also, which census did you use for the US numbers ? 2010? Did you use “white only” numbers? If so why?
I really don’t know how to interpret your map. Sorry to say but it makes no sense.
on Sun Jun 22nd 2014 at 06:00:37 Paul
The truth is as can be discerned from some of the comments and the map is that in many cases white is more state of mind than color of skin. In a lot of cases it’s social and financial and can be taken to mean ” I’m better than whoever is nonwhite.”
on Sun Jun 22nd 2014 at 16:42:17 abagond
@ Kotkoda
The numbers for the US are from 2010. It includes white Hispanics since otherwise I would find myself saying there are no white people in Latin America, which I think is nuts.
The Wikipedia numbers almost always come from government figures.
Only one country uses numbers from before like 2006 and that is Mexico.
on Sun Jun 22nd 2014 at 19:49:04 Joghn
What is the purpose of such a map? It seems like the same sort of thing eugenicists publish. What is the goal of publishing racial demographic maps?
on Mon Jun 23rd 2014 at 01:55:29 abagond
@ Joghn
I made he map because I wanted to know.
on Mon Jun 23rd 2014 at 03:49:23 drukermeister
It looks like you didn’t do your homework. Per Wikipedia, Mizrakhi and Sefardi Jews constitute about 2,721,000. The vast, vast majority of them are from other Middle Eastern and North African countries. So, they should be considered non-white. (Unless, of course, you’re using one-drop-of-white-blood for them.)
Ethiopian Jews constitute another 130,000. So, together that would make 2,851,000 non-white Jews. Add to that 1,688,600 Palestinians residing within Green Line. That makes a total of 4,539,600. Out of total population of 8,134,100.
That makes Israel about 55.81% non-white or about 44.19 white. So, Israel should be two shades lighter, if I understood your color scheme correctly.
@gatobranco1
Thanks, interesting portraits. I have never seen them before. It’s funny, but to me they look like modern Armenians/Georgians/Jews. (I have met Armenians and Georgians live as I was born in the former USSR.)
@ drukermeister
It looks like you did not read the post. According to the definition of “white” that I used all Jews are considered white.
My definition is not perfect, I admit. It is at best an approximation. But I needed something that was easy to apply uniformly across the whole world based on the information available in 2014. I tried different definitions. This one created the fewest paradoxes. Yours, for example, would apparently see Ralph Nader as non-white and Steve Jobs as half-white.
No, I did read the post. I just think it’s ridiculous, considering that you defined the surrounding Arabs/Middle Easterners among whom the majority of these Jews have lived for centuries as non-white. But, I guess, when you have an agenda to follow, why care about reality or even consistency?
on Mon Jun 23rd 2014 at 14:45:24 Kartoffel
If you read the map as a map of how americans view the world It’s perfectly viable. The inconsitencies are due to the inconsitent american view of race, it’s blurred borders.
@Kartoffel
I see what you mean and would even agree with you re: Americans’ view. The map does resemble that, but the issue then is two-fold. 1. As I understood it, the map is, at least partially, based on self-identification, in which case Americans’ views don’t matter, and 2. even if we get past 1, the map would need to lose internal boundaries for Canada, Russia, etc.
You can make insulting insinuations or maybe you could give me a better definition of white that I can apply consistently to the whole world with available information. I tried different ones. This was the one that I found to work best in practice, consistently.
on Wed Jun 25th 2014 at 20:02:14 Race Relations | Clarita Bombita
[…] Village in Chicago, a predominantly Latin@ neighborhood, to Costa Rica which according to this map https://abagond.wordpress.com/2014/04/11/the-map-of-white-people/ is 75-100% made up of white people. It is the only country in the region that is predominantly […]
on Sat Jun 28th 2014 at 18:07:31 Joghn
You made the map because you wanted to know what? Racial demography?
on Sun Jul 6th 2014 at 16:50:08 Njujorkezi
This map is wrong in so many levels. Albanians and other Muslims in Balkans are white, but I see you have problem with the religion. Second, if Albanians, Bosniaks are not white, are Israelis and Armenians white ? Lol.
on Sun Jul 6th 2014 at 17:22:28 abagond
@ Njujorkezi
By all means, suggest a more workable definition of what white is.
on Fri Jul 25th 2014 at 07:38:22 Person of Candor
Ha ha. You have a tumblr account don’t you Abagond.
on Sat Jul 26th 2014 at 02:20:59 limelite
Around 1900, the census in South Africa showed that the black to white ratio was around 2:1. Now it’s 10;1. Apartheid sure was real bad for the black population,eh? Maybe you should look again at your ‘before the bad evil white people arrived’ map for South Africa. Oh, and in case you weren’t aware of it, there were no “blacks” in South Africa – they arrived from the north by migration, around the time the whites arrived in Cape Town. Yeah, I know, shocking, right? I mean, you wouldn’t want to appear racist against white people or anything!
on Sun Sep 7th 2014 at 09:01:04 Michael Cooper
Kiwi, I totally agree with. Dude needs a history lesson. But that’s the white fragile ego syndrome that Agabond broke down perfectly.
limelite is definitely “limelight” in the head. His misinformation is from those guys who “discovered” everything. White racists are hilarious.
on Sat Oct 25th 2014 at 00:34:23 Gjirokastriti SHQIPTAR
Albania and Kosovo = grey: 0% to 25% white AHAHAHAH. NICE PROPAGANDA !!
on Fri Jan 16th 2015 at 00:46:13 Chris santana
if you excluded “white hispanics” then why is argentina there. Hispanics are anyone who comes from a SPANISH speaking country, hispanic has nothing to do with race! You yourself said “white hispanic” signifying that they are a person of european decent from a spanish speaking country or background, you said you would not include them because they would not count.. How if they are WHITE hispanics, yet you included argentina in which case you just contradicted yourself, very smart.
on Fri Jan 16th 2015 at 04:20:59 sharinalr
@Chris santana
Where in the post did he say he excluded “white Hispanics”? Plus I believe the map is based on how people identify not so much what he believes they are.
@ Chris Santana
I said in the post that I include White Hispanics.
on Fri Jan 16th 2015 at 05:09:42 Anna Stevens
Wow. The funny thing is, if I created a map called “A Map of Colored People” you would get mad because you were lumped together with all the other races, yet you didn’t seem to have a problem doing that to us “Whites”. I would also be blasted as an insensitive racist, but as long as you’re only being racist to people who are not in your lump sum of “white” you don’t seem to care do you? You are insensitive and ignorant and you’ve created this site to find shelter (in your few followers) for your ideals and opinions that are rude to others. You make me sick. You are wasting the hard work that was sacrificed by Civil Rights movements across the world. Oh, but you probably only think that “Civil Rights Movements” happen in America with white people oppressing non-white people. Well you’re wrong. They’re happening everywhere between all types of races not just whites. Get a grip of ACTUAL reality. Go explore the world. I did mission work in Honduras, I was chastised endlessly because they assumed I did not speak Spanish. Yes, I was persecuted for being white. “Stupid gringa doesn’t know we are making fun of her.” “She has ugly hair for a gringa.” Shocker, I know. So wake up and smell the roses. NOT ALL WHITE PEOPLE ARE RACIST. And YOU are being RACIST when you say “whites are always looking down on others.” or even, “white people are so racist.” Because you’re doing exactly what you are accusing “whites” of doing. You are assuming that because my skin is white that I will automatically be racist. It’s funny how that works huh.
And I’m from the Mississippi, where everyone says is SOOOO racist. Guess what, we’ve dealt with it and we’ve put it behind us. And everyone hear (disregarding there race or religion) is SICK AND TIRED of people always assuming everyone here is a racist or insensitive, or (my favorite) “stupid, fat, country people”. Ding ding ding, if you automatically assume that someone from a certain region behaves a certain way or believes a certain thing, YOU ARE BEING RACIST. Just like you grouped entire NATIONS of people onto your “white people map” I have a feeling a lot of people would feel extremely offended by your assumptions. Just like if I said, oh Latinos are darker than white people, I’ll just group them in with black people. That’s not how it works, they are there own people group. Seriously, get it together.
on Tue Feb 24th 2015 at 19:02:53 Speak Out
You’re going to have a hard time finding people in Baja, Sonora, and Chihuahua who “look white” but don’t have dark-skinned parents and/or children. Tourists excepted.
“would apparently see Ralph Nader as non-white”
Ralph Nader was called the n-word by white people growing up. I took his sister’s class and she is brown-skinned and was very supportive of the paper I wrote for her class analyzing the “Hispanic/Latino” racial project and how the U.S. has historically alternated between calling Mexican Americans “Indian” and “white” according to which better serves its interests in particular situations.
on Mon Mar 30th 2015 at 14:30:15 Pλulλ Ⓖ ♏♜ (@PauOrue)
This is the most racist I saw in my life . Please evolve , there is nothing wrong with being black , Indian , mestizo, etc. Every day we delaying us by people like YOU. Greetings from Argentina
on Thu Apr 9th 2015 at 23:02:44 Andrés
on Wed May 27th 2015 at 20:05:45 javier
I’m from Argentina, and the whole north of the country is mostly amerindian. In all the country, the percent of white people is about the 68%, amerindians are about 30% and the rest are black and east Asians (a few).
People whi is called mestizos, are very mixed amerindians (most part) or very mixed whites.
on Wed May 27th 2015 at 22:20:21 biggiefriez
“I thought of using both linguistics and genetics to define “white”. The trouble is that, either way, Iran, Pakistan and much of India would become part of “white”. That was not the sort of white I had in mind.”
I think you’re working too hard Abagond. In my opinion and in my experience as part of the white-European diaspora, most white people who consider themselves the ancestors of the pilgrims, settlers, George Washington, Shakespeare, Kant, Newton, Alfred Nobel, Mozart etc etc and generally of British Isles and northern European descent define whiteness fairly closely to the Nazi model even if only subconsciously. And since these whites are the ones that invented the world order, the philosophical, economic and governmental paradigms we live under and still dominate it for the most part and whose features, languages, and culture are still deemed to be the most desirable and preeminent throughout the world, their definition probably is – definitive. Why invent the wheel?
For your purposes I’d stick with that model and assume anyone who isn’t 100% northern European Anglo-Saxon looking along with the correct names and language isn’t considered fully white by Anglo-Saxons but rather “ethnic white”. Celts may be an exception but I’m not sure. So there is a hierarchy to European whiteness just as there is a hierarchy to race generally, with as you know, blacks at the bottom. Clearly being “ethnic white” isn’t as desirable as being northern European-white which is why some “ethnic whites” seem to display inferiority complexes. You’ve met the type. I recall “Pino” from Do the Right Thing. Ethnic whites hold parades. Parades, special days, parts of town (little this, little that) and other forms of attention seeking are ways people who feel they are not part of the mainstream conversation bring attention to their groups accomplishments and hopefully increase the self-confidence and pride of their members.
Many of the ethnic whites you mention like Greeks, Albanians, Slavs, some southern Italians, Caucasians etc, European looking Persians, Jews are accepted as white on a government census but less so by Anglo-Saxon civil society. Within Anglo-Saxon civil society they are considered “ethnic whites”. Ethnic whites are for the most part the ones you are referring to when you reference the “expansion of whiteness”.
I read that in Europe, Greeks and Italians often face discrimination from northern Europeans. Imagine that.
So whiteness isn’t really so hard to figure out. Just ask the people who decided what whiteness was in the first place, after all, it’s not like any of us get to decide anyway.
on Mon Jun 1st 2015 at 16:43:43 abagond
@ biggiefriez
I thought that that idea of Whiteness – Nordics as the “true” Whites, the rest as “ethnic” Whites – died out in the US in the 1950s, certainly by the 1980s. Rates of intermarriage seem to show that. So does the way the words “race” and “ethnic” have been used from the 1910s to 2010s:
In the 1970s I can remember “ethnic” meaning like Italians or Poles, whereas now in the US it means non-Whites. People use “race” and “ethnicity” almost interchangeably. Likewise, in the early 1900s, many saw Europe as divided into maybe three “races” – Nordic, Alpine and Mediterranean – using skull measurements and everything. Back then Franz Boas could talk about the “race” problem and mean among White people. If you say “the race problem” now in the US, people think you mean Blacks and Whites.
on Thu Jun 25th 2015 at 09:07:15 Omar Ortiz
Northern Mexico have more white population, in the states with light blue you should put medium blue…and in the rest of the border states should be medium blue as well.
For example, the state of Sonora has 65% approx. of white people, and it’s colored with light blue that means less than 50%…I live in Nuevo Leon, and I’m sure that there’s more than 50% of white people here.
on Thu Jun 25th 2015 at 12:44:01 abagond
@ Omar Ortiz
As noted in the post, the numbers for Mexico are way out of date. Can you point me to more recent numbers?
on Tue Jul 21st 2015 at 13:45:54 Marko
Why the hell did you classfiyed Albania as a “grey” country ? Do you think in Albania live black people or what ? Albania is a country with fully white people you ignorant people 1
on Tue Jul 21st 2015 at 18:57:23 Herneith
@Marko:
Better to be grey than psychedelic purple!
on Wed Jul 29th 2015 at 17:28:23 Bess
This makes no sense when you say that Albanians are not WHITE??! Your one retarded Moran
on Wed Jul 29th 2015 at 17:49:52 abagond
@ Bess
Tip: If you are going to call someone a moron, you should check your spelling first.
Calling someone a moron is not an argument. It proves nothing.
on Thu Jul 30th 2015 at 00:36:18 Mz.Nikita
@Abagond, LmaOooo X-D
on Sat Aug 1st 2015 at 14:53:22 drake
the albanians are whiter than greeks you mooron have u seen greek they are all darker than albanian ..albanians are white
on Sat Aug 1st 2015 at 16:42:37 Herneith
What’s ‘mooron’, moron?
In these peoples’ case they would not comprehend the above sentiment.
on Sun Aug 16th 2015 at 22:40:51 Italian man
Hi I would like to speak my mind, sometimes consider someone white. and not in the logic. but one thing geopolitical or cultural. it is true! people Kosovar Albanian and Bosnian and Muslim, but the lifestyle and racial and quite European! I am silly. white label not only someone for religion! it is also true that the same thing in Europe and uses Austalia and happened to Portuguese Italian southern Sicilian and Greek being seen as non-white. as in Europe and also in Italy the Arab populations! only some slightly darker shade of skin. the truth and the real part of the white race from that area that starts from the axis jerusalem-kuwait city up talking for asia, from cairo Casablanca-up to the east from the Urals to Portugal including descendants of those people who colonized the Americas and Australia
on Mon Aug 17th 2015 at 04:04:32 Danish Butter
This is stupid and ignorant. As a muslim, I don’t identify that as my race, and you are only contributing to that problem and know nothing about history.
on Sat Sep 12th 2015 at 23:54:40 ANGETS
I am sorry but Sephardi Jews are NOT whites (so don’t put Israel in dark blue). And Albanians, Bosnians and Macedonians ARE whites.
on Tue Oct 20th 2015 at 19:07:24 DyaniB
Not a good map at all. You forgot South Africa and many other places. Whites are dispersed all over the globe, ALL OVER THE GLOBE.
on Tue Oct 20th 2015 at 21:36:10 abagond
@ DyaniB
I did not forget South Africa at all. I even talked about it in the post.
on Fri Oct 30th 2015 at 16:23:41 mike
Who cares who is White in this day and age when president of USA is black. What most normal people care this days there are only four kind of people that matters: rich, poor, beautiful and ugly.
I mean Russians and Slavs are mostly White and many blond but no one trust them in contrary to for example Japanese and east Asians
on Sat Dec 12th 2015 at 21:43:26 Bllblla
Just that Albanians are muslim they are not white are u stupid? Wow!!!!
on Wed May 25th 2016 at 04:01:03 Mike
soon there will be no more dark blue spots because of immigration and low birth rate of whites.
on Wed May 25th 2016 at 12:22:41 Alan Schlickmann
The map doesn’t take absolute numbers in consideration, only percentage. Absolute numbers can also help to picture a global figure.
The USA has the largest White population on the planet with 223 million Whites. The US is followed by Russia with 146 million people, mostly Whites but Eurasians also included. Germany has 81 million people, France 66, the UK 65, Italy 60 and Spain 46, but those countries are not entirely composed of Whites.
Brazil has the third largest White population in absolute numbers with 89 million European descendants, 10 million Levantine Arabs, mostly Christian Lebanese and Syrians, 162 thousand Ashkenazi and Sephardi Jews and 800 thousand Anusim or descendants of colonial Dutch and Portuguese Crypto Jews/Marranos. Brazil is also home to 800 thousand Gypsies or Roma people, mostly Portuguese followed by Baltic and Eastern Europe Gypsies.
Brazil has 42 million Lusitanians or Portuguese people, including 1.5 million Lusitanian citizens, followed by 31 million Italian descendants, 19 million Spanish descendants, 16 million descendants of German-speaking nationalities, i.e., German, Austrian, Luxembourger and Swiss (including 7 million of full German ancestry), Pomeranians and Volga included, 6 million Slavs, mostly Poles, Ukranians, Russians, Belarusians, Croatians, Czech and Slovenes, 1.5 million Dutch descendants, 1 million French descendants, 1 million Scandinavian descendants, mostly Norwegians, 850 thousand Lithuanians and Latvians, 300 thousand Hungarians, 250 thousand British descendants including Charles Miller and Oscar Cox who popularized football in Brazil, 180 thousand White Americans, mostly descendants of 19th century Confederate colonies. American descendants include Pérola (Pearl) Ellis Byington, an accoladed educator, social activist, philanthropist and volunteer for the American and Brazilian Red Cross, Chief Justice of Brazil Ellen Gracie Northfleet, first woman to be appointed to the Supreme Court, and the singer Rita Lee Jones, dubbed “the mother of Brazilian rock’n’roll”. Brazil also has 150 thousand Finnish descendants, 150 thousand Greeks, 40 thousand Armenians and other groups like Georgians, Irish etc. The ethnicities overlap just like in Argentina. São Paulo has the largest absolute number with 30 million Whites and the state of Santa Catarina that is 49% German and Austrian has the highest percentage of whites with 86%. It used to be 95% in the 1940s. São Paulo has the largest number of Italians with 15 million people. The city of São Paulo has the largest number of Jews in the nation, also the largest Japanese diaspora. Brazil has the largest number of Japanese people outside Japan. Peru also has Japanese descendants. The other South American countries also have Chinese and Korean populations, as well as Jewish minorities.
The second most spoken language in Brazil or mother tongue is German or assorted German dialects. The Hunsrückisch dialect from Rio Grande do Sul is called Riograndenser while the local one from Santa Catarina is called Katharinensisch. 4 million people have German as their mother tongue in Brazil and 3.6 million speak Venetian Italian. Polish, Japanese, Ukrainian, Dutch, Lithuanian, Lettish, Norwegian and Russian, Yidish and Hebrew are other immigrant languages.
Argentina has over 20 million Italian descendants and Italian is the second most spoken language in the country. The number of Spaniards is also over 20 million people. Argentina is home to 6 million French descendants, 3 million Germans mostly Volga, 3 million Arabs, almost a million Irish descendants. Che Guevara had Irish ancestors. Argentina is also home to Welsh and Swedish colonies in Patagonia. There are still several Welsh speakers. Chile is home to a large number of British descendants from 19th century immigration who helped during war against Peru and Bolivia. Argentina has the largest number of Jews in Latin America, followed by Brazil. Argentina used to have around 400 thousand Jews but a few thousands moved to Israel.
The entire number of Europeans living in Sub-Saharan Africa is not much higher than 5 million. The majority live in South Africa followed by Angola. South Africa has 4 million Whites including Brits, Dutch, Portuguese and Italian. Several Boers or Boeroes (Afrikaners) migrated to North and South America during the 20th century, including US, Canada, Argentina and Brazil.
Most Whites who lived in Suriname and Guyana left after independence. Brazil received several Dutch Surinamese (or Boeroes)
Whites or Europeans in diaspora are (absolute numbers):
US 223 million;
Brazil 99 million;
Argentina between 39 and 40;
Canada 25;
Australia 20;
Mexico 20;
Colombia 18;
Venezuela 13;
Chile some estatistics say between 6 and 8, others between 8 and 10 million (Chile has 18 million people, a large Castizo population, people who are mostly European DNA with Native assimilation, and around 3 million Natives);
Cuba 7;
South Africa between 3.5 and 4.8 or 5;
Peru 5 million;
Costa Rica 3.5;
New Zealand 3.3;
Uruguay 3.1 (around 90% of Uruguay is White) ;
Puerto Rico 3;
Guatemala 2;
Dominican Republic 2;
Bolivia 2 (including several Mennonite colonies);
Ecuador 1.3;
Paraguay 1.3;
Nicaragua 1 million;
The Falklands (Malvinas) in South America have a population of 2 thousand people with several Welsh and Scottish descendants but also people from France, Gibraltar, Saint Helena, Sweden and Chile. Haiti has a very small White population between 200 and 400 thousand. Belize and Jamaica too. The White population in the Guyanas region does not reach over 60 thousand. French Guiana has the largest number, followed by Suriname.
According to DNA research people identified as Mestizo, Castizo or Caboclo in the Americas (Jessica Alba and Taylor Lautner phenotype) have a span of 70% to 90% European DNA markers with the rest being Native admixture and Mulatto or Black and White mix have a range of 60 to 80% European DNA markers. It was found that some Black people in the US aka African Americans carry Chinese blood from 19th century contact as well as European, while several White Americans carry Native genes and some African too. DNA tests with White phenotype citizens of Australia and New Zealand also showed Aboriginal and Maori blood assimilation as well as Chinese and several White phenotype South Africans have Sub-Saharan blood admixture. DNA tests with French and British Canadians have also showed Indigenous genes assimilation.
@ Mike
White Mormons still have dozens of babies. Mormons are probably the only reason why Whites won’t go extinct Heh heh! Hahaha!
Argentina and Brazil also have a few thousands of Afghans and Iranians.
Some statistics give 23 or 24 million Whites for Mexico.
on Wed May 25th 2016 at 16:24:20 Afrofem
@Alan Schlickmann
White/European descent people are not going “extinct” anytime soon.
According to this 2011 Guardian article, African descent people are the majority in Brazil.
http://www.theguardian.com/world/2011/nov/17/brazil-census-african-brazilians-majority
This comes after concerted efforts by Euro-Brazilians to dilute the African population in the late 1800s and early 1900s. Euro-Brazilians went to far as to encourage immigration from Europe and award idigenous land to the European immigrants as a lure. (Hmmm, where have we heard that story before?)
Alan Schlickmann, you dumped a lot of uncorroborated data in your comments. I would love to see some sources. Links?
*Dutch Surinamese were called Boeroes, while Afrikaners or Dutch South African farmers are called Boeren.
on Wed May 25th 2016 at 21:08:56 Schlickmann
@Afrofem
I think it was pretty obvious I was joking about the fact Mike said Whites were going extinct.
The Guardian is a leftist paper that serves their own populist agenda. It is wrong to count Castizos, Mestizos, Caboclos, Gypsies, Arabs and Eurasians as Black. It is a crime to deprive them of their identity. There are Mestizo and Eurasian groups protesting against that.
http://www.nacaomestica.org/pardo.htm
^ Flavia C. Parra et al., “Color and genomic ancestry in Brazilians”, Proceedings of the National Academy of Sciences of the United States of America 100 (2003). Second paragraph. Accessed 12 December 2009.
^ Denise R. Carvalho-Silva et al., “The Phylogeography of Brazilian Y-Chromosome Lineages”, American Journal of Human Genetics 68 (2001): 281–286. Accessed 13 December 2009.
^ “Pardo category includes Castizos, Mestizos, Caboclos, Gypsies, Eurasians, Hafus and Mulattoes Cafuzos”. http://www.nacaomestica.org/. 2015. Retrieved 2015-04-15.
The number of Blacks and Mulattoes in Brazil are actually not that higher than the US. The US has 42 million African Americans while Brazil has 56 million Blacks and Black and White miscigenation people. Those figures you mentioned are actually counting all mixed people and non-Whites as Black. The pardo group stands for mixed and includes Castizos, Mestizos, Gypsies and Eurasians. More than half of those counted as Black are actually Mestizo or Castizo and look like Jessica Alba and Taylor Lautner. The Northern region or North-West (Amazon basin area) is actually mostly Castizo, Caboclo and Indigenous with a White minority.
Brazil has 89 million European descendants; 10 million Levantine Arabs, mostly Christian Lebanese; 162 thousand Ashkenazi and Sephardi Jews and 800 thousand Anusim, descendants of colonial Dutch and Portuguese Crypto Jews or Marranos.
800 thousand Roma people or Gypsies; 400 thousand Eurasians, mostly Ainoko or hafu, meaning Japanese and European. 2.3 million East Asians and 30 thousand South Asians and East Indians. Most Asians are Japanese. Brazil has 1.8 million Japanese people, 300 thousand Chinese, 50 thousand Taiwanese and 150 thousand Koreans.
Caboclo people are people whose genes span from 70% to 90% European (mostly colonial Portuguese, Dutch, French and Spanish) with the rest being Native blood admixture. In Spanish they use the word Castizo. Brazil has 43 million Caboclos or Castizos/Mestizos. The number of Indigenous people who live in reservations is 500 thousand. 160 thousand people speak speak Indigenous languages. Brazil has 42 million Mulattos and 13 million Blacks. According to DNA research people who identify as Mulatto or Black and White mix have a range of 62 to 80% European DNA markers (colonial Portuguese, Dutch and French) with the other markers being Sub-Saharan African blood assimilation.
Argentina and Uruguay have small Mulatto populations. Peru has a Black minority and Colombia, Venezuela, Suriname and Guyana have a considerable Black and Mulatto population. In French Guiana, Suriname and Guyana there are the Maroon people, formerly called Bush Negroes. Peru also has East Asians and Colombia and Venezuela also received European and Arab immigration. They also have Jewish minorities. Peru and Venezuela have large Chinese populations.
https://en.m.wikipedia.org/wiki/African_diaspora
Brazil 55,900,000 including multiracial people, 6.84% (black) + 20.6% (mulatto pardos) Flavia C. Parra et al., http://www.ncbi.nlm.nih.gov/pmc/articles/PMC140919/#id2601616 Color and genomic ancestry in Brazilians. Proceedings of the National Academy of Sciences of the United States of America 100 (2003). Second paragraph.
Denise R. Carvalho-Silva et al., http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1234928/ The Phylogeography of Brazilian Y-Chromosome Lineages
American Journal of Human Genetics” 68 (2001): 281–286. http://www.nacaomestica.org/pardo.htm
Pardo category includes Castizos, Mestizos, Caboclos, Gypsies, Eurasians, Hafus and Mulattoes Cafuzos
USA 42,020,743 including 3,091,424 citing both Black and another race
https://en.m.wikipedia.org/wiki/White_Brazilians
https://en.m.wikipedia.org/wiki/White_Latin_Americans
https://en.m.wikipedia.org/wiki/European_diaspora
https://en.m.wikipedia.org/wiki/Argentines_of_European_descent
on Wed May 25th 2016 at 22:43:45 Sharina
@Schlickmann
You are using 2009 stats to counter 2011 statistically data provided by Afrofem. This does not really support your claim. I will try to respond in depth when I feel like it.
Correction….your source has 2000-2002 data.
on Thu May 26th 2016 at 00:49:53 Afrofem
“It is a crime to deprive them of their identity.”
I see this issue of identity differently.
It did not seem to be a “crime” to deprive African descent people of their identity during centuries of European domination in Brazil and throughout the Americas. To me all of these racial sub-classifications (such as Castizos, Mestizos and Mulattoes) were a way to deny and deprive people of African descent pride in their all parts of their heritage,
their contributions to the greater culture and most importantly, their political power.
The primary reason the Portugeuse and Spanish devised all of these spurious sub-classifications was to create division among people of African descent and antipathy toward Blackness and worship of Whiteness.
It worked for a long time, but in the words of that B.B. King song, the thrill is gone. African Brazilians and “blended” Brazilians, regardless of their degree of African heritage seem to be entering a period of respecting everyone in their family tree, not just the Europeans or the Indigenous members.
That may seem like deprivation to some, but to me, the majority of Brazilians pride and respect in their African ancestry is long overdue.
✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦✦
Linking to a source in Portuguese such as nacaomestica.org is unhelpful. English language sources are preferable.
Wikipedia, to me, is a source of last resort. With that site, the question of who wrote this article(?) is always topmost in my evaluation of data and conclusions presented in the articles.
All of that being said, thank you for supplying some links. We will have to agree to disagree on what the information you presented means in the lives of Brazilians.
on Thu May 26th 2016 at 01:02:22 Herneith
The white men should be out and about breeding more white women instead of watching porn and masturbating in their mother’s basement. What woman wants to bree with such men?
on Thu May 26th 2016 at 04:14:13 Alan Schlickmann
Wow! How is a person who’s mostly European DNA and partially Native American Black? They identify themselves as Castizo, Mestizo or Caboclo. They don’t have recent Sub-Saharan ancestors. Only if you count 400 thousand years ago. How is an Eurasian Black? Do Americans label Eurasian Keanu Reeves as Black? How is a Roma (Gypsy) individual Black? Is Kate Beckinsale who has Chinese-Burmese ancestors Black? Angelina Jolie has Native American assimilation. Is she Black? Are Jessica Alba and Taylor Lautner deemed as Black?
Are people from New Zealand who are mostly White and partially Maori as well as Canadians with Métis admixture Black people? Would they be African American?
The last census took place in 2010. There are several pdf links provided.
This seems like a trolling using pseudo-leftism to serve your own agenda and justify your own invested interests just like The NY Times and The Guardian overrating or underestimating numbers to fit their agenda.
It is a crime to label Levantine Arabs, Jews, Roma people aka Gypsies, Asians, Eurasians, Mestizos and Indigenous peoples from the Americas as Black.
Mestizo, Castizo and Mulatto are terms that American and Brittish English borrowed from Spanish. That’s the reason I used them.
Brazil is in the Americas. The majority of the people who identify as mixed is Mestizo and Genetic tests showed that they have a span of 70% to 90% European markers with Native American Pre-Columbian admixture. That is the reason why Jessica Alba and Taylor Lautner have the phenotype they have. Other mixed include Gypsies, Eurasians, Mulattos and Cafuzos. The figures are clear you just have to read them.
In 1498 Brazil had 3.2 million Natives. A large percentage died from the flu and smallpox. Brazil received 3.6 million Sub-Saharan Africans as slaves from the 1550s untill the 19th century. 4 million Portuguese migrated to Brazil. 1.5 million between 1951 and 1975. Between the 1820s and 1940s Brazil received another 7 million Europeans, including Ashkenazi and Sephardi Jews, plus 600 thousand Levantine Arabs and starting in 1908 the country received 270 thousand Japanese people, and later 100 thousand Koreans and 200 thousand Chinese people.
Mixed people descend from settlers from the colonial period.
European descendants, Levantine Arabs, Jews and East Asians descend from 19th century and 20th century immigration during the Imperial and Republican periods. Recent immigration.
It is pretty obvious. Just like the History of Hispanic America, US and Canada.
on Thu May 26th 2016 at 04:51:34 Sharina
Nothing you provided has any recent data to it. On top of that your argument is based solely on how you believe it should be rather than facts presented in your sources. You opinion is people should identify as white because of their mostly European DNA, but fact of the matter is people are often pushed into a category based on a drop of black blood. Pull all the numbers you want, but how a person chooses to identify is up to them not you. That is not pseudo-leftism that is reality.
Re: White Mormons
Many of them suffer from fertility issues, so if you are counting on them to save the white race then you will be counting a long time.
on Thu May 26th 2016 at 04:56:16 abagond
White people have mainly themselves to blame. They are not having enough babies. No one is forcing them to do that. As a consequence, they depend on immigration just to keep their countries going, to make up for the children they did not have.
Also, they screwed up many of the very countries that immigrants come from.
on Thu May 26th 2016 at 05:40:30 Benjamin
Maybe that is why the birthrate in Israel is so high compared to other developed nations. They’re worried that if falls too low, they’ll be forced to rely on (non-Jewish) immigration. And of course they’d never consider that option.
Over 50 percent of Brazilians self identify as African descent people. People who cling to those antiquated racial subcategories and their European cousins are a numerical minority in Brazil.
The blog, Black Women of Brazil, has many fine articles about how this new majority see themselves. This article is instructive: Mulata? Morena? Not anymore!: The power and liberation of recognizing one’s self as black
https://blackwomenofbrazil.co/2014/06/05/mulata-morena-not-anymore-the-power-and-liberation-of-recognizing-ones-self-as-black/
This is how African Brazilians see themselves.
“We are black women! Without (any of) this mulata, parda, moreninha…”
To me, it is a crime to not recognize and celebrate their Blackness.
You also might want to peruse this article: We are empowered black women! We will not whiten ourselves anymore
https://blackwomenofbrazil.co/2015/04/12/we-are-empowered-black-women-we-will-not-whiten-ourselves-anymore/
If they are ready to move beyond antiquated racial subclassifications, perhaps you could consider accepting them as they present themselves—–as proud people of African descent.
on Tue May 31st 2016 at 06:55:24 bruce (@dibran)
My 10 year old daughter can divide race in world map better then you
on Tue May 31st 2016 at 12:36:32 abagond
@ bruce
So where is her map?
on Wed Jun 8th 2016 at 04:33:30 Benjamin
The map of white people was not on the Internet, so I made one.
On the “European Diaspora” page on wikipedia, there is a map of people of European descent. It matches closely to yours but is not identical (it includes the Balkans as White, for example). I wonder if it was influenced by your map or not, since you had not come across a “map of White people” before.
on Wed Jun 8th 2016 at 05:13:18 abagond
@ Benjamin
Seems like it was. It is suspiciously close and even uses shades of blue!
Yes! It was the shades of blue that reminded me of your map. Upon reading further, that map is even more similar to yours than I thought. I guess the creator of that map does NOT consider Muslims in the Balkans to be White after all. I guess the reason they shaded it light blue is to reflect the Christian minorities there.
on Wed Jun 8th 2016 at 09:56:52 jefe
Good catch, Benjamin!
on Thu Jun 9th 2016 at 01:29:55 abagond
I thought I had fixed that. It should be good now. Thanks.
He says he excludes Muslims as “European” since otherwise he would have to count much of South West Asia as European. Same as me.
He counts Ashkenazic Jews as European but not other Jews. I counted all Jews as White, but I agree with him. After all, according to my definition, Ethiopian Jews are “White”. It was never an issue though, since it did not show up on the map.
Where we do disagree and where it does show up on the map is Lebanese Christians. I count them, he does not. He counts Christians in Armenia, but not those in Lebanon or Egypt. He seems to base that on language: Armenians speak an Indo-European language, Arab Christians do not. He does admit that it was an arbitrary decision.
All this confirms for me that all those drive-by commenters who say I am an idiot for not including Albanians have never tried to make a map like this – or even seriously thought about what they mean by “White”. It is just one of those contradictory ideas they complacently base their life on.
The link to his map and commentary:
https://en.wikipedia.org/wiki/European_diaspora#/media/File:European_Ancestry_Large.svg
on Sat Jun 25th 2016 at 03:25:18 Isaac
Israel is not anymore ‘white’ than Syria, Lebanon, or Iraq. Jews are closest related to northern middle eastern and south caucasian populations. Jews are descended mainly from Hebrews and other mediterranean peoples from Italy and Greece.
In fact, the only significant admixture that Ashkenazi Jews have is italian/greek. Sefaradi Jews also have this admixture and are no darker than many ashkenazi jews. Both groups are more related to each other than to any other populations. Same race.
Plenty of ashkenazi jews look kurdish, armenian, lebanese, or persian. Others look greek or italian or spanish.
And not all sefaradi jews are dark either. Plenty have white skin. They have similar levels of southern european admixture that ashkenazim have.
Mizrahi Jews make up the majority of Israel anyway and are pure hebrew (middle eastern).
Furthermore 1/5 of Israeli citizens are arabs. 20% of the population.
There are many black people that converted to judaism living in Israel, or that descend from black converts and hebrews (ethiopians).
Israelis are no whiter than Assyrians and Kurds (people from northern iraq).
Seriously, there are some really dark ashkenazi jews out there, entire families. Very light sefaradi families too.
You people are so sheltered when it comes to Israel. For years you said Ashkenazi Jews descended from Turkic-Mongol Khazars (epic fail), you were all wrong.
They are a middle eastern/mediterranean hybrid population. Virtually identical to sefaradi jews, and extremely close to mizrahi jews (jews that never migrated to europe).
All autosomal studies and mt-dna studies confirm this.
And of course someone will post a few white skinned ashkenazi jews on here to show how ‘white’ all ashkenazim are which is bs.
Consider this. Judah Benjaim, a sefaradi jew, was the brains behind the southern confederacy. How can you possibly consider him to be a person of color yet consider a darker ashkenazi jew to be white?
Technically anyone from the middle east, north africa, and europe is white/caucasian anyway.
You guys have obviously never seen many sefaradi jews, who are not all brown people. Seriously, there are tons of white skinned jews from Morocco and Algeria and Tunisia.
Plenty of sefaradim from europe are white too. Serbia, Macedonia/Greece, the netherlands, portugal, england, bulgaria.
A prime minister of England was a sefaradi jew, Benjamin d’israeli,, are you seriously saying he is not white? But that some olive skinned or brown skinned ashkenazi from Israel is white? That makes zero sense.
As for mizrahim, you really need to get out more. Plenty of Syrian Jews are lighter than ashkenazi jews. It goes both ways. Even some Iraqi Jews are white. And Iranian Jews have their share of white skinned people.
A genetic study done even showed that Azerbaijani Jews (descended from persian speaking jews) cluster with Ashkenazi Jews. This was an mt-dna study too.
If Israel is white, then so is Lebanon, Syria, Iraq, Azerbaijan, Armenia, Iran, etc.
on Tue Jul 12th 2016 at 19:01:26 Raul
Are you really going to classify race on base of the religion?? Are you kidding? This is such a crap?
on Tue Jul 12th 2016 at 19:21:02 abagond
@ Raul
It seems you just got Internet service.
Go to this website:
https://www.google.com/
And in the search box at top, type in “9/11” and hit the ENTER key.
on Fri Jul 15th 2016 at 19:59:49 Ettore
I was in Albania recently ( 3 months ago), believe me their whiter than Portuguese people, Spanish people, Turks, Greeks, or Bulgarians. I also think that turks are whiter than Portuguese people from what i have seen… however the point was that cuz Albanians are muslims their not white? this has no logic, especially in a country like Albania where you find catholics, orthodox,muslims and other stuff and they all claim to be Albanians, thats funny and beautiful to see a country like Albania, however the one who wrote or made is web page i think knows little bit Albanians and belives to much in imaginary friends…whom all are from ASIA (christians and muslims)— all religions have been born there
on Wed Sep 21st 2016 at 16:14:32 abagond
White-majority countries outside of Europe:
on Fri Sep 23rd 2016 at 16:37:49 tifa
Wff albanian and kosovo are purest clean white race in europe stupid ignorants
Muslims are not race is religion dont mix religion with ethnicity
How many muslims are white 4exemple im white albanian muslim from north west fyrom
U think siberians are white and african albinos are white too l white race have dna not
Surface looking
Racists of religion cristians was white, jesus was white lol
on Sat Dec 17th 2016 at 16:04:32 Ardian
Abagong I am absolutely certain that you’re not white! Would think you’re Jewish, Serbian and Greek! I am Albanian, and proud of my nation, we are the cleanest people in Europe, we do not mix with other races like in western Europe)) And we are Albanians, we do not care about religion))) if you think you can be white thanks that you are Christian, you have deceived yourself thoroughly for Jesus was not white)) would think you’ve never read history.
on Sun Dec 18th 2016 at 02:09:30 Herneith
Abagond loves bieng white. There is nothing you or your goat can do to put a damper on that! albanian yoghurt is also the best in Europe!
on Sun Jan 8th 2017 at 20:01:08 lalbanais
what do you tell ???????
i’m albanian i’m white and i have green eyes, my mum has grey eyes, my dead has green eyes, my cousins are blond…
albanian poeple is the oldest for europe!!!
How we can’t be white?????
it’s me ! http://www.cjoint.com/c/GAit7PV16pQ
on Mon Jan 9th 2017 at 11:59:26 abagond
@ lalbanais
There are Black people with green eyes too, and tons of White people with brown eyes.
on Tue Jan 10th 2017 at 18:06:32 lalbanais
@abagond please change the map she is false , you change the reality , please go in albania and kosovo and see it, we are white,
EXEMPLE ALBANIAN OF KOSOVO AND ALBANIA
PLEASE CHANGE YOUR MAP!
on Tue Jan 10th 2017 at 19:54:22 Benjamin
Albania is only 60% Muslim, so why is the country entirely gray? Do you not see Christian and atheist Albanians as White either?
on Tue Jan 10th 2017 at 22:08:13 Afrofem
If you don’t declare Albanians “White”, lalbanais may jump off a cliff from fright and worry. LOL!
The wages of “whiteness” are as greatly desired on the periphery of Europe as they are in the USA.
He must tell the truth! And not what he thinks.
Religion has nothing to do with race.
To determine whether Albania is historically Muslim or Christian, I go by the religious population.
Wages of whiteness is just what I was thinking too!
How do you propose I draw the line between Whites and non-Whites? What is your definition?
on Wed Jan 11th 2017 at 17:24:13 lalbanais
@abagond The Albanians we descend from the Illyrians, We are the oldest population of Europe, it’s proved scientifically , We were polytheistic, after catholic and only from 1500 we were forced to be converted to the Islam, albanian we are white people , i’m white my family are white , my freunds albanian are white , the all albanian are white , We Albanians we do not mix with other origins! Romania is black , Bulgaria is black , 50% and more of greece are black , the religion is religion the race is the race ! the religion is not a race.
LOOK The prince and princess of albania (Albania and kosovo)
thay are black ? no they are white like me and de all albanian(Albania and Kosovo).
please Don’t judge a people for a religion.
on Wed Jan 11th 2017 at 17:47:11 Benjamin
Albanians were historically Christian, only converting to Islam in large numbers in the 1600s. And it appears that most converted to escape discrimination rather than out of genuine belief. In any case if you count Lebanese Christians as White than why not Albanian Christians?
on Wed Jan 11th 2017 at 18:02:09 resw
Wow, white privilege is powerful indeed! I’ve never heard of people grovelling and begging to be classified as black or anything else for that matter.
While I disagree about Costa Rica and Puerto Rico being dark blue, I have to side with abagond on Albania.
And all the talk about being “purest” white Europeans is hogwash. There is no such thing, and if there were, it sure wouldn’t apply to Albanians!
Albania was under Ottoman rule for 500 years. So are we to believe the Albanians stayed “pure” that whole time and didn’t mix with people from Turkey?
@Benjamin
exactly, the All Muslim Albanians Muslim of today were Catholic before 1600s.
We are white.
The religion is religion the race is the race ! the religion is not a race.
“The Albanians we descend from the Illyrians, We are the oldest population of Europe”
And what evidence suggests “Illyrians” are the oldest?
“it’s proved scientifically”
Do share this scientific proof.
The Ottoman Empire has massacred us the Albanians,
Serbian has massacred us the Albanians,
Greece has massacred us the Albanians,
Bulgarie has massacred us the Albanians,
Because we are white!
But the USA tey protect us , he They bombed serbian , turks , greek.
Austria was also in the Ottoman Empire but they are white same for the albanian we are white.
serbian has massacred crotian and albanian because we are white.
@resw Do some research yourself and you will see it.
Look albanian people we are white juste see it’s simple.
(https://www.youtube.com/watch?v=lCEzii0QC9I)
(https://www.youtube.com/watch?v=WGhkj_PSgH0)
Yes, I would count Albanian Christians as White, but not the Muslims.
@lalbanais
Invaded by so many people, and yet Albanians still managed to stay so pure? Miraculous!
“Do some research yourself and you will see it”
I did, which is why I was so surprised that I could not find any scientific evidence that Albanians are the “oldest population of Europe”.
And guess what? I found no scientific proof that “Illyrians” were the oldest.
So no, I don’t buy your theory, especially considering most archaeological evidence that could possibly be attributed to “Illyrians” doesn’t even date beyond the 7th century BC.
You did not answer my question: What is your definition of White?
Race and religion are very much bound up. Muslims are an out-group that most Whites see as an Other against which they define themselves. Thus all the Islamophobia, even from Whites who probably have not gone to church for years, if ever, like Mr Trump.
Starting with the Crusades, Westerners enslaved, killed and took the land of non-Christians and used religion as an excuse. But when said non-Christians converted in numbers (Muslims and Jews in Spain, Blacks and Natives in the Americas), that no longer worked, so race became the new excuse.
Not buying it. It shows a level of assimilation into the Ottoman Empire that you do not see in, say, the Serbs or Greeks.
i have give you the prove and you no, de world know albanian are white USA protect us , you don’t believe he is your problem , you went to Albania ? no ,Then you know nothing! , you just juge albanian for religion , it’s funny , the world know. hahahaha
ALBANIAN USA FOR EVER ❤ ❤
Why is Albania entirely Gray while Lebanon is not? Both contain Christians and Muslims. If Lebanon is light blue than why not Albania?
It is not just me. Google: are Albanians white.
You are trying to prove they are White without a definition. Why is that?
A point I am trying to make with my map is that there is no consistent meaning, that it is arbitrary and subjective. Even the US Supreme Court could not define the term.
Because Lebanon is like 40% Christian while Albania is only 17%.
on Thu Jan 12th 2017 at 05:17:00 Afrofem
“…We Albanians we do not mix with other origins! Romania is black , Bulgaria is black , 50% and more of greece are black …”
Please define what you mean by “White” and “Black”. I’m sure it would be news to the Romanians, Bulgarians and Greeks that they are “black”. Even the Roma (Gypsies, Romani people) in those countries are of South Asian descent mixed with Europeans from their time in slavery in Eastern Europe.
This is how modern Roma people look:
According to an article on the Romedia Foundation website, Roma slavery is described in detail:
“For almost five centuries, Roma lived as slaves in the Romanian Principalities, from the moment of their birth, as the code of Wallachia mentions in the 19th century. They were treated as objects with exchange value, being sold in auctions, donated, given as gifts at weddings, or simply used to repay debt. The slave was the master’s property, with no legal status. Marriage at a young age was encouraged, having as many children as possible being expected in order to increase the master’s property. Still not widely known, the details of the Roma slavery are one of the first institutionalised discriminatory practices against this group.
[…] in the case in which a free person wanted to marry a slave, automatically that person became a slave, too, along with any child born from a Roma mother. Thinking about rebelling? The master, having complete rights over the slaves, could apply any punishment considered to be appropriate, from flogging, to the cutting of the lips and ears, whipping the sole of the feet, public beatings, the only constraint being not to kill the slave, action which, anyway, would have been counterproductive for the estate.
The abolition [of Roma slavery] came only … as a response to the freeing of the slaves in USA and introduction of mechanization.
https://romediafoundation.wordpress.com/2014/04/18/roma-slavery-in-the-romanian-territories-a-catch-22-of-history-and-recognition/
Do the Roma people make the Romanians, Greeks and Bulgarians “black” to you?
on Thu Jan 12th 2017 at 19:50:19 Herneith
But the USA tey protect us , he They bombed serbian , turks , greek
That was mighty white of them.
What colour are the Serbians?
Folks, don’t try to explain things to him. It’s way over his head.
on Fri Jan 13th 2017 at 00:24:02 Paola
This is so stupid . Albania and Kosovo don’t count as white just because they are muslims??? , what has to do the belief of a country with their race? Go to Albania , and Kosovo and see the people there, 100% white . And to sum up Albanians are one of the whitest race in Europe as they do not mix with other races , but I don’t have to talk . It’s obvious that the person who did this map is totally ignorant . Visit Albania and see how we are 100% white
on Fri Jan 13th 2017 at 01:17:50 Fan ...
An Scríbhneor Gael-Mheiricéanach
Sock puppet patrol!
mirkwood.. you inglorious imposter! lol
AGAIN… Is that YOU???
on Sat Jan 28th 2017 at 23:10:56 Cristina Conner
I always encounter this issue when I go to a website on race, ethnicity, etc. You say Muslims are not white. Why? Did you know that Muslim is a religion like Christianity, Catholicism, Judaism, Buddhism etc. You can be any race and be any religion. Please don’t confuse apples with oranges. And I would suggest as a friend, that you go to a library and get information about the different racial groups. You will see that there is no mention of religion as a race identifier. Cheers.
on Sat Jan 28th 2017 at 23:29:46 cristina king
I thought I had posted a comment but I forgot that submit it. It was about cautioning you not to confuse race with religion. You mention in your article that Albanians are not white because they’re Muslim? Is like saying French and Italian are not white because they’re Christians? It’s comparing apples to oranges! I would suggest as a friend to go to a library and consult reference books on race and you will see there’s absolutely no connection with religion. It’s a common mistake among those who decide to get a website and write about topics that that they have done little or no research on. Once you publish, shame on you for misguiding others. It’s like the blind leading the blind. Good luck.
on Sun Jan 29th 2017 at 00:09:22 abagond
@ cristina
What definition of White should I use then? Where and how do you draw the line between Berlin and Beijing? Between London and Lagos?
on Sun Jan 29th 2017 at 00:24:23 Benjamin
Do you consider the Mizrahi Jews to be White?
on Sun Jan 29th 2017 at 00:32:51 Cristina King
I just posted that Judaism is a religion not a race. You can be from Tonga or Pango Pango and you can be Jewish by faith if you so choose. And by the way I’ve never heard of Mizrahi Jews. I do know Isaac Mizrahi and he is Jewish.
@Cristina King
While Judaism is indeed a religion that anybody can potentially convert to, it has generally been practiced by a select few ethnic groups throughout history. One of them is the Mizrahi Jews, the Jews who never left the Middle East and went to Europe (or elsewhere). Sort of like how anybody can potentially be Amish, but virtually all the Amish are of Germanic heritage.
on Sun Jan 29th 2017 at 01:30:18 Afrofem
I notice that commenters who vehemently object to your definition of “White” tend to choke when you ask them to define “White”. Seems to be a recurring theme.
on Sun Jan 29th 2017 at 04:11:49 v8driver
lol this reminds me of this newish tv commercial they have: the tissue test for tooth whiteness!
on Sun Jan 29th 2017 at 12:21:49 Herneith
@Afrofem:
They can’t.
on Fri Feb 3rd 2017 at 23:08:18 Osman bardhylu
What a fucking dumbass retard whoever constructed the map,jow dare you say since albania and kosovo is muslim you fucking piece ofahit ,we are whiter than what you are you fucking mutt ,go fuckyourself
on Fri Feb 3rd 2017 at 23:48:09 Solitaire
My, how people in the “Old World” do get butthurt over the suggestion that they might not be 100% lily white.
The next time a French troll like apportune or jacques comes by and declares people in the USA are “too hung up” on race because we “don’t understand the Old World and its long history” and that in Europe “race doesn’t matter,” I’m going to have to remember to direct them to this comment thread.
on Sat Feb 4th 2017 at 00:59:37 Herneith
@Osman:
Learn how to cuss properly in English. The impact will be muich greater! Carry on!
on Sat Feb 4th 2017 at 05:16:32 Afrofem
It’s hilarious!
Osman yells “mutt” from the armpit of two continents. A stuck pig, er mutt, always squeals loudest.
on Sat Feb 4th 2017 at 05:26:48 abagond
@ Osman bardhylu
Why does it matter so much that people in Albania and Kosovo be considered White?
on Mon Feb 13th 2017 at 04:26:58 Chilean monkey
Street perceptions of White people in Chile and Argentina are always tricky because White people in those countries is “stirred but not mixed”: In Argentina, most europeans settled in the capital, and a minority of germans in the South (Bariloche).The northern provinces bordering Bolivia and Paraguay are definitely Amerindian/andean/Amazonian, and those close to the Andes are white/mestizo/castizo.
Chile is the same story: the Far North is mostly black/amerindian (example: the 33 San Jose miners), center is the typical mestizo, and as you move further south, the white/mestizo rate changes (example: http://bit.ly/2kAWBqq )
on Mon Feb 27th 2017 at 13:01:20 abagond
@Era1
Comment deleted for moderated language.
on Thu Mar 30th 2017 at 05:14:41 Vojsava
You are just a dumb ass trying to act smart !! Im albanian there are all white people in Albania , about 80% have fair skin !! Im albanian my skin is more faire than that of a french girl and î have blond hair!! Have you learnt some history you loser ? Albania is Christian for more than 2000 years and 50% still is !! Islam came from the ottoman empire is not a religion of origins !! You should be some black dude yourself I think !! And since when race and religion are the same thing ? Idiot
@Vojsava:
Ever heard of Rosetta Stone language software?
on Thu Mar 30th 2017 at 17:23:46 v8driver
Isn’t it mecca and medina, saudi arabia, where mohommed received the word of allah
@ Paul Joseph Watson
Comment deleted for racial slur.
on Fri May 19th 2017 at 05:48:35 Paul Joseph Watson
@Sharina
Typical angry Black SJW women attacking White people. The bloke was making a point about demographics and the absolute numbers of whites in the Americas and these two tried to interfere with the debate imposing themselves and wresting terms like Mestizo and Eurasian. Just like all fat acceptance SJWs who wrench reality and deny biology.
According to the UN, governmental and CIA statistics the numbers for the Americas seem accurate. Chile does have a large Castizo and Native population.
Brazil is bigger than Europe and the contiguous US. The bloke was saying that half of Brazil is Caucasoid (European and Ashkenazi Jew), a quarter is Mestizo, less than a quarter is Black and Mulatto, with East Asians (mostly Japanese), Eurasians, Gypsies and Natives being the minorities that complete the total number. If the whites in the Southern Cone were a country they would be bigger than most European countries, and the white populations in Canada, Australia and New Zealand together. South African whites are a lost cause and currently living under discrimination, with many Afrikaners living in extreme poverty. They should migrate and receive asylum.
on Fri May 19th 2017 at 08:12:15 Solitaire
and these two tried to interfere with the debate imposing themselves
Sharina and Afrofem are regulars here and comment freely and frequently. They don’t require your permission or your approval.
Typical angry white male racist, coming to a black-owned blog written for black people and thinking his voice is still more important because he’s a white male. Trying to belittle and shame black women for taking equal part in a debate. Using racial slurs. Imposing his superior white male attitude and expecting everyone to meekly put up with his offensive interference. Typical atrocious manners of a white supremacist.
on Fri May 19th 2017 at 12:37:17 sharinalr
@Paul Joseph Watson
Nothing in my comments were angry so you are basically mad at the truth. I also never mention Mestizo and Eurasian, so WTF are you even talking about? The dude didn’t make a good point if it was so easily debunked. You can’t make a point off of outdated sources as if in that time period the population did not grow. The population changed drastically in 2002 to more recently. So you point was a moot one.
Sources were provided and his very own sources debunked what he was claiming at the time. The most recent stats on Brazil say only 47.7 claim to be white in Brazil. That is less than half. Do research.
on Fri May 19th 2017 at 15:23:20 Afrofem
@ Sharinalr
“Brazil is bigger than Europe and the contiguous US.”
Can you cite any independent sources to back up that claim? First you would need to define “Europe” since it is part of a larger continent.
“South African whites are a lost cause and currently living under discrimination, with many Afrikaners living in extreme poverty. They should migrate and receive asylum.”
Not true. More hysterical White Supremacist propaganda.
No one is holding White South Africans hostage. They are free to emigrate to Europe, Australia, New Zealand or Antarctica, whichever place suits them
You expected different?
Trolls like PJW think they have a divine right to talk smack to any and everyone, wherever they encounter them. Par for the course.
Nope. I just wanted to give him a taste of his own medicine.
on Fri May 19th 2017 at 23:13:21 unwantedtg
It is pretty well-known in Europe that Brazil is larger than Europe including Eastern Europe. Australia the same and Brazil is bigger than Australia. Have u heard about the Mercator distortion that makes Africa seem much smaller than Russia and even Greenland? It’s insane how grossly disproportionate Greenland is when compared to giant Africa. And we still use the Mercator map.
http://onlinedatingsoundbarrier.blogspot.com.br/2014/05/all-european-countries-fit-in-brazil-or.html?m=1
https://www.google.com.br/amp/s/www.buzzfeed.com/amphtml/hnigatu/19-maps-that-will-help-you-put-the-united-states-in-perspect
Buzzfeed – 19 Maps That Will Help You Put The United States In Perspective.
The U.S. is basically an overcompensating, attention-seeking brat.
I guess the original claim was that the Pardo people group means multiracial and it includes a lot of Mestizo people, Native and European, encompassing Black and White, Black plus White plus Native, Eurasian aka Asian and White. And even Gypsies cuz the Roma are European with distant Northern East Indian ancestry.
South America is indeed a pretty diverse place. They have ethnicities from every continent. I was surprised to learn that Confederates moved to Mexico and Brazil.
And that Venezuela and Peru have millions of Chinese with coolie background. I’m aware that Mexico is in North Murica, NAFTA lol.
Actually Brazil was the first region to be called America after Amerigo Vespucci. I guess German cartographers started the tribute.
And also that Argentina’s Jewish community suffered terrorist attacks claimed by radical Muslims. Wow!
@ unwantedtg
Paul Joseph Watson’s claim was that, “Brazil is bigger than Europe and the contiguous US.”
Europe is a tiny bit of land. The continental US is a lot more substantial. Is Brazil larger than both? The Buzzfeed article says no.
His objections have to do with this comment:
https://abagond.wordpress.com/2014/04/11/the-map-of-white-people/comment-page-1/#comment-316501
I was basing my comment on how Brazilians perceive themselves at this point in time. They are embracing their African heritage instead of running from it like the Dominicans.
To me, that is refreshing. To people like Paul Joseph Watson, that is anathema.
I’ve seen this stunning map before and it really put things into perspective for me:
on Sat May 20th 2017 at 21:02:17 unwantedtg
Oh I didn’t realize he meant both land masses. As big as Brazil might be that’s still impossible hehe! Not even the entire Russian territory is that big
I like the humor in the Buzzfeed article.
The US government states that China is smaller than US cuz China has a lot of territorial disputes with its neighbours and is pushing their maritime borders over Philippines, while China says the US claims interior water bodies as land to overcompensate. So I guess in this case, size matters. For projecting political power purposes. Some experts say Russia with its shrinking population faces a future threat of Chinese population invading the Federation’s Southeast.
I guess I heard about the Dominican case. That’s sad. While in the rest of the Americas people are using DNA research to learn more about their past. I’ve seen some YouTube videos about it.
The Haitian refugees issue reminds me of Saudi Arabia and the United Emirates not accepting a single Syrian refugee.
on Sun May 21st 2017 at 01:34:32 abagond
unwantedtg / Paul Joseph Watson
is banned for using sock puppets.
on Sun May 21st 2017 at 01:44:33 Afrofem
The attack of the pseudo-sneaky trolls/sock puppets. LOL!
on Wed Jul 12th 2017 at 01:37:35 Ilirian
How can u say Albanians are not white when they defended Europe alone for 25 years against Ottoman Empire, you have no rights to do these kinda of maps if you don’t know the history of white people in EU.Religion doesn’t tell your race, Albanians have all religions and Albanians have never had an religious disruption.
on Mon Dec 4th 2017 at 16:53:57 Flori
What the fuck is this. Albanian are not caucasian because most of them are Muslim. 🤣😂🤣😂🤣😂🤣😂🤣😂🤣😂. If you go to Albania you are going to see 0 black people. Ass hole
on Mon Dec 4th 2017 at 17:32:01 abagond
@ Flori
If you go to the post you are going to see 0 references to Caucasians.
“White” and “Caucasian” are not always the same thing. Just ask Bhagat Singh Thind:
https://abagond.wordpress.com/2014/04/16/bhagat-singh-thind/
on Wed Jan 17th 2018 at 15:44:42 Tony
This article was written by an uneducated dumbass that doesn’t know the difference between religion and race.
That’s all you need to know about this shit-post.
@Flori: You spelt a$$hole wrong, it’s one word.
@Tony:
LOLZ!!
These white supremacists are becoming boringly predictable in their responses! I almost long for the days of no_slappz and some of these other clowns who used to come here. Almost, not quite!
on Sun Feb 4th 2018 at 00:12:47 Albanopolis
Albanians the descendants of the Illyrians not white LOL
IN FACT,you piece of filth,according to a study of the University of California “Genetic Ancestry across Europe”,not only have same genetic like all other Europians,but Albanians have the highest rates of IDB within a population in Europe,sharing about 90 ancestors in the last 500 years and about 600 ancestors between 500 years and 1,500 years ago.
Not only we are white you filth,but are the most pure not mixed in Europe,even for your beloved Nazi scum,we were a “Aryan race”!
Oh…now i see …the problem is that “they are muslims” LOL
abagond by the way..about Rita Ora
Rita whith her parents
“Solar” is a new invention you know…
on Mon Feb 5th 2018 at 05:22:18 abagond
@ Albanopolis
Why is it so important for you to be regarded as white?
on Mon Feb 5th 2018 at 07:43:48 gatobranco1
Since somebody speaks here about Albanians as “Caucasians” probably they confuse the Caucasian Albania(a polity which existed in the antiquity in the territory of the modern Azerbaijan Republic in Southern Caucasus) with Balcanic Albania(ethnically it includes the Republic of Albania, Kosovo and a part of the Fyrom(Former yugoslav republic of macedonia).
As far as I know, Balkanian Albanians are fully indigenous to the Balkan Area and have no relation whatsoever to Caucasus or Caucasians. There is an ongoing scientific dispute whether they stem from Illyrians or maybe Thracians or Dacians, but indigenous Balcanic peoples in any case.
The most of Kosovar Albanians are Sunni Muslims, but the people in the Republic of Albania can be Roman Catholic, Sunni Muslim, Bektashi Muslim and Orthodox Christian).
As for Caucasians(taken geographically), they are either Muslims( Adyghe/Circassian/Cabardians, Chechen/Ingush, Qarachay-Malkar, Daghestanis(Avar, Lak, Lezgi, Noghay, Kumyk), Orthodox Christians, as Georgians, Svan, Mingrelian, many Ossetians and Abkhaz or Armenian Orthodox Christians.
There are 5 or 6 linguistic groups in Caucasus – Indoeuropean(Armenians, Ossetians), Turkic(Qarachay-Malkar, Kumyk, Noghay), Adyghe-Abkhaz, Kartvelian(Georgians, Svan, Mingrelians), Checheno-Ingush and Daghestani(Avar, Lak, Lezgi etc.)
on Mon Feb 5th 2018 at 15:38:44 Herneith
Albanopolis, give it a rest.
on Tue Feb 6th 2018 at 16:58:20 Albanopolis@yahao.com
abagond@ BECAUSE WE ARE
Quit the crap.
on Tue Feb 6th 2018 at 17:43:38 Afrofem
Being second level White people is a sore spot for Eastern Europeans. Even the Russians look down on Albanians…being so close to Turkey and all.
The creation of Whiteness by colonial slaveholders has spread around the globe. That successful bit of social engineering causes marginal White people to nearly lose their minds at the slightest hint they are not considered White.
on Tue Feb 6th 2018 at 17:54:22 abagond
Why would you want to be associated with the worst band of thieves and killers the world has ever seen?
on Tue Feb 6th 2018 at 21:20:09 Albanopolis
abagond@ Are you a moron,or you just act like one?
By the way in Albania religion doesn’t matter! Only 15/100 muslims say religion matters. That makes them 2-3% of Albania population. And even them don’t cover,and drink alchohol.
And since you are a Donald Trump suporter:
I am being serious. Please explain it to me like I am a five-year-old: why is it so important for you to identify yourself with the worst band of killers and thieves in history?
It does not make sense to me. What makes sense is to be embarrassed, ashamed, sheepish, to try to distance yourself from them as much as possible. Albania, as far as I know, did not take part in the West’s crimes, certainly not on a huge scale, so why assert a connection with them? It does not make sense. I am missing something.
I did change schools at one point and was never taught long division, so maybe I missed out on this too. Along with the memo on the beauty of skinny blonde women.
on Tue Feb 6th 2018 at 22:11:48 Solitaire
Was the bolded text added in a later edit? Because if not, if it was part of the original post, you are prescient.
“Even Albanians” was in the original text but it was not bolded.
I am not a Donald Trump supporter. Not even close.
In the US only about 35% think he is doing a good job. Most people I know despise him, myself included.
Right, the bold was my addition just now for emphasis.
It just struck me as eerily prophetic, considering how many butt-hurt Albanians there have been on this thread.
on Wed Feb 7th 2018 at 08:08:48 jefe
the worst band of thieves and killers the world has ever seen
worse than the mongols?
Well, I guess landwise, sure. The Americas and Australasia is a big chunk of the world.
on Wed Feb 7th 2018 at 10:30:06 abagond
In terms of land taken and people killed, no one (so far) has outdone White countries over the past 500 years. The Mongols come second.
on Wed Feb 7th 2018 at 15:22:20 Albanopolis
@abagond your Trolling is awful!
Anyway i am done here,god help you with your brain! But since i don’t believe in religion, you are hopeless.Sad!
on Wed Feb 7th 2018 at 16:40:16 blakksage
@abagond your Trolling is awful! Anyway i am done here,god help you with your brain! But since i don’t believe in religion, you are hopeless.Sad! – Albanopolis
Wow, that’s a heavily vacuous statement. Why don’t you further express yourself so that we may understand your point? I’ll wait!……
on Wed Feb 7th 2018 at 17:49:47 satanforce
Really? I didn’t know that the sun was that recent.
Exactly. Evil races are just evil. The bigly evillness of them puts them on the level of orcs. Sad!
It does not make sense to me. What makes sense is to be embarrassed, ashamed, sheepish, to try to distance yourself from them as much as possible. Albania, as far as I know, did not take part in the West’s crimes, certainly not on a huge scale, so why assert a connection with them? It does not make sense. I am missing something…… so maybe I missed out on this too. Along with the memo on the beauty of skinny blonde women.
on Thu Feb 8th 2018 at 00:07:31 Afrofem
How does a blogger “troll” his or her own blog? LOL!
on Thu Feb 8th 2018 at 03:07:21 abagond
So you are just going to insult me instead of answering the question?
on Thu Feb 8th 2018 at 04:30:17 Albanopolis
When i google it “white countries” and saw my countriy was not in the white countries,i thought you were some Serbian prick who just wanted to troll Albanians,or some Christian supremacist who thinks Muslims can’t be white LOL
But no,i was mistaken,and all the Albanians above were to!
By the way,paint that map because Albanians will never be on your side of opinion.
About white people, they created this civilization,others just follow it…
For you blakcs,your self victimization today is your biggest problem.
I am out here.
Don’t believe to much in the MSM polls,they said he couldn’t get the nominee and look what happend!
You should despise more the Democrats …
Black vote for DNC is always +90%. If the number drops to 80% for the DNC would be very difficult to win an election. So they use racism card with MSM help to keep the tension high among blacks so they can get their vote.
They never talk for blacks real problems,in fact they avoid them,and attack anyone who talks about it as a racist.
DNC and MSM scream all day long for racism “white privilege”etc. because “Racism” is the only thing they have to offer to blacks,since they don’t say or do nothing for the high murder rate blacks against blacks,for they poor conditions,they failed cites,etc. And unfortunately the blacks buy it.
Democrats treat blacks like their personal electoral slaves,and accuse others for “racism” LOL
“Black vote for DNC is always +90%. If the number drops to 80% for the DNC would be very difficult to win an election.”
Actually the Repubs have diminished Black, Latinx, student and elder votes with various voter suppression schemes such as gerrymandering, voter ID requirements and poll closures. The outdated Electoral College is all that allowed your hero to become president. He actually lost the election by 2.8 million votes.
It doesn’t matter what percentage of eligible Black people vote, the elections are stacked against Black voters and in favor of minority Repub voters.
Neither the RNC nor the DNC cares about the percentage of Black voters.
You have been reading too many White Supremacist websites. Repeating their racist propaganda shows your ignorance about US politics.
on Thu Feb 8th 2018 at 19:15:02 satanforce
About white people, they created this civilization,others just follow it…For you blakcs,your self victimization today is your biggest problem. I am out here.
Then he goes and adds another comment below! Sad!
And the other parties have, what to offer exactly?
on Thu Feb 8th 2018 at 19:41:20 Solitaire
“DNC and MSM scream all day long for racism “white privilege”etc.”
If white privilege doesn’t exist, why are you so anxious to be categorized as white? How could it possibly matter whether or not you’re considered to be white, unless you believe you gain something from it?
Why does it matter so much to you that you call people nasty names like “filth” and “moron” for suggesting you might not be white?
on Fri Feb 9th 2018 at 00:26:02 Afrofem
Mr. “I’m Outraged That You Don’t Consider Me White” really shows his colossal ignorance about the dysfunctional two party system in the USA with his comments about Black people voting for the Dems.
I still want to see his response to Abagond’s question about why he wants to identify himself with the “worst band of killers and thieves in history”. Of course that would take honesty and guts.
on Fri Feb 9th 2018 at 02:02:42 satanforce
Of course.cause we really do know how much these people really do care about the about the neighbourhood safety, economic protection, public services and other civil amenities and issues that affect the Afro-American constituency on a day-to-day basis. Right?
Just like they are so very concerned about the daily nutritional intake of the average Zimbabwean that they are always so concerned about. Right?
The sad thing about these Scolders is that when they scold us, they don’t realize that they reveal their own inadequecies. They want that feeling of moral superiority – that dopamine rush – of scolding their morally bankrupt neighbours, whether they be educated blacks , poor blacks, activist blacks, or any Venn Diagram intersection thereof. But if your only claim to moral superiority is to scold people who are morally bankrupt….what does that say about the Scolder?
I suppose being Nominally White may be another way to achieve moral superiority.
on Fri Feb 9th 2018 at 15:25:32 Herneith
What do you expect from an Albanian? Sad!
on Fri Feb 9th 2018 at 17:08:10 Albanopolis
@Solitaire,
Because we are white,and that’s not an opinion that’s a fact. Quit the crap.
@Afrofem,
I understand the two party system better than you!
The blacks have the power to change their situation they don’t need another party! The Dems can’t win without the black vote,they can put conditions for their vote,but don’t! They just vote for them,the Dems keep brainwashing with the racism card,and that’s it! They take 90% of the black vote,and give nothing back!
What have Obama done for the Black Community?
What social policies have he take to improve black life?
Black marriage is a disaster,black cites are a disaster,black crime to the sky,the black fathers who abandon their children,a catastrophe!
He spent billions for Middle-east Pakistan etc but nothing for the problems above.
Be smart,and use the power of your vote to improve your community conditions,before they replace your vote with the hispanics one. And don’t need you anymore.
A common sense that you don’t have it! Sad!
P.S/This is my last post. May the force be with you!
@Albanian, you are as white as the driven snow in July. Sad!
on Fri Feb 9th 2018 at 19:45:18 sharinalr
@Albanopolis
Obviously you don’t know much about the two party system if you think anyone has power by voting. Voting is a show.
“lack marriage is a disaster”—Not entirely true as most blacks get married later in life. The stats were re-evaluated years ago and showed it is not that blacks aren’t getting married just later.
“black cites are a disaster”–Depends on where you go. Some are, but then again what poor city is fantastic.
“black crime to the sky”–Crime is to the sky but if you analyze data most reporting methods are based on arrest and an arrest is not a conviction. Being arrested more does not mean you are committing more crime.
“the black fathers who abandon their children,a catastrophe!”–False. A study came out some years back showing black fathers to be more involved that other races despite not being in the home.
on Fri Feb 9th 2018 at 20:37:39 Solitaire
I never said you were not white. I asked you why it matters so much to you, which is different.
Personally I think that you are white. I’m even willing to agree that you might be pale, blonde, and blue-eyed.
But my question remains: why does the possibility of being considered non-white make you so angry?
What would happen, good or bad, if someone considered you not to be white? How would it make you feel, and why?
on Fri Feb 9th 2018 at 23:23:35 Mary Burrell
Whiteness is a helluva drug.
on Sat Feb 10th 2018 at 02:55:49 Afrofem
Albanopolis’ rants and White Supremacist deflections are par for the course.
He still did not have the honesty or guts to respond to the central question.
No guts, no glory.
Their mediocrity makes them fearful and angry. White Supremacy even hurts whites.
The plot thickens being “nominally white” and second level on the hierarchy of whiteness makes for angry Albanopolis. It takes so much energy being bitter and butt hurt about not being at the top of the pyramid of whiteness. How tragic.
I should rephrase that white supremacy hurts whites and wanna be whites as well they are just to dumb to realize it.
You still have not answered my question.
on Sun Feb 11th 2018 at 02:26:54 satanforce
Concern troll is a concern troll.
The blacks have the power to change their situation they don’t need another party!
Black people. The Saviours of American Democracy. I suppose it has to do with American blacks Hive Mind psychic ability. I wonder when the Hispanics will evolve this ability.
Considering that the Dems have lost over 1000 seats during the Obama administration, ignored Bernie, lost the Obama coalition and failed, I think they may be doing a little bit more listening and less fundraising.
Crooked Albinopolis thinks he’s white when he can’t be white. Can’t ever be white because White people can’t be Muslims. Crooked Albinopolis is a Muslim. So he’s not white. Sad! He never talks about how bigly the Republicans sell out their own kind. Albinopolis and his sock-puppet troll friends are don’t understand how bad the two-party system – believe me.
It was mildly amusing to see A-polis squirm and lash out with tired anti-Black propaganda in his effort to avoid answering one simple question.
“Crooked” A-polis indeed.
on Sun Feb 11th 2018 at 11:01:46 Herneith
In actuality, these replies and recycled tropes show just how stupid and unoriginal they are. It’s not even funny anymore. Please, white supremacists, be more original!
on Tue Mar 6th 2018 at 04:05:04 Turkey
this map is wrong… im turkish very pale blonde guy and have blonde family, muslims can be white too… turkey is multi ethnic country there is browns asians and whites in country… iif u go close to middle east u will see brown looking people if u go towards west u will see white people,
also kosova,bosnia, albania,south africa shud be white too … albania kosova should be dark blue and south africa turkey should be medium…
israel should be medium too they are so mixed like turkey aswell so many brown and white people together.
you are linking religion to skin color which is wrong…
(i see comments saying white supramacy hurts white ppl and white ppl wanna be white)
lmao its funny you say that, my problem here is that ppl think turkey is like arab country and have camels and deserts or speak arabic and shit..
but its wrong we dont have desert or camels, we dont speak arabic.
we ”turks” in turkey arent even turk anymore we lost our genetics, look at real other turk countries they are all asian, turkish ppl are just like so many ethnic groups got mixed and live under 1 flag, turkey country is not nation its just a flag tbh.. cause when u walk at street u will see asian looking ppl brown ppl white ppl all call theirself turkish.
+im not muslim, pretty sure half of turkey isnt muslim too.. they just write muslim in your id when you born and you can get rid of it when u grow up but no one cares to change ur religionon paper cause it means nothing xD
if u look at me and my non religious friends ids it says muslim on all
if you still dont wantto call blonde turkish white, i dont wantto be white anyway but dont call me or put me in brown arab section or anything too just call me turkish then.
im not saying we are european or we are middle eastern asian or african.
we are just all of them
on Tue Mar 6th 2018 at 12:37:07 Herneith
The article doesn’t state that Islam is a race. That would be like stating Catholicism is a race. Where does the article state this? I am not referring to ensuing commentary either.
on Tue Mar 6th 2018 at 17:14:16 Afrofem
@ Turkey
Good point. Probably the only good point you made.
The rest of your statements are half truths at best.
on Tue Mar 6th 2018 at 20:48:03 eick74
Abalone said this in the original post.
“Albania and Kosovo are mostly Muslim so they do not count as white”
on Tue Mar 6th 2018 at 21:22:33 abagond
@ eick74
Gee, why the need to insult me by getting my name wrong?
on Wed Mar 7th 2018 at 16:00:57 eick74
Sorry, blame it on autocorrect and not paying enough attention.
on Fri Mar 9th 2018 at 14:58:48 Herneith
You have your fellow ‘Europeans’ for labelling you and your fellow Albanians thus. He, ‘Abalone’ alludes to that.
Whos Abalone?
on Fri Mar 9th 2018 at 16:24:27 eick74
Please dont make assumptions about me. I am not Albanian. I do not consider myself European except by ancestry.
You said the article did not say that Islam was a race but Abagond did indeed say in the article that he was excluding them because they were Muslim.
My apologies. Now, who is Abalone?
on Fri Mar 9th 2018 at 17:45:30 Solitaire
True, he does say that, but I don’t see anywhere in the article where he explicitly states Islam is a race.
What he does say is this: “For this map two kinds of people are [white]: …Those who belong to an ethnic group that is historically Christian or Jewish, with roots in West Eurasia”
He also talks about how he tried different definitions before settling on the two he chose to use for the map, which he calls a “general approximation.”
To me, all of that taken together shows he is aware of the arbitrariness of the definitions he chose for the map. If anything, it points out how nebulous the concept of whiteness really is.
The truth is, most of the white people in predominately Christian countries consider Muslims as “other”. All this map does is reflect that mindset. It does not necessarily condone it.
Abalone was autocorrect on my phone mistakenly correcting Abagond and me not noticing it. I said that and apologized to Abagond about it above. There was no offense intended.
on Tue Apr 3rd 2018 at 18:52:12 Albanian
You are a stupid ignorant, because the whole world knows that Albanians are white race and they have a christian history.
Today the most Albanians dont give a fuck about religions, so they are agnostics and athesits.
I am 100% sure that this “Abagond“ is a serbian psychopathic liar.
on Wed Apr 4th 2018 at 03:28:18 Paige
Lol, I hope someone calls me a Serbian psychopathic liar someday.
on Wed Apr 4th 2018 at 09:28:41 Solitaire
“Today the most Albanians dont give a fuck about religions”
But clearly they still give a big f-ck about race.
on Wed Apr 4th 2018 at 14:04:21 Herneith
Not only that, a dyed-in-the-wool shopaholic. Which is worse? Discuss!
on Wed Apr 4th 2018 at 23:13:29 Erri
Abalesh, you classified Albanians as non white? you are a fucking mad!? Have you never seen an Albanian or never been there. Do you know that the Albanian are in Europe even before Greeks. Don’t write shit because you don’t know a shit. If there wasn’t the Albanians with Skanderbeg to stop the Turks, now Europe was going to be called Europistan. O go away you cow 😠😠😠
on Thu Apr 5th 2018 at 16:09:27 hahahaa
hey Abagond , you serbians are “white” !?
on Thu Apr 5th 2018 at 16:39:55 Alban
every person defends him self when someone lies about him … no matter what kind of lies. so do not make a fool of yourself.
@ Paige
yea, you are glad if ever someone talks to you 😉
on Thu Apr 5th 2018 at 17:11:11 v8driver
Wow it’s a troll trap, it just takes one i guess.
on Thu Apr 5th 2018 at 17:17:25 Solitaire
Interesting how so many of them assume Abagond is a Serb or some other close neighbor with whom the Albanians have bad history. Makes me wonder how often they lob “you’re not white” at each other as an insult in that part of the world.
LOOOOL. I must be Serbian because only a Serbian would think so little of Albanians as to call them non-White?
If you look at the rest of my blog you might notice I do not hold a particularly high opinion of White people. They wiped out people on two and a half continents (as shown by the map itself) and enslaved millions of Black people. They are worse than the Mongols. So if anyone should be offended by my map it should be Serbs, not Albanians.
Here is my basic take on White people:
https://abagond.wordpress.com/2008/07/05/white-people/
@ Albanian readers (and anyone else who wants to answer)
Are Turks White? Why or why not?
If Turks are NOT White, then why are Albanians White?
If Turks ARE White, then where in Asia and Africa do you draw the line between White people and everyone else? If you walk from Albania to Kenya, where do White people end and Black or Brown people begin?
These are the questions I had to answer to make this map. And they are the questions that people who do not like my map have yet to answer. Calling me names might be emotionally satisfying, but it leaves the map unchanged.
Some of us are blessed, others not.
on Thu Apr 5th 2018 at 18:48:01 Erri
Albanians are not the same as Turks. Is like saying that Algerians are the same as French or Indians are the same as English. Albanians have fight with Turks for 500 years.
@ Erri
now he compares us to turks hahahaaa
he talks the same bullshit like serbian politicians.
but it is very interesting how many idiots protect his garbage …
PS.: let the idiot talk idiotic things to other idiots … they have found each other tsehehehe
“Albanians are not the same as Turks.”
Where did anyone here say that Albanians are the same as Turks?
That’s the problem, you do not understand.
My reaction has nothing to do with racism, but with the fact that he is a liar and claims false things. Understand it.
PS .: Albanians are NOT a muslim nation and they are white. That’s a fact. (Albanians are the most tolerant people in the world to races, religions, nations, etc.)
on Thu Apr 5th 2018 at 22:38:04 Afrofem
These comments by alleged Albanians about their “White” status are real howlers! The frequency and intensity of their outrage shows how marginal they really are to the the general European/White population.
Also highlights how potent a drug “Whiteness” is for millions of beige people.
At least I’m not Black or African….sniff!
on Fri Apr 6th 2018 at 03:50:16 abagond
@ Albanian
Why is it so important that you be considered White? This is the part that I do not get.
on Fri Apr 6th 2018 at 12:44:08 Herneith
Neither does he.
on Fri Apr 6th 2018 at 16:34:01 Alban
Because the Albanians are white, and not green or blue or other colors from the fantasy of a mentally disturbed person on the internet who (for any sick intention that he will not say) has made so much effort to produce such a stupid map where he makes a fool of himself by insist the opposite of reality about the Albanians.
I know it’s very hard for you and your “friends” to understand such “complicated things”, but don’t worry, time clears everything up. if not this year then in 50 years you will get it.
Bye and take care of yourself, you are really not well.
on Fri Apr 6th 2018 at 17:16:22 Open Minded Observer
This discussion really sums it all up doesn’t it? Since race is a made up social construct that was invented to belittle others, then it’s never up to a person to decide their own race. I’m only called White because others around me perceive me to be. Rachel Dolezal tried/is trying to declare herself Black or transracial, but it’s not up to her. Trevor Noah may have identified as Black, but was often perceived differently based on where he grew up… None of us gets to choose our race, it is chosen for us by idiotic group-think.
So, Abagond’s map is Abagond’s map. Alban, Erri, me, and all of us can all create our own maps based on our own definitions of “Whiteness”… at the end of the day, it’s all just made up… unfortunately, with very real consequences. We’ve all bought into it, which is why we’re arguing the Whiteness of Albanians… Honestly, arguing for recognition as White because you perceive non-Whites as inferior based on the made up concept of race… Sounds pretty White to me.
on Fri Apr 6th 2018 at 17:44:24 Solitaire
@ Alban
What is the race of the girl on the left?
If you were making a map of white people, obviously you would include Albania as a white-majority country.
Fine. But you still haven’t answered the question of where you would place the dividing line on your map.
Would you include Turkey? Greece? Serbia? Croatia? Lebanon? Syria? Egypt? Israel?
And what would you base your decision on?
on Fri Apr 6th 2018 at 17:56:34 Mary Burrell
Wow, all this vitriol over Abagond’s map and the discourse of “whiteness “ and Albanians is quite interesting to say the least. The negative responses to who is white and who isn’t says a lot about how being “white” is coveted on the European hierarchy of White Supremacy.
How to argue like Alban:
#1. I am right because I say so.
#2. If you disagree then you are an idiot.
#3. Duck all questions.
#4, Call people names.
“Albanians are the most tolerant people in the world to races”
Right. You’re on a predominantly black blog calling black people idiots, fools, mentally ill, etc. over an issue concerning race. How is that tolerant?
Such idiotic maps makes only racists like you all. (you are black racists that copy white racists … white racists, black racist, yellow racists, red racists; you all have exactly the same stupid mentality. You are all a shame of mankind)
I’am sorry, but your consciousness is too deep and your intellect too limited to discuss scientifically. It feels for me like I talk to a wall.
How do you imagine an intellectual discussion with me, when for you it’s all “greek” what I have said so far !?
Once you become civilized and live in the 21st century and dont copy more white racist from 18-19 century, then we can discuss about smart things.
PS.: I have many dark-skinned friends, very good friends from africa and asia, but I do not say that they are “not dark-skinned” and “nonreligious” like me, and they do not say about me i am “not white” and “muslim” or “christian” or “hindus” or “buddhist”, because we are not stupid and retarded racists and extremists. We acept us so like we are. Finish.
Ah one more thing, I dont want that you think like me and my acquaintances, I just want that you think.
on Fri Apr 6th 2018 at 20:28:58 gro jo
Alban baby, unlike mean old Abagond and his friends, let me reassure you that you and your people are white. Latin for white, as Abagond knows all too well, is Albus. Albania, no doubt a derivation like albumen, etc., by definition, probably means Land of the Whites, i.e. you and yours, just as Kmt, the name of ancient Egypt, meant land of the blacks. I hope that reassures you of your whiteness and you will move on to more productive fields where you won’t be the butt of cruel jokes as you’ve endured here.
People, we must have compassion for even our ‘Alban’ brothers.
Alban baby, you need to develop a sense of humor. Just a thought.
Accept the people so like mother nature had made them. Please.
Otherwise I do not know what I should say to such people like you.
Now we’re veering into “Some of my best friends are black” territory, along with a good dose of “Talking about race is racist!”
gro jo: “Alban baby, you need to develop a sense of humor. Just a thought.”
yea you are so right … why the f*ck I take seriously such people and dont laugh at them …
maybe because I perceive their pain that they really need someone to talk to them. tsehehehehe
on Sat Apr 7th 2018 at 03:38:20 sharinalr
@Alban
Please by all means highlight this intellectual conversation you were attempting to have? So far you did a great job at name calling and I applaud you, but don’t claim to be something or doing something I doubt you could accomplish.
FYI gro jo was making fun of you and if you didn’t catch that then please don’t proclaim ever to speak on intellect.
on Sat Apr 7th 2018 at 13:04:14 Herneith
How about: Do you want a cup of coffee, I’m paying?
on Sun Apr 29th 2018 at 19:36:04 Albanian86
Albanians are whiter than greeks and bulgars yet you havent included them because 50% are muslim? Douche. We are the one single people who has taken the biggest bladt of an inadin non-white force in the 1400s, and saved entire europe from islamization by the ottomans. Even if we were hindus, obly because of that historic fact, you should included us. Our language is the springboard to ALL european languages… this makes me sad. Shame on you.
on Sun Apr 29th 2018 at 22:07:01 Afrofem
@ Albanian86
Shame on you for beating the bones of a dead horse.
Go stuff you face with some Fëgesë or Tavë Kosi. If you were really White, Albanian86, you and your comrades would laugh at this post and move on.
All of this kvetching from various Albanians means that you are not secure in your own skin.
You are the ones not sure of your own Whiteness. No one cares about this issue but you.
Poseurs!!!
on Mon Apr 30th 2018 at 01:35:40 Solitaire
“Even if we were hindus, obly because of that historic fact, you should included us.”
Well, that statement was a dead giveaway to the racism behind this commenter’s argument.
Why “even if we were hindus”? Why not include the Hindus? If anything, Sanskrit has a much stronger claim to be “the springboard to ALL european languages.”
on Sun May 13th 2018 at 21:33:55 Rober Blanche
Excellent information. Do you have information regarding the amount contributed to the world economy by white people?
on Mon May 14th 2018 at 13:39:16 Herneith
@Rober :
Nice try, LOL!
on Mon May 21st 2018 at 21:33:27 Mariana
I don´t know, white in Latin America has a completely different meaning countries like Chile, Costa Rica, Argentina, Uruguay and Puerto Rico have large “white” populations but most of them are mixed but predominately european, around 58% of argentines have some degree of native american blood, the average costa rican is 70% white, 25% native and 5% black, most white cubans live now in the USA and black, mulatoes and mixed are now majority back in the island, something similar happened with Puerto Rico and Uruguay has a lot of black heritage but they try to hide it by all means, the Americas is a mixed continent, most of “white” americans are also mixed, Obama was not even black for latin american terms, he was a mulato-mixed-average guy in Dominicana.
on Tue May 22nd 2018 at 00:00:55 Afrofem
@ Mariana
Where did you get your percentages for race in Costa Rica?
They don’t represent the Costa Ricans I’ve met.
on Tue May 22nd 2018 at 02:12:49 abagond
The Americas are mostly based on self-identification in polls and censuses. As pointed out in the post:
If the map was based on, say, a non-Hispanic White person in the US judging pictures of random people from different countries, then the Americas, even the US itself, would probably be much less White than is shown on this map.
on Tue May 22nd 2018 at 04:07:18 sharinalr
Rober Blanche
Only if that amount is minus what was stolen from others.
@ Rober Blanche
https://abagond.wordpress.com/2010/02/25/how-white-america-got-rich/
on Sun Jul 22nd 2018 at 13:43:39 Klevis Dine
Well its obvious that for some reason you hate Albanians, but even with your categories you’re wrong. In Albania there are over 30-40% christians, So atleast make them light blue.
on Mon Jul 23rd 2018 at 12:32:34 Solitaire
@ Klevis Dine
“Well its obvious that for some reason you hate Albanians”
Why, because he categorizes them as non-white?
on Mon Jul 23rd 2018 at 18:13:05 A Russian Nagpo
Now, quite ironically, this map reminds me somehow of an artwork stylized as a Russian map with a writing ‘The Great Beautiful Russia’ and pejorative names for other nations and countries around it.
It’s a pity that the artwork has been prohibited by a Russian court as ‘extremist propaganda’.
on Tue Nov 6th 2018 at 12:15:26 potato
who ever created this didnt go unviersity
on Tue Nov 6th 2018 at 12:19:45 arab looking jews wanna be white its funny
israel is white im dead xD
on Tue Nov 6th 2018 at 14:32:17 Paige
@ potato
Actually, the person who created this went to an Ivy League university. Meanwhile, you managed to make six errors in the span of one sentence.
Your comment should read, “Whoever created this didn’t go to university.” The first letter of a sentence is always capitalized. “Whoever” is one word. “Didn’t” contains an apostrophe. You completely forgot the word “to”. Your spelling of “university” didn’t even make phonetic sense. Finally, you forgot a period at the end of your sentence.
I literally know elementary schoolers who write better than you, including some who don’t speak English as a first language. Come back and comment when you’ve passed the first grade – or don’t, since I doubt anyone will miss you.
on Tue Jan 15th 2019 at 23:32:48 Burrel
Fuck off you dickhead you must be some slavic prick what you mean Albanians are not because they are Muslim why don’t you go and put some stocking and thongs on and then a big dildo up ur fucking asshole you racist fuck we Albanians we are the only white race with big dicks
on Tue Jan 15th 2019 at 23:56:40 abagond
^^ NOT to be confused with Mary Burrell.
on Wed Jan 16th 2019 at 02:02:28 Solitaire
I’m so glad you added that disclaimer, LOL!!!
on Wed Jan 16th 2019 at 11:59:16 Mary Burrell
@Abagond: Please check out that Burrel person. I don’t spell my name like that. Probably a Russian troll or bot.
on Wed Jan 16th 2019 at 13:40:10 Herneith
LOL, his obscenities are almost as bad as mine!
I really want him to provide the empirical data for this claim:
“we are the only white race with big dicks”
on Wed Jan 16th 2019 at 17:22:16 Alberto Monteiro
This biggus dickus troll reminded me of an old brazilian joke
A girl was reading a magazine that stated that black men had the biggest “guns”. A white man who was nearby approaches and says:
– Excuse me, but this statistics is innacurate
– What do you mean?
– There are two nonblack groups who have even bigger “documents” than blacks
– Who are they?
– Native brazilians and Jews
They chat a lot, and the man impresses the girl with his knowledge of biology, anatomy, anthropoly and biostatistics. When they depart, the girl asks:
– So glad to meet you. But I don’t know your name!
– Ubirajara Rosenstein
on Fri Jan 18th 2019 at 12:20:40 Gjon
Allbania is white, majority AND historically Christian. We probably are probably under the top 10 contributors of European civilization. We’ve lived in Europe for over 3,500 years! Simply awful and misleading.
on Fri Jan 18th 2019 at 12:27:27 Herneith
Simply awful and misleading.
What, the fact that they have the biggest dirks or their 3500 years of history?
on Tue Feb 5th 2019 at 12:15:39 Adel
Race has nothing to do with religion ! Your mind is a mess ! You have decided that peoples from North Africa, Middle East and from some parts of Europe are non-white juste because they are muslm : this is bullshit ! The white race includes Europeans, North Africains and middle-easterners as well whatever the culture or the religion ….
on Tue Feb 19th 2019 at 16:37:36 Albert Kreshi
I’m so confused as to why you don’t classify Albanians or Bosnians as white. Both of these people have European and Christian ancestry. The difference is a lot of these people were converted to Islam as a result of the ottoman empire. Plus I should mention that Albanians/Bosnains are quite secular people too! So your map is just incorrect in this regard 100%.
on Sun Jun 2nd 2019 at 23:03:37 世界の白人分布図ｗｗｗｗｗｗｗｗｗｗｗ | おすすめまとめアンテナ
[…] https://abagond.wordpress.com/2014/04/11/the-map-of-white-people/ […]
on Sun Jun 2nd 2019 at 23:07:18 世界の白人分布図ｗｗｗｗｗｗｗｗｗｗｗ | arcanum
on Sun Jun 2nd 2019 at 23:11:27 世界の白人分布図ｗｗｗｗｗｗｗｗｗｗｗ | 不思議ｃｈ 2ちゃんまとめ
on Sun Jun 2nd 2019 at 23:16:04 ニュース 速報 | ニュース耳より速報！気になるキジの記事！
on Mon Jun 3rd 2019 at 06:38:08 世界の白人分布図ｗｗｗｗｗｗｗｗｗｗｗ | ぽにーてーる速報
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« Times Square through time
Whitney Houston: Run To You »
Fri Feb 10th 2017 by abagond
It is two and a half minutes to midnight.
The Doomsday Clock (1947- ) marks how close the world is to self-destruction in the judgement of the Bulletin of the Atomic Scientists, with input from 15 Nobel Prize laureates. It uses:
“the imagery of apocalypse (midnight) and the contemporary idiom of nuclear explosion (countdown to zero) to convey threats to humanity and the planet.”
In 2017 it now stands at two and a half minutes to midnight, the worst it has been since the 1950s.
The Bulletin of the Atomic Scientists was founded by scientists who created the first atom bomb. The founding editor was concerned not just with an atomic end of days but more generally with the “Pandora’s box of modern science”.
They set the clock according to not just the in/action of political leaders but stuff like the number and kind of nuclear weapons in use, how much carbon dioxide is in the air, the acidity of the oceans and how fast the sea level is rising.
The clock through the years, showing some of the highlights:
1947: It is 7 minutes to midnight when the clock first appears.
1949: 3 minutes: The Soviet Union gets the bomb.
1953: 2 minutes: US tests the first hydrogen bomb.
1963: 12 minutes: Partial Test Ban treaty, signed in the wake of the Cuban Missile Crisis.
1974: 9 minutes: India gets the bomb.
1981: 4 minutes: Soviets invade Afghanistan.
1984: 3 minutes: arms control talks are just for show.
1988: 6 minutes: Intermediate-Range Nuclear Forces Treaty.
1990: 10 minutes: Fall of the Berlin Wall.
1991: 17 minutes: START treaty.
1998: 9 minutes: India and Pakistan test nuclear weapons.
2007: 5 minutes: Climate change, North Korea gets the bomb, Iran is close.
A chart showing all the changes:
Of 2017: A week after Trump became US president, they moved the clock a half minute closer to midnight:
“events surrounding the US presidential campaign – including cyber offensives and deception campaigns apparently directed by the Russian government and aimed at disrupting the US election – have brought American democracy and Russian intentions into question and thereby made the world more dangerous than was the case a year ago.”
Of Trump:
“He has shown a troubling propensity to discount or outright reject expert advice related to international security, including the conclusions of intelligence experts. And his nominees to head the Energy Department and the Environmental Protection Agency dispute the basics of climate science.”
North Korea is also a concern.
The way forward is to cut nuclear arms and carbon emissions, which in turn will decrease global warming and the likelihood of nuclear war. In 2016, carbon emissions were flat, while the number of nuclear weapons increased.
A good first step for the US:
“the Trump administration needs to make a clear, unequivocal statement that it accepts climate change, caused by human activity, as a scientific reality. No problem can be solved, unless its existence is recognized.”
What ordinary citizens can do:
Learn about climate change and nuclear weapons.
Share what they learn.
Inform government representatives of their concerns.
The Bulletin:
“Facts are indeed stubborn things, and they must be taken into account if the future of humanity is to be preserved, long term.”
– Abagond, 2017.
Update (January 26th 2018): The clock has moved forward 30 seconds to two minutes before midnight, the worst it has been since 1953. BBC.
website – see where the clock is now
The 2017 Doomsday Clock statement (PDF)
Republican Bubble
Clock of the Long Now
Muzak – somehow I am reminded of Muzak.
on Fri Feb 10th 2017 at 23:55:24 Solitaire
“The way forward is to cut nuclear arms…”
http://www.reuters.com/article/us-usa-trump-putin-idUSKBN15O2A5
In his first call as president with Russian leader Vladimir Putin, Donald Trump denounced a treaty that caps U.S. and Russian deployment of nuclear warheads as a bad deal for the United States, according to two U.S. officials and one former U.S. official with knowledge of the call.
When Putin raised the possibility of extending the 2010 treaty, known as New START, Trump paused to ask his aides in an aside what the treaty was, these sources said.
Trump then told Putin the treaty was one of several bad deals negotiated by the Obama administration, saying that New START favored Russia….
New START gives both countries until February 2018 to reduce their deployed strategic nuclear warheads to no more than 1,550, the lowest level in decades. It also limits deployed land- and submarine-based missiles and nuclear-capable bombers.
During a debate in the 2016 presidential election, Trump said Russia had “outsmarted” the United States with the treaty, which he called “START-Up.” He asserted incorrectly then that it had allowed Russia to continue to produce nuclear warheads while the United States could not….
In the phone call, the Russian leader raised the possibility of reviving talks on a range of disputes and suggested extending New START, the sources said.
New START can be extended for another five years, beyond 2021, by mutual agreement. Unless they agree to do that or negotiate new cuts, the world’s two biggest nuclear powers would be freed from the treaty’s limits, potentially setting the stage for a new arms race.
With Orange Hitler at the helm and his adlepated brain this could be any day our days are numbered he is the one with access to send us to a nuclear holocaust.
on Sat Feb 11th 2017 at 12:10:04 nomad
Keep repeating this myth often enough and it becomes fact. There is no evidence that Russia hacked US election. The nation that has moved us closer to Doomsday is the US under the leadership of Barack Obama. Trump has had the opposite effect with regard to Russia, resisting the Obama/Hillary agenda of pushing for war with that country, though he has on the other hand been belligerent towards Iran and China. That too can lead to nuclear war but not as certainly as a military clash with Russia. When Hillary lost the election the Doomsday clock should actually moved back a minute. She was more prone to war with Russia than Trump.
no mention of shift in US leadership opinion from MAD to a belief that war with Russia is winnable nor of expelling Russian diplomats and sending NATO troops to Russia border in December 2016 under Obama as having any effect on the Doomsday clock.
on Sat Feb 11th 2017 at 15:24:53 Fan ...
“3. Inform government representatives of their concerns.”
Ha! You got jokes.. But you forgot to mention that you better bring a big bag of cash with you while INFORMING those representatives of your concerns because THAT’S HOW Amerika’s system works. Money talks.
Concerns? lol Not so much! In one ear (if you’re lucky enough to get an audience) then out the other ear.
Cash gets stuff done in a lobbyist fed system.
At least Putin cares something about the Russian people should a doomsday scenario occur. They have prepared underground cities/bunkers for ordinary Russian people (not just for the elites) to avoid complete death and annihilation. Russia may or may not win a nuclear exchange, but they have insured that at least a good amount of their people will survive a holocaust!
Can the same be said of the Amerikan (Democrat/Republican) leadership?
No. I think they want us dead.
on Sat Feb 11th 2017 at 16:01:14 sharinalr
@Nomad
If we are dead then who can they use and abuse? Then again our death is a sick pleasure to them so…
@ Nomad – Sharina
I think the satanists’ plan is to keep just enough people/servants alive to serve them. Everyone else, according to them, are just useless eaters.
Be polite. Use a calm voice. In the face of Armageddon.
on Sat Feb 11th 2017 at 19:29:57 TheHipHopRecords (@TheHipHopRecord)
I’m ready for oblivion
on Sun Feb 12th 2017 at 16:52:27 blakksage
There are those who are still (insert Bulletin of Atomic Scientists) attempting to make God out to be a liar (1 John 5:10); that a nuclear war will not take place (Zechariah 14:12) and therefore, averted by mortal men; that the so-called elitarians amongst us aren’t prepared to temporarily escape to their Deep Underground Military Bases (DUMBs, Cheyenne Mountains) at the initial stages of Armageddon (Revelation 6:15).
They’ll be safe for a little while. But after the nuclear dust settles, they better brace themselves because the hunters will be tearing the doors down. Personally, I hope and pray to God that I’m selected as one of His 144,000 hunters to exact terror on the elites that will survive. (Revelation 7:4)
It is unquestionable that a large sum of humanity will die, but not all of us, due to radiation exposure. Those who believe in Him will live and those who think otherwise will die (John 11:26). The Most High will put the warrior Spirit on his hunters and send them to every mountain (bunkers) in order to finish off the so-called elites who have wreak havoc on this planet (Jeremiah 16:16) in an attempt to supplant themselves as being G-d.
To me, it’s truly comical that mortal men (Atomic Scientists) with their diminutive level of wisdom would even attempt to prevent something from happening that’s already been prophesied to happen and WRITTEN by the Most High true God! (Wisdom of Solomon 17:7-8)
All of the Lord’s prophecies will come to pass and not even one of them will fail! (Isaiah 34:16)
(https://www.youtube.com/watch?v=E2oxLR-e2bI)
Revelation 6:15 And the kings of the earth, and the great men, and the rich men, and the chief captains, and the mighty men, and every bondman, and every free man, hid themselves in the dens and in the rocks of the mountains;
2 Esdras 16 Like as an arrow (missiles) which is shot of a mighty archer returneth not backward: even so the plagues that shall be sent upon earth shall not return again.
John 11:26 And whosoever liveth and believeth in me shall never die. Believest thou this?
Jeremiah 16:16 Behold, I will send for many fishers, saith the LORD, and they shall fish them; and after will I send for many hunters, and they shall hunt them from every mountain, and from every hill, and out of the holes of the rocks.
Zechariah 14:12 And this shall be the plague wherewith the LORD will smite all the people that have fought against Jerusalem; Their flesh shall consume away while they stand upon their feet, and their eyes shall consume away in their holes, and their tongue shall consume away in their mouth.
Wisdom of Solomon 17:7-8 As for the illusions of art magick, they were put down, and their vaunting in wisdom was reproved with disgrace. 8 For they, that promised to drive away terrors and troubles from a sick soul, were sick themselves of fear, worthy to be laughed at. (the Bilderberg Group; the Illuminati and the Atomic Scientists)
Revelation 7:4 And I heard the number of them which were sealed: and there were sealed an hundred and forty and four thousand of all the tribes of the children of Israel.
2 Peter 3:10-15 But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up.
Isaiah 34:16 Seek ye out of the book of the LORD, and read: no one of these shall fail,
on Mon Feb 13th 2017 at 15:36:34 nomad
Did I say ‘sending NATO troops to Russia border in December 2016 under Obama’?
It was US troops. That’s even more provocative. It’s a curious Doomsday clock that does not take into account US efforts to bring about conflict with Russia, Especially the US engineered Ukrainian coup.
on Tue Feb 14th 2017 at 01:48:05 v8driver
on Wed Feb 15th 2017 at 17:22:47 nomad
Well, there you go. Both the Hillary road and the Trump road led to the same end, didn’t it. Potential war with Russia and inevitably WW III.
I didn’t think Trump would capitulate so soon, giving his campaign rhetoric about getting along with Russia. Obviously there has been some behind the scenes arm twisting going on, leveraging this manufactured Mike Flynn scandal.
The controllers of this nation, whoever they may be (the president is only a figurehead), the real Big Brother, want war with Russia. The ones that gave Barama his marching orders. They would have gone with the Hillary fork. They would have gone to war with Russia with no resistance. But Hillary lost so they went with the contingency plan of coercing Trump into following through on that agenda. Both forks in the road led to the same end.
http://www.washingtonsblog.com/2017/02/trump-declares-war-russia.html
on Wed Feb 15th 2017 at 17:37:17 abagond
@ nomad
Your deep state paradigm explains nothing because it explains everything. It has no predictive value. And it can never be proved or disproved. It is a conspiracy theory par excellence.
If anything was going to disprove it, it was the election of Donald Trump. But nope, you keep right on rolling. It has all the intellectual rigour of a wet noodle.
Thank you. I intend to. In spite of your disapprobation.
“Your deep state paradigm explains nothing because it explains everything.”
Your dismissal of it explains you.
So let me be sure I am interpreting you correctly. It is a conspiracy theory that cannot be proved or disproved. Therefore what? It doesn’t exist? Is this what you are saying?
on Thu Feb 16th 2017 at 07:13:43 Solitaire
How do we know that Putin doesn’t want a war with the U.S.?
Here’s a conspiracy theory: Putin wanted Trump in as president to soften us up before launching a conventional war against us.
Here we are, less than a month after the inauguration, and the White House is almost paralyzed due to scandals, incompetency, and in-fighting. Trump’s already alienating key allies, hasn’t yet filled many ambassador positions around the globe, and looks to be gearing up for a witchhunt against his own intelligence community.
Trump has also said (think it was quoted on a different thread) that he wants to tear everything down so he can build it back up again. But what if after he tears it all down, Putin picks that moment to invade?
on Thu Feb 16th 2017 at 12:18:45 nomad
@Solitaire
I would call that Russophobia and Trump hysteria.
Russia has giving no indication of wanting war with the US.
The witch hunt is obviously the Intelligence Community’s against Trump. The stuff yall smoking is dangerously absurd and an inversion of reality.
no response? I’m going to assume my interpretation is correct.
BTW, in the comment you were responding to, I did not mention the Deep State. Doesn’t even sound like a term I have used. But I’m not adverse to using it.
I said “The controllers of this nation, whoever they may be (the president is only a figurehead), the real Big Brother”
We could call these controllers the Deep State. Or perhaps the Deep State is their means of control. We know there are people working behind the scenes to set the agenda. There are names of people of considerable political influence thrown about. Soros, Rockefeller, Kissinger. Maybe bankers are a part of the Deep State cabal that controls presidents. We know for example that a banker chose Obama’s cabinet. And since much of what our government does is secret, the Intel community plays a large roll, along with the driving engine of the Deep State, the MIC. Who knows who these controllers are?
Because it is hidden does not mean it doesn’t exist.
“I would call that Russophobia and Trump hysteria…. The stuff yall smoking is dangerously absurd and an inversion of reality.”
Except that I don’t believe it, any more than I believe Hillary Clinton wanted a nuclear war with Russia.
All I’m saying is if you fit certain pieces of a puzzle together in a certain way, you could equally argue that Putin wants a war with us as long as he can have it under his terms with a good chance of winning. That doesn’t mean I believe it to be true — I’m just saying.
It is probably more likely that Putin wants to see the US weakened and destabilized economically and militarily but has no intention of attacking. And even here, I’m not saying that he definitely wants a weakened America or that I thoroughly believe he does. I think it’s a possibility; it would make strategic sense. But it is equally likely not to be true.
“The witch hunt is obviously the Intelligence Community’s against Trump.”
Trump is currently planning to investigate the intelligence community and root out those he doesn’t like.
“Who knows who these controllers are?”
So in your opinion, is the US government the only one being controlled by secret players behind the scene? Or does this apply also to England, Canada, Germany, etc.? Is it possible that Putin is also being controlled?
If you disregard empirical evidence you could. Nate has been tightening the noose around Russia since the end of the Cold War. The US has surrounded Russia with military basis. The US has provoked an anti-Russian coup in Ukraine. Sent US troops to the Russian border and expelled Russian diplomats on the basis of allegations not yet supported by evidence. And the anti Russian hostility that issues from the mouths of our elected officials, which BTW contrasts markedly to the restrained rhetoric of Putin. All Russia is has done is defend itself from US aggression. Any objective observer can see who the war mongering state is here.
You’d have to deny reality to argue that Putin wants war.
on Thu Feb 16th 2017 at 17:42:15 resw
“Any objective observer can see who the war mongering state is here.”
That’s the problem. Few are objective observers. Most, like abagond and his retinue, can’t even see the New York Times’ anti-Russian propaganda for what it is.
I gave a clear example of it, and the first thing out of abagond’s mouth was another unsubstantiated conspiracy theory. There really is no reasoning with people who don’t want to deal with the facts.
“The US has provoked an anti-Russian coup in Ukraine.”
And Putin’s response was to invade an independent, sovereign nation and annex part of its territory. He had other, less aggressive options open to him, but he chose not to take them.
Correct me if I’m wrong, but I get the impression you think if someone disapproves of Putin’s actions, they must approve of the US and NATO. I disagree. I believe they are all jockeying for power. I believe that all parties view their questionable actions as necessary for their self-defense. I believe this mindset puts the world in danger. The Cold War may have ended, but the old lines are still in place and the old mentality still holds sway. All parties share the blame.
You don’t have to answer this next question if you don’t want, but I’ll ask it a second time in case you missed it because I am interested in your opinion: Is Putin also a puppet of unseen masters, or is he his own man?
I was just thinking about the Trump/O’Reilly factor, where O’Reilly called Putin a murderer. Of course any head of state that has ever caused the death of anyone can be accused rightly or wrongly of murder. But here he is speaking from a MSM platform, MSM complicit in the murder of tens of thousands, in a government that reserves the right to murder anyone anywhere in the world. If any leader there is who is specifically known for murder it is Barack Obama; the guy who claimed to be good at it and bragged about killing Osama bin Ladin. O’Reilly cries ‘Putin is a murderer!’ Why does this astound him? He has just had a president who famously personally chose persons to be assassinated by drone on a weekly basis. Did O’Reilly, at any time during this eight years call Obama a murderer? (Somebody knows the answer to that.) The Russophobic double standard is mind boggling.
He didn’t invade. He was invited by Crimea to defend them from Russia hating Nazis, which Obama supported. Imagine that. A black president supporting Nazis. I don’t think Putin’s other options, whatever they may have been, were feasible. Or beneficial to Russia. Why should he bow to US hegemony on his doorstep?
Bottom line. Russia would have taken no action in Crimea had it not been for the coup sponsored by and provoked by the USA. As I say. Russia is only reacting to US aggression.
” …O’Reilly called Putin a murderer…. But here he is speaking from a MSM platform, MSM complicit in the murder of tens of thousands, in a government that reserves the right to murder anyone anywhere in the world. ”
Right, if anyone’s a murderer it’s O’Reilly and the msm executives/faux journalists who conned Americans into supporting the Iraqi invasion based on completely false pretenses, leading to the deaths of at least 100,000.
“Did O’Reilly, at any time during this eight years call Obama a murderer? (Somebody knows the answer to that.)”
Abagond usually knows what happens on Fox News, so maybe he can answer that.
“And Putin’s response was to invade an independent, sovereign nation and annex part of its territory.”
More msm propaganda.
The US gov’t is the one with troops stationed in Ukraine, Poland, Norway, Latvia, Lithuania, etc., not Russia.
US supported a coup in Ukraine, not Russia.
Several UN polls conducted over 3 years well before the referendum showed the vast majority of Crimean voters wanted to join Russia.
Crimeans voted overwhelmingly to secede from Ukraine and join Russia.
Ok ‘deep state’ is neospeak for a good old fashioned ‘5th column’ or ‘fourth estate’ but extremely anti-populist
on Thu Feb 16th 2017 at 23:46:52 abagond
Sure it could be true, but without proof or without any predictive value, it is idle speculation.
on Fri Feb 17th 2017 at 00:44:09 v8driver
My cynicism was inculcated before i could walk, pretty sure, and the british/scottish sarcasm didnt help matters at all eh {insert moderatable comment here}
on Fri Feb 17th 2017 at 00:45:28 nomad
I suppose the implication is that The New York Times, Washington Post and NPR are doing their best to report the truth and the others, including RT, are purveyors of falsehoods. That, as regards RT, is a lie. More propaganda. More subtle Russophobia, but propaganda still. That’s not likely to restore MSM’s credibility, so ignominiously surrendered during the Hillary election debacle. The cynicism didn’t just arise out of nowhere. MSM brought it upon itself. This finger pointing is not going to help restore that credibility. I don’t really know if MSM is redeemable. I’m certainly getting my news from somewhere else and a lots more people besides me. These charlatans can F off for all I care.
Oh an btw being the recipient of my cynicism non est sui generis
on Fri Feb 17th 2017 at 01:06:25 Afrofem
@Scribh
I wrote a response to your Frum comment on The Trump Era thread:
https://abagond.wordpress.com/2016/11/09/the-trump-era/#comment-365369
There is a large body of literature on this subject and various branches of it, as I indicated, from MIC to CIA to banksters and NGOs and groups like Bilderbergs, Skull and Bones and on and on.. To say it is not worth investigating is simply wrong. In fact it’s absurd. You will not be able to determine a ‘predictive value’ until you have examined the evidence. There is nothing idle about revealing the truth.
on Fri Feb 17th 2017 at 01:59:44 abagond
I never said it should not be investigated.
“I never said it should not be investigated ”
Sure you did.
“without proof or without any predictive value, it is idle speculation.”
Proofs are available in the various literatures that I mentioned. Predictive value emerges from research in those areas. Investigating rather than dismissing as conspiracy theory, in all the pejorative sense of that label.
“BTW, in the comment you were responding to, I did not mention the Deep State. Doesn’t even sound like a term I have used. ”
Huh? You have been using the term regulary since Trump won. You first used it here on November 20th 2016:
https://abagond.wordpress.com/2016/11/12/its-not-about-racism/#comment-358657
Michael Jon Barker uses it regulary too. So does Breitbart News:
http://www.breitbart.com/big-government/2017/02/15/virgil-deep-state-bumps-off-general-flynn-whos-next-target/
“I suppose the implication is that The New York Times, Washington Post and NPR are doing their best to report the truth and the others, including RT, are purveyors of falsehoods. That, as regards RT, is a lie. More propaganda. ”
If the New York Times is propaganda, then RT most certainly is. When has RT ever broken a scandal on Vladimir Putin? But to their credit they did denounce PizzaGate as fake news.
oh I stand corrected. but as I say I have no qualms about using the term.
on the merits of RT versus MSM, MSM is not even in the same league. it is much more propagandistic than RT. as I say MSMs job is to hide geopolitical realities from Americans. RT is the antidote to that mind control because they report what MSM won’t. I think that’s their motto.
on Fri Feb 17th 2017 at 05:58:43 michaeljonbarker
Abagond said : “Michael Jon Barker uses it regulary too. So does Breitbart News:”
That uncomfortable feeling you get when you see your name in the same paragraph with Breitbart news. lol
To clarify when I use the term “the State” I am using it differently then Breitbart news and president Trump.
Trump and friends see the deep state as some kind of shadow government thus they wants to go after intelligence agencies that they imagine are behind it.
https://en.m.wikipedia.org/wiki/State_within_a_state
When I use the term “the State” I am referring to the apparatus of the State and it’s monopoly on violence. “War is the health of the State”.
Most governments around the world have States structured like the example above. Citizens think that a State is like a car. If there political party or idiology comes to power they will be able to steer the State to do the good things that they belive in. So they participate in political theater not realizing that the State is the collective “id” of their culture (in the West, white supremacy) and functions instinctively to preserve that. The State works in partnership with banks, corperations, the rich ect. to protect, maintain and expand that wealth at the expense of the average citizen.
States continue to expand until they collapse. Then a new set of thugs take over. Rarely has revolution brought real political change. The Arab Spring is a good example of that.
@MJB
I just want to be sure I’m interpreting this correctly. What you seem to be talking about is the state, not the deep state. So, I ask you like I asked Abagond, Is there a deep state? With all the Intel originating attacks against Trump, the legitimately elected president, from P gate dossier to the Flynn assassination, are you really going to assert that there is no deep state? With an agenda in this case that contradicts the president’s?
“The intel community is a government unto itself.” Michael Maloof.
People in debates like to change the terminology of the discussion to take control of it by getting their opponent to use their words. I’m just pointing out that that is what has happened here. I tend to guard against such shifts in terminology, just to be sure people aren’t distorting what I’m saying. Controllers was my term. At least for this thread. However, I have no objection to using the term you substituted. It doesn’t seem to alter the discussion any.
aaahhaahhaahaaa…
trump changes opinion about cnn being fake news.
now he thinks its VERY fake news.
@michaeljonbarker
“So [citizens] participate in political theater not realizing that the State is the collective “id” of their culture (in the West, white supremacy) and functions instinctively to preserve that. The State works in partnership with banks, corperations, the rich ect. to protect, maintain and expand that wealth at the expense of the average citizen.
States continue to expand until they collapse. Then a new set of thugs take over. Rarely has revolution brought real political change.”
Well said. That is also my understanding of modern nation-states and real effects of most revolutions.
Glenn Greenwald indulges in idle speculation.
Greenwald asserted in an interview with Democracy Now, published on Thursday, that this [Flynn situation] boils down to a fight between the Deep State and the Trump administration.
According to an in-depth report by journalist Mike Lofgren:
“The Deep State does not consist of the entire government. It is a hybrid of national security and law enforcement agencies: the Department of Defense, the Department of State, the Department of Homeland Security, the Central Intelligence Agency and the Justice Department. I also include the Department of the Treasury because of its jurisdiction over financial flows, its enforcement of international sanctions and its organic symbiosis with Wall Street.”
As Greenwald explained during his interview:
“It’s agencies like the CIA, the NSA and the other intelligence agencies, that are essentially designed to disseminate disinformation and deceit and propaganda, and have a long history of doing not only that, but also have a long history of the world’s worst war crimes, atrocities and death squads.”
http://sorendreier.com/chilling-warnings-about-deep-states-war-on-trump/
Thank you. I saw that interview and posted it on my Tumblr:
(http://abagond.tumblr.com/post/157349443149/greenwald-empowering-the-deep-state-to)
I will be doing a post on the deep state.
cool. looking forward to it.
Trump versus the Deep State. What a quandary. Who to root for? The racist or the police state? It’s only fair. The elite have been pitting us left right people against each other for so long, it’s about time for the shoe to be on the other foot. The president against the Deep State. Let’s you and him fight.
Just read an excellent 2014 essay on the Deep State by Mike Lofgren. He describes the Deep State this way:
“It is the red thread that runs through the war on terrorism, the financialization and deindustrialization of the American economy, the rise of a plutocratic social structure and political dysfunction. Washington is the headquarters of the Deep State, and its time in the sun as a rival to Rome, Constantinople or London may be term-limited by its overweening sense of self-importance and its habit, as Winwood Reade said of Rome, to “live upon its principal till ruin stared it in the face.” “Living upon its principal,” in this case, means that the Deep State has been extracting value from the American people in vampire-like fashion.”
http://billmoyers.com/2014/02/21/anatomy-of-the-deep-state/
on Sun Feb 19th 2017 at 22:24:25 nomad
“the Deep State has been extracting value from the American people in vampire-like fashion.”
Sucking the blood of the sufferers. And like vampires doing evil under the cloak of darkness, taking possession of people’s minds and doing evil. Deep state might be the Babylon system.
on Sun Feb 19th 2017 at 22:31:54 Fan ...
Did I hear kiwi’s (nick)name mentioned????
on Mon Feb 20th 2017 at 15:47:32 v8driver
Wait a second, deep state is as i described but wnd is saying ‘pro-obama’ ie [tacitly] democratic or maybe overtly even, calling it that but my gut is a ‘top tier’ military-industrial complex bubble or something, ‘presidential curiosity is not sufficient… Like making the regular govt the congress as opposed to the senate, and grooming the populace’s not only conscious nut experience vis a vis controlling news eh whatever
damn. i had a more thoughtful comment but lost it in trying to insert a link.
basically Obama is the last in the dynasty of CIA presidents and actually works for the CIA. you can tell by his policies that he wasn’t a real democrat. he was a DINO. he’s staying on to help the Deep State overthrow Trump. to orchestrate the coup actually.
Is an American Coup d’etat in Progress?
“Have you asked yourself the question of why Former President Obama is hunkering down in a secure fortress in DC to lead the new “Regime Change” against duly elected President Donald Trump? ”
https://geopolitics.co/2017/02/20/is-an-american-coup-detat-in-progress/
It’s skewed right wing, but makes an important point.
oh yeah. I also said that the fact that Trump is in acrimony with the Deep State indicates that he is not a part of it, as has been every president at least since Reagan and possibly since Kennedy. And I also said, that’s a good thing.
‘Sources say maybe’
like maybe the sun will rise tomorrow?
Like magic 8 ball, the toy that is, just in case it was confusing…
on Wed Feb 22nd 2017 at 02:23:59 abagond
By the same logic, Hillary Clinton was not part of the deep state either given the way Comey, the FBI director, broke with protocol and said he was still investigating her email scandal.
on Wed Feb 22nd 2017 at 05:10:19 michaeljonbarker
I don’t see the “deep state” the same way as has been described. I belive their is a corporatacracy that includes the media and is driven by corperations but I’m not convinced the “deep state” is as entrenched against Trump as Breitbart and the Alt Right describe it.
They see the deep state as interfering with Trump ect but what they really want is to control those institutions within government that deal with intelligence and enforcement. They wish to use the state as a mechanism to enact violence lawfully against their perceived enemies as well as against immigrants and non whites.
They want to harden the facism we already have.
on Wed Feb 22nd 2017 at 13:06:03 nomad
“By the same logic, Hillary Clinton was not part of the deep state ”
Oh yeah. Like the Deep State would not throw one of their own under the bus when they become a liability and too carelessly crooked even for them. Hillary never challenged the Deep State, as Trump is doing. That would be a sign that she’s not a part of it. The fact that she was following the Obama agenda says that she was in alignment with the Deep State.
“They see the deep state as interfering with Trump ” and so do I.
That’s because they are creditable and have journalistic integrity sorely missing from MSM. Instead of smearing RT as propaganda you, as a commentator on black culture, should be praising them for their coverage of black issues. Today I watched a segment on Watching the Hawks “Remembering Malcolm X” featuring his daughter. When has MSM done such reporting?
on Thu Feb 23rd 2017 at 03:53:55 abagond
Huh? RT has journalistic integrity? They are Putin’s little lapdog, just like Fox News is now Trump’s little lapdog. Neither speak truth to power within their own country. Both are political hacks.
RT, from what I have seen of it (mainly the headline news), seems to have a White nationalist / Clash-of-Civilizations theme. Its stories strangely track Fox News and Breitbart News. In fact, you first came off as a Fox News viewer to me. And some of what you say is echoed in Breitbart, like about the Deep State and the profound corruption of the Democratic Party.
RT seems to run stories about Blacks in the US for the same reason East German television did back in the 1980s: to make the US look bad. I doubt they do it out of any concern for Black people.
After all, what Black commentators and reporters does RT have? Every time I watch it, all I see is White people telling me the news. Why is that?
on Thu Feb 23rd 2017 at 05:24:09 nomad
“In fact, you first came off as a Fox News viewer to me. And some of what you say is echoed in Breitbart, like about the Deep State and the profound corruption of the Democratic Party.”
I guess great minds think alike
tsk tsk. so cynical. and such a true believer In the uprightness of US. US dont need RT to make US look bad, too bad you’ll never see whats just outside the blinders you wear.
“After all, what Black commentators and reporters does RT have?”
as we know from Obama, black misleaders and news regurgitaters, black skin does not mean black friend.
“Every time I watch it, all I see is White people telling me the news. Why is that?”
I don’t know. I guess ’cause they’re white. you gon’ hold that against them?
You like to make these unfounded equivalencies. E.g. Because one is a hack, the other has got to be a hack. By definition, Russia’s has got to be worse than America’s. Whatever America’s guilty of, Russia is even more guilty. Face the fact. Our media are the propagandistic even criminal hacks, in that they lie us into wars that cause the lives of millions. They hide news. RT reveals it. US media is not in the same class with RT.
And you keep making these claims without backing them up. Show me the proof that RT is Putin’s lapdog.
I know you’re blind to Wearechange too, but he articulates the truth about the propaganda mill called MSM.
(https://youtu.be/RKhSg2uVVB4)
on Thu Feb 23rd 2017 at 17:11:43 resw
“And you keep making these claims without backing them up.”
Propagandists don’t need to back up claims.
“Face the fact. Our media are the propagandistic even criminal hacks, in that they lie us into wars that cause the lives of millions. They hide news. RT reveals it.”
Like what? What great truths does RT reveal that are hidden by the US media?
” US media is not in the same class with RT.”
Right, because RT is directly controlled by the Russian government.
I will be doing a post on RT.
So then Trump is part of the Russian deep state, since he freely compares the CIA to Nazis and yet has never a bad word to say about Vladimir Putin and even ran on a strangely pro-Russian platform.
You’d think between abagond’s provincial Univision Communications and Breitbart news “diets”, he’d actually want to go on an RT “diet” so he can actually know what he’s talking about instead of spreading propaganda.
I’m tellinya. Go on an RT diet, abagond. Get cured.
I’m sure you have name for this fallacious argument type. Where can I find it?
-never a bad word to say about Vladimir Putin
I don’t know if that’s true or not and if it is its a good thing, but only by wildly stretching the imagination does that make him a part of the deep state. please return to sanity, abagond. your credibility is taking a hit.
-ran on a strangely pro-Russian platform
this a lie and pure propaganda straight from the hoary womb of Hillary Clinton, midwifed by Barack Obama and delivered to the Deep State.
“please return to sanity, abagond. your credibility is taking a hit.”
I am mocking your logic. You are the one who needs to return to sanity.
The video. It doesn’t get any clearer than that. The scion of Zbigniew Brzezinski says that the job of the MSM is to control what people think. She inadvertently let the truth out the bag. MSM is propaganda. I didn’t need her to tell me that. I discovered it on my own. But perhaps you do, since nothing for you can be true unless it comes from the official news source. Well here it is. Delivered by MSM itself.
‘Well, Russia is too.’ I know. The all sides do it argument.
Well no. RT isn’t. These are reporters with journalistic integrity. Not like our sycophantic warmongering media.
“I am mocking your logic.”
people living in glass houses should not throw stones
Off the top of my head that ISIS as prosecuted by Obama was a phony war.
The US provoked the coup in Ukraine. Americans believe Russia invaded. The rest of the world knows this is not true. already discussed above, numerous things, many of which I have posted to this blog.
“RT is directly controlled by the Russian government.”
I’ve already refuted it. Resw has already debunked. And yet you’re going to make that statement as if it were a proven fact. Your credibility is crumbling.
What you and resw debunked and I was wrong about is that RT is OWNED by the government. It is not. I agree. But it still gets most of its money from the government.
“Americans believe Russia invaded”
Huh? Are you and RT saying Russia did not invade Ukraine?
Just to be clear, some parts of the MSM are clearly propagandistic, like Fox News and MSNBC, meaning that they are more interested in pushing a particular political message than in seeking the truth. RT is in the same class, from what I have seen. CNN, the BBC and the New York Times, on the other hand, do seem to make a serious attempt at getting their facts right. That hardly means they are always right or that they are without bias. All three, for example, have a clear pro-Israeli bias.
‘Huh? Are you and RT saying Russia did not invade Ukraine?”
some bright spots amid the blight spots. on the whole its mind control. that’s why you can live in an alternate reality where Russia invaded Ukraine.
the government does not control its content, as you repeatedly assert,
you make it sound like putin issues talking points to Chris Hedges, Jesse Ventura, Larry King and the lesser known journalists and news people, every one of the journalists there that i observed were independent thinkers. every bit as abby whatshername that you have mentioned. no. no more than Obama issued talking points to cnn abc and cbs. which by the way still carried water for the his administration, well aware that they were the propaganda wing of the federal government.
Back to the machinations of the Deep State.
http://theantimedia.org/cia-coup-us-government/
“These wartime developments are not necessarily the work of a democratically elected government, but a shadowy cocktail hybrid of a number of different agencies who will oust anyone they view as a threat to their agenda.”
“Americans believe Russia invaded. The rest of the world knows this is not true.”
The rest of the world??
https://en.m.wikipedia.org/wiki/International_reactions_to_the_annexation_of_Crimea_by_the_Russian_Federation
The so called invasion of Ukraine.
http://www.vox.com/2014/8/15/6006281/russia-ukraine-war-what-we-know
PRESENTATION OF THE CASE
“Obama-Trump economic sanctions against Russia are based upon the lies that are to be exposed as lies, in the links here. So too are the NATO movements of U.S. troops and missiles right up to Russia’s very borders — ready to invade Russia — based especially upon the lie of ‘Russian aggression in Crimea’. All of the thrust for WW III is based upon U.S. President Barack Obama’s vicious lie against Russia: his saying that the transfer of Crimea from Ukraine to Russia was not (which it actually was) an example of the U.N.-and-U.S. universally recognized right of self-determination of peoples (such as the U.S. recognizes to apply both in Catalonia and in Scotland, but not in Crimea) but was instead an alleged ‘conquest’ of Crimea by Russia. (As that link there documents, Obama’s allegation that it was ‘Putin’s conquest’ of Crimea is false, and he knew it to be false; he was well informed that the people of Crimea overwhelmingly wanted their land to be restored to Russia, and to be protected by Russia, so as not to be invaded by the Ukrainian government’s troops and weapons, after a bloody U.S. coup by Obama had — less than a month earlier — overthrown the democratically elected President of Ukraine, for whom 75% of Crimeans had voted. Obama’s own agents were behind that coup; they were doing his bidding. The aggressor here is entirely the U.S., not Russia, despite Obama’s lies.)”
http://www.washingtonsblog.com/2017/02/things-will-get-worse-u-s-stops-lying-crimea.html
on Fri Feb 24th 2017 at 19:06:58 resw
“CNN, the BBC and the New York Times, on the other hand, do seem to make a serious attempt at getting their facts right.”
And that has nothing to do with whether or not something is propaganda. An article can be full of errors and not be propaganda, and one can contain mostly factual information and still be propaganda.
A perfect example is NYT’s article, “A Powerful Russian Weapon: The Spread of False Stories” which accurately says Swedish officials found no links to Russia, but still talks about Russia anyway, and even includes a photo of “unidentified soldiers” in Crimea, as if that has anything to do with fake news in Sweden.
And using abagond’s own standard regarding RT, BBC shouldn’t be trusted because it’s “controlled” by the UK government. And you need look no further than its coverage of Brexit, Syria and Israel to see that it too engages in propaganda.
It is a fact that BBC editor instructed staff to be pro-Israel and not blame Israel for its attacks in Gaza. It is a fact that he said ““Please remember, Israel doesn’t maintain a blockade around Gaza. Egypt controls the southern border.” Forget the fact that Israel with US help built a wall on that southern border, patrols it, and only allows one entrance between Gaza and Egypt.
And CNN? Don’t make us laugh. Its election coverage proved it has a clear agenda. But of course you’re going to defend the network that shilled for your boss, and I don’t blame you since you’re still collecting a cheque.
You live in an alternate reality created by MSM.
@An Scríbhneoir Gael-Mheiriceánach
No. Nobody nor nothing is controlling everything you do. Just your thoughts about geopolitical realities. To the degree that you passively accept the programming. And while somewhere along the line Bilderbergs and lizard people may play a roll, your outlook on the world is primarily being controlled by the CIA and MSM. That’s why you believe that Russia hacked the election, installed Trump, and invaded Ukraine. You believe what the state tells you to believe. Its 1984. How many fingers am I holding up?
Trump being briefed by the deep state
“Greetings, Mr. President. Thank you for taking a few minutes to see me today. I understand your time is valuable, so let me get to the point: …
You need to pull a Mukden maneuver. A Tonkin trick. A Swedish stitch-up. A Gleiwitz gambit. A Lavon lark. A Moscow machination.
You know, a false flag.
I know most people would balk at the idea of telling such a brazen lie, but that’s what I like about you, sir. You’re not afraid to lie, and lie bigly. That’s what this country needs. And the way you got Sean Spicer to straight up lie to the public’s face and tell them that Iran has fired missiles on a US naval vessel was masterful. Who else could think of taking a Houthi rebel attack on a Saudi frigate and turning it into an Iranian attack on the US Navy? It’s so unbelievable, only the American public could buy it!
Now, Mr. President, among your many excellent choices of warmongers, banksters and establishment hacks for your cabinet, I have to especially congratulate you on the choice of Rudy “Butcher of New York” Giuliani on the position of cybersecurity advisor. It’s brilliant on every level. First of all, he has no education, training, experience or displayed interest in technology or cybersecurity, so he won’t get bogged down in actual issues. Secondly, he’s a legitimate 9/11 suspect! He helped illegally clear the 9/11 crime scene! He admitted to foreknowledge of the towers’ collapse! Who better to cover up the next false flag then the man who covered up the last one! It’s like poetry, it rhymes.
…I’m sorry, what’s that? Your opinion? Hahaha. You really are a character, Mr. President, I’ll give you that. Do you think you get an opinion on this? Do you think I’m here to solicit your suggestions? Oh, that’s rich, sir. No, I’m here to let you know some of the options we’re considering. So that, when the time comes, wherever you are, whatever you’re doing, even if you’re sitting in a classroom full of kids reading a story about a pet goat, you will know to sit quietly and await your further orders.
https://steemit.com/news/@corbettreport/what-will-be-trump-s-reichstag-fire
on Sat Feb 25th 2017 at 18:08:58 Solitaire
Don’t be silly. Putin didn’t invade Crimea, he liberated it! /s
Reminds me of Reagan’s “freedom fighters” rhetoric.
on Sat Feb 25th 2017 at 18:20:01 v8driver
@nomad that’s interesting/wierd coincidence? that the uss cole is involved in that mess.
https://www.google.com/amp/www.foxnews.com/world/2017/02/03/uss-cole-patrolling-off-yemen-after-iran-backed-rebels-attack-saudi-ship.amp.html
So, yall still buying that Russia invaded Ukraine crap? That’s why America is so exceptional.
Yes — just like the U.S. invaded Mexico to take over territory. Regardless of how we sought to justify that (e.g., protecting Americans living in those regions), it was still an invasion.
Putin’s actions in your opinion may be justified, but it still constitutes an invasion. Crimea was legally part of Ukraine, a status recognized internationally and by the United Nations. Putin used military action to take Crimea away from Ukraine.
Ukraine (not just the region of Crimea) has a history of being subsumed by Russia and its independence movements repeatedly crushed.
There’s opinions and then theres facts. Ask the Crimeans if they think it was an invasion.
Yes, and, according to RT, Assad in Syria “liberated” eastern Aleppo after bombing it to bits. Something else the do-no-wrong Russians had a hand in.
Well, that would be people’s opinions, wouldn’t it? And I expect the opinions of “the Crimeans” would break largely across ethnic lines.
What’s really sad is the Crimean Tartars are the ethnic group who have the strongest and oldest claim to Crimea, but they have been virtually ignored in this controversy.
Stalin exiled the entire Crimean Tatar population and forcibly removed them from Crimea in 1944. It’s only been relatively recently that any Crimean Tartars have been allowed to return, but they now constitute an estimated 12% of the Crimean population.
After the annexation, the Russian government told the Crimean Tartars who live on the coast that they would be relocated to other parts of Crimea, whether they want to move or not.
So the people to whom the land belonged for hundreds of years have no voice in this argument between Russia and Ukraine, no autonomy, and not even enough power to prevent their forced removal from their coastal homes.
They’re also Muslim, and we can see from Chechnya what they probably have to look forward to.
“the do-no-wrong Russians”
So much dichotomous thinking in this thread. The U.S. is bad, so therefore Russia must be good. They can’t both be bad. And anyone who points out Russia’s faults must automatically think the U.S. is faultless — no matter what they say to the contrary. It’s all good/evil and no shades of gray allowed.
“Well, that would be people’s opinions, wouldn’t it?”
They are the ones who would know. Did the Russians rape and pillage and firebomb while they were invading? Or did the population of Crimea petition Russia for annexation?
“The U.S. is bad, so therefore Russia must be good.”
You’re the one making it dichotomous. The only reason you think I’m saying Russia can do no wrong is because you believe they can do no right. So it seems odd to you that they can. And they have. They are defeating ISIS where the US couldn’t. Or wouldn’t. And They’re news media is better.
Yes, and, according to RT, Assad in Syria “liberated” eastern Aleppo after bombing it to bits.
Sorry, given your bias against Russia, you need a link. Not saying its not true. Just not taking your word for it.
You guys are such faithful supporters of the government that has abused, murdered and exploited you so. I bet yall stand and put your hand your heart when they play the national anthem.
Unbelievable! So the US funding of ISIS is a conspiracy theory too?
Oh say can you see
True Americans you do be.
“alleges it was intentional – and by Clinton and Obama.)”
It was! Has it not been clear what an evil bunch of malefactors we have running this government? This. is. what. they. do.
even if you go to the gov’t of ukraine’s websites it’s not clear about not crimea the ukraine itself east ukraine
and really? ‘top of the pack’ like as in cards or wth?!?!?!? front of the pack, leader of the pack a trumpism for sure
on Sun Feb 26th 2017 at 00:30:03 Solitaire
” you believe they can do no right.”
Not true at all. For starters, the Russians defeated Nazi Germany.
Can you name one thing you believe Russia has done wrong?
“Or did the population of Crimea petition Russia for annexation?”
Some of the population of Crimea petitioned Russia. The Crimean Tartars didn’t, and look what’s already starting to happen to them.
This is ethnic conflict. There is nationalist foment on the part of both ethnic Ukrainians and ethnic Russians who wouldn’t even be in Crimea except for the past colonialist policies of failed empires.
on Sun Feb 26th 2017 at 01:59:37 abagond
This is the very sort of dichotomous thinking Solitaire was talking about. Anyone who is critical of Trump, Russia or RT is assumed to be a mindless follower of Hillary Clinton, the US or the MSM.
There are tons of RT stories about the “liberation” of East Aleppo. For example:
Syrian govt forces liberate about 40% of east Aleppo from terrorists …
https://www.rt.com/news/368400-east-aleppo-civilians-liberated/
Liberation of E. Aleppo from militants complete – Russian military …
https://www.rt.com/news/370510-aleppo-women-children-evacuated/
Liberation of E. Aleppo has allowed ‘genuine’ separation of ‘moderate …
https://www.rt.com/news/370628-russia-aleppo-separation-militants/
Civilians return to ‘normal’ life in liberated, ruined E. Aleppo (VIDEO …
https://www.rt.com/news/370717-aleppo-vide-locals-return/
Aleppo liberated, country-wide ceasefire now possible – Russian …
https://www.rt.com/news/371427-aleppo-evacuation-syria-truce/
‘Only road’ to deliver aid to eastern Aleppo liberated – Russian MoD …
https://www.rt.com/news/368713-aleppo-castello-road-liberated/
UN stopped offering aid after 40% of east Aleppo liberated from …
https://www.rt.com/news/369027-aleppo-un-russia-aid/
“They wanted us to invade” and “We were protecting them” is classic imperialistic apologetics.
I find it telling that nomad, who has no trouble seeing through the hypocrisy of Hillary Clinton, cannot see through the hypocrisy of Vladimir Putin.
I guess I should be flattered that I rate at least two Russian trolls.
Don’t be flattered. You’re Russiaphobic and paranoid. Anybody who doesn’t buy the propaganda you and the US government is pushing is a Russian troll.
I see the links there. Which one accuses Assad of bombing it to bits? Was he bombing his people or ISIS?
And I see nothing about a “liberation”. I see liberation. You use quotes to deny that they did what they actually did do. The same kind of denial you use regarding Russia. They like Russia can do no right. You are as exceptional and as American as lynching.
*Got to go back that far, huh? They haven’t done anything right in 72 years?
*Why should I? They’ve actually earned my admiration these past eight years.
“I did a Google search for “US funds ISIS.” What I found:”
Counterpunch? Fake news? Come on.
Here’s another fake news site claiming US funded ISIS.
http://www.blackagendareport.com/obama_clinton_created_isis
Thus, a year after Obama and his European and Arab friends brought down Libya’s Gaddafi and shifted their proxy war of regime change to Syria, U.S. military intelligence saw clearly the imminent rise of ISIS — and that “this is exactly” what “the West, Gulf countries and Turkey…want, in order to isolate the Syrian regime.”
Yes, Obama created ISIS, with the enthusiastic assistance of Hillary Clinton, and he is still nurturing al Nusra, the erstwhile affiliate of al Qaida
“Got to go back that far, huh? They haven’t done anything right in 72 years?”
How shall I say this? Oh yes, let me quote your phrasing: “Why should I?”
You claimed that I believed Russia couldn’t do anything right. I gave you one example as proof that your belief about my sentiments was incorrect. You then moved the goalposts on me while simultaneously refusing to give similar proof that you don’t believe Russia is perfect. Just one fricking example, even from 70 years ago. You simply refuse.
So why should I? You’ll just find a reason to dismiss anything I say because apparently you need to continue thinking of me as a mindless brainwashed supporter of the Murican gummint.
Although you know what? This is quick and easy, so here’s example number two: Run up to the top of this thread, take a look at the very first comment, where I copied and pasted a long quote about nuclear disarmament.
One of the two world leaders in that article was trying to do a good thing, and one sounded like a deluded fool. Putin and Russia are being far more reasonable about extending the treaty and continuing to reduce the nuclear weapon stockpile than our current leader.
And I shouldn’t have had to spell that out for you, because it’s my first post on this thread. Right there this whole blankety-blank time.
‘I shouldn’t have had to spell that out for you”
don’t know why you felt you needed to, I can read, I’m just not jumping thru your hoops. you feel you’ve got to make a list. go ahead. that’s your agenda. not mine.
you are the one who characterized my thoughts as dichotomous.
when actually its yours.
So much dichotomous thinking in this thread. The U.S. is bad, so therefore Russia must be good.”
Because I said Russia was justified in this case you asserted that I think they can do no wrong. That is dichotomous thinking on your part. I feel no need to engage in the straw man argument.
The first sentence of this post states:
“The Doomsday Clock (1947- ) marks how close the world is to self-destruction in the judgement of the Bulletin of the Atomic Scientists, with input from 15 Nobel Prize laureates.”
You got that blatantly wrong.
Amerika IS THE DOOMSDAY CLOCK!
There would probably be no such thing or thought of such a thing (as a doomsday clock) if not for how Amerika conducts it affairs (hegemony) throughout the world!
http://www.blacklistednews.com/Dick_Cheney_Poisoned_Hundreds_Of_US_Troops_In_Iraq._Now_They%E2%80%99re_Dying%2C_And_The_Media_Is_Silent/57022/0/38/38/Y/M.html
Confronting these evil treacherous merchants of doom.
(https://youtu.be/H8SycdU3QDk)
Abagond’s view of RT is typical of Americans, the victims of their own MSM propaganda.
Huh? RT has journalistic integrity? They are Putin’s little lapdog
But it’s wrong.
The U.S. view of Russian media is that it is all propaganda all the time to keep the Russian people in line, but it actually encourages diverse and even hostile opinions, says Gilbert Doctorow.
https://consortiumnews.com/2017/02/26/assessing-diversity-on-russian-tv/
on Mon Feb 27th 2017 at 20:30:21 resw
The propagandists already know the US funded ISIS, as I have proved on this blog several months ago:
John McCain said back in 2014:
“Hillary Clinton has described already the meeting in the White House over 2 years ago. Everyone on the National Security team recommended arming ISIS.”
And as they know, Obama admitted to training ISIS or ISIL as he likes to call it: (https://youtu.be/mOYm_CCxxKk)
Rep. Tulsi Gabbard even told us that Syrians “expressed the question, why is it that the United States, its allies and other countries, are providing support, are providing arms, to terrorist groups like Al-Nusra, Al-Qaeda, ISIS, who are on the ground there, raping, kidnapping, torturing, and killing the Syrian people? Children, men, women and people of all ages.”
Then she introduced the “Stop Arming Terrorists Act”: (https://gabbard.house.gov/news/press-releases/video-rep-tulsi-gabbard-urges-support-stop-arming-terrorists-act)
on Tue Feb 28th 2017 at 13:50:33 nomad
It’s as if proof doesn’t matter.
on Tue Feb 28th 2017 at 15:36:20 resw
Proof be damned. Abagond, et al. need to see it on CNN for it to be true.
Oh. Well CNN. I see. That’s definitely not fake news.
on Thu Mar 2nd 2017 at 04:56:44 nomad
Well dam. I guess I was wrong. I thought the existence of the deep state was an uncontroversial issue. Got to stay off the alternative media. They are misinforming me. The New York Times says we don’t have a deep state in US. That’s something that only happens in other less savory countries. Like Egypt, Turkey and probably Russia. What appears to be deep state activity has only emerged with the Trump presidency, the intel community having no recourse but to resort to leaks to undermine him. But its not really a deep state. Even though most of what our government does is secret, i.e. classified. That’s not really deep state.
As Leaks Multiply, Fears of a ‘Deep State’ in America
WASHINGTON — A wave of leaks from government officials has hobbled the Trump administration, leading some to draw comparisons to countries like Egypt, Turkey and Pakistan, where shadowy networks within government bureaucracies, often referred to as “deep states,” undermine and coerce elected governments.
So is the United States seeing the rise of its own deep state?
Not quite, experts say, but the echoes are real — and disturbing.
Though leaks can be a normal and healthy check on a president’s power, what’s happening now extends much further. The United States, those experts warn, risks developing an entrenched culture of conflict between the president and his own bureaucracy.
And you can believe the New York Times. They are not propaganda trying to disguise whats actually going on. And they are definitely not fake news.
Right-wing pundit Bill Kristol believes in the existence of the deep state. He tweets:
Obviously strongly prefer normal democratic and constitutional politics. But if it comes to it, prefer the deep state to the Trump state.
The long hidden Deep state surfaces to meet the threat of Trump.
Both conservatives like Kristol and liberals state “publically, that the “deep state” should take out Trump. Both believe, without evidence, that the Russians intervened to try to get Trump elected. Therefore, both no doubt feel justified in openly espousing a coup d’etat. They match Trump’s blatancy with their own. Nothing deep about this.
Liberals and conservatives are now publically allied in demonizing Putin and Russia, and supporting a very dangerous military confrontation initiated by Obama and championed by the defeated Hillary Clinton. In the past these opposed political factions accepted that they would rotate their titular leaders into and out of the White House, and whenever the need arose to depose one or the other, that business would be left to deep state forces to effect in secret and everyone would play dumb.
Now the game has changed. It’s all “obvious.” The deep state has seemingly gone shallow.”
*The Deep State. Not so deep anymore.
https://off-guardian.org/2017/02/28/the-deep-state-goes-shallow-a-reality-tv-coup-detat-in-prime-time/
forgot link. while I’m adding it might as well quote this passage
Obama, CIA groomed, was smoothly moved into power by the faction that felt Bush needed to be succeeded by a slick smiling assassin who symbolized “diversity,” could speak well, and played hoops. Hit them with the right hand; hit them with the left. Same coin: Take your pick – heads or tails. Hillary Clinton was expected to complete the trinity.
But surprises happen, and now we have Trump
on Fri Mar 3rd 2017 at 06:24:02 nomad
The Deep State’s Hatred of Trump Is Not the Same as Yours
http://www.truthdig.com/report/item/the_deep_states_hatred_of_trump_is_not_the_same_as_yours_20170302
on Tue Mar 21st 2017 at 23:04:17 nomad
I used to think there was a deep state. but some mainstream sources are saying there isnt. And I know these sources are not propaganda or fake news. So it must be true. These sources could not all be under the influence of the CIA. That would be, like, wrong. You know. Brainwashing. ‘Pay no attention to the man behind the curtain’ kind of thing. ‘These are not the droids youre looking for’. Jedi mind tricks.
Last week the New Yorker, and yesterday Salon magazine, published editorials arguing against the very existence of an “American Deep State”. The arguments presented are very…interesting. Both are, perhaps, classic cases of protesting too much
So two…
…wait, did I say two? I meant three four five six seven. [links provided]
Seven non-members of the non-deep state are so enraged by the idea that people might think the totally fake American deep state might be real, that they accidentally publish seemingly coordinated attacks on the very idea. Under very similar titles. All within the same few days. Citing the same “counter examples” of Egypt and Turkey. All acting with symmetrical umbrage.
https://off-guardian.org/2017/03/21/there-is-no-american-deep-state-it-just-looks-like-there-is/
Yeah. There is no deep state. That’s just a conspiracy theory. Worse. It’s a conspiracy theory created by Trump.
on Wed Mar 22nd 2017 at 12:04:11 nomad
on Wed Mar 22nd 2017 at 12:33:17 abagond
Fair enough, but let me post on Neil Gorsuch first.
no sweat. just thought you might have forgotten.
on Thu Mar 23rd 2017 at 20:36:37 nomad
I do like it when people get right to the crux of an issue, as Eric Zeusse does here. Here’s the problem in a nut shell; beginning with the Obama lie that was then enshrined in MSM and implanted into the American mind. That’s how propaganda and social control works and how they funnel us down the path to war.
If the March 2014 annexation of Crimea by Russia was based upon the overwhelming desire by Crimeans that Crimea become again a part of Russia such as Crimea had been until 1954, instead of upon Russia’s ‘conquest’ of Crimea such as Obama has charged, then the economic sanctions that Obama placed against Russia on the basis of that annexation is on false ground, and has no authentic justification in law or in fact. Also, in that case, NATO’s subsequent military buildup against Russia, purportedly to protect NATO against ‘another such conquest by Russia’, would be based upon this same lie: the lie that Crimea’s becoming again a part of Russia was something other than a legitimate carrying-out of any people’s sovereign right, of self-determination of peoples — a right that the West recognizes for Catalonians in Spain, and for Scotch in UK, but not for Crimeans in Ukraine. Consequently, essential to addressing this crucial matter is forthrightly to address misrepresentations that are commonly asserted regarding it, and also to address in a credible way what the motivations might be for any such commonly asserted misrepresentations of this historically crucial matter. In other words: an unusually frank discussion is necessary here, which does not mince words where outright lies have been stated and become widespread in The West, and which instead presents the facts that stand forth the most clearly upon the basis of the evidence that is of the very highest reliability and credibility concerning each respective point in question in the matter. The most reliable evidence is presented here, and is consistently in favor of the Russian position, and against The West’s (the U.S. and its allies) position, on this crucial, even mega-historical, issue.
http://www.strategic-culture.org/news/2017/01/06/are-us-economic-sanctions-against-russia-based-on-obama-lie.html
@ nomad, etc
I will be doing a post on the deep state soon. If you have any links you particularly recommend, please let me know.
on Fri Mar 24th 2017 at 21:56:05 nomad
Nothing in particular. Just various interesting articles. Washingtons Blog does a good job covering the subject. Here’s an interesting MSM piece.
Mr. Giraldi, executive director of the Council for the National Interest, a foreign-policy advocacy group in Washington, called the American deep state of today an “unelected, unappointed, and unaccountable presence within the system that actually manages what is taking place behind the scenes.”
on Fri Mar 24th 2017 at 22:36:20 Afrofem
@ Abagond (and @Deb)
I recently heard a podcast on Project Censored that went in depth on the subject of the Deep State. The show hosts were joined by Peter Dale Scott and David Talbot.
Peter Dale Scott is a retired Canadian diplomat, professor, and a prolific author on politics and history. His books include Deep Politics and the Death of JFK, Drugs, Oil and War, and The American Deep State.
David Talbot is the founder of Salon.com, and now writes for the San Francisco Chronicle. His most recent book is The Devil’s Chessboard: Allen Dulles, the CIA, and the Rise of America’s Secret Government.
In little under an hour they briefly give a history of the Deep State, define the sectors of the Deep State and discuss how factions of the Deep State are working against other factions to control the US and global economies.
They also discuss how groups as disparate as scientists, seniors and BLM are all facing the same adversaries and how they could mobilize and build effective coalitions to fight various right wing factions.
http://projectcensored.org/peter-dale-scott-david-talbot-2/
The podcast where the book The Devil’s Chessboard: Allen Dulles, the CIA and the Rise of America’s Secret Government. was discussed:
http://projectcensored.org/14779-2/
If you have time to listen, both podcasts are utterly fascinating and deeply disturbing.
on Sun Mar 26th 2017 at 14:29:03 nomad
The Ministry of Truth
U.S. government developed its sophisticated psychological operations capabilities that – over the past three decades – have created an alternative reality both for people in targeted countries and for American citizens.
https://consortiumnews.com/2017/03/25/how-us-flooded-the-world-with-psyops/
that’s the alternate reality you live in.
your outlook on the world is primarily being controlled by the CIA and MSM. That’s why you believe that Russia hacked the election, installed Trump, and invaded Ukraine. You believe what the state tells you to believe. Its 1984. How many fingers am I holding up?
bunch of good info in this article. Rupert Murdoch, Fox News mogul, part of CIA media control? part of deep state?
Another figure in Raymond’s constellation of propaganda assets was media mogul Rupert Murdoch, who was viewed as both a key political ally of President Reagan and a valuable source of funding for private groups that were coordinating with White House propaganda operations. [See Consortiumnews.com’s “Rupert Murdoch: Propaganda Recruit.”]
Aint it funny? The Ministry of Truth, as I call this perception management bureaucracy, begins around 1984. How appropriate.
The more recently released documents – declassified between 2013 and 2017 – show how these earlier Casey-Raymond efforts merged with the creation of a formal psyop bureaucracy in 1986 also under the control of Raymond’s NSC operation. The combination of the propaganda and psyop programs underscored the powerful capability that the U.S. government developed more than three decades ago for planting slanted, distorted or fake news. (Casey died in 1987; Raymond died in 2003.)
Over those several decades, even as the White House changed hands from Republicans to Democrats to Republicans to Democrats, the momentum created by William Casey and Walter Raymond continued to push these “perception management/psyops” strategies forward. In more recent years, the wording has changed, giving way to more pleasing euphemisms, like “smart power” and “strategic communications.” But the idea is still the same: how you can use propaganda to sell U.S. government policies abroad and at home.
are you with me so far?
on Mon Mar 27th 2017 at 12:21:37 nomad
I see why people here don’t know about the deep state.
the info is readily available.
you don’t know because you don’t want to know.
its called willful ignorance.
on Tue Mar 28th 2017 at 16:07:52 nomad
Ukraine Annexed Crimea in the 1990s
Something else “our” government and its media whores did not tell us is that under the Crimean Constitution of 1992, Crimea existed as a legal, democratic, secular state. Crimea’s relationship with Ukraine was based on bilateral agreements. In 1995 Ukrainian special ops forces and Ukrainian Army troops invaded Crimea and annexed the territory.
Here is the report from Arina Tsukanova: http://www.strategic-culture.org/news/2017/03/28/so-who-annexed-crimea-peninsular-then.html
The Autonomous Republic of Crimea was established by the 1991 All-Union Referendum in which 94% of Crimeans voted in favor of re-establishing their status as an autonomous republic. Crimeans repeated the vote in 2014 by an even higher percentage, and this time prevented another Ukrainian invasion by reuniting with Russia.
Why didn’t you know this? [’cause MSMs job is to hide it] Why instead do you hear nothing but lies about a “Russian invasion and annexation of Crimea”?
http://www.paulcraigroberts.org/2017/03/28/ukraine-annexed-crimea-1990s/
US in Iraq “liberated” Mosul after bombing it to bits.
on Wed Mar 29th 2017 at 09:33:39 nomad
and viet nam. got to do that too. very important for the crisis we are facing.
lol. did I say ‘crisis’? the first article I read today talks about ‘crisis’. I seem to be right on target.
By Bill Binney and Ray McGovern.
Binney is the NSA executive who created the agency’s mass surveillance program for digital information, who served as the senior technical director within the agency, who managed six thousand NSA employees, the 36-year NSA veteran widely regarded as a “legend” within the agency …
McGovern is a 27-year CIA veteran, who chaired National Intelligence Estimates and personally delivered intelligence briefings to Presidents Ronald Reagan and George H.W. Bush, their Vice Presidents, Secretaries of State, the Joint Chiefs of Staff, and many other senior government officials.
Although many details are still hazy because of secrecy – and further befogged by politics – it appears House Intelligence Committee Chairman Devin Nunes was informed last week about invasive electronic surveillance of senior U.S. government officials and, in turn, passed that information onto President Trump.
This news presents Trump with an unwelcome but unavoidable choice: confront those who have kept him in the dark about such rogue activities or live fearfully in their shadow. (The latter was the path chosen by President Obama. Will Trump choose the road less traveled?)
What President Trump decides will largely determine the freedom of action he enjoys as president on many key security and other issues. But even more so, his choice may decide whether there is a future for this constitutional republic. Either he can acquiesce to or fight against a Deep State of intelligence officials who have a myriad of ways to spy on politicians (and other citizens) and thus amass derogatory material that can be easily transformed into blackmail.
This crisis (yes, “crisis” is an overused word, but in this highly unusual set of circumstances we believe it is appropriate) came to light mostly by accident after President Trump tweeted on March 4 that his team in New York City’s Trump Towers had been “wiretapped” by President Obama.
The Surveillance State Behind Russia-gate
http://www.washingtonsblog.com/2017/03/surveillance-state-behind-russia-gate.html
on Fri Apr 7th 2017 at 14:23:45 nomad
Move that clock ahead 2 minutes. Trump has become Hillary Clinton. It happened a lot faster than I thought it would.
they are marching us inexorably into WW III. Both forks in the road led to the same place.
(https://youtu.be/HuvgyTnmUZ0)
Update: The Doomsday Clock has moved forward 30 seconds to two minutes before midnight, the worst it has been since 1953.
http://www.bbc.com/news/world-42823734
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Kinkade paintings worth $300K stolen in Fresno
By ABC30
CLOVIS, Calif.
A former Old Town Clovis shop owner lost about $300 thousand worth of Thomas Kinkade paintings and other artwork.
Patrick Patterson can trace the steps of the burglars who stole hundreds of thousands of dollars in artwork from him.
They left behind a haphazard mess, but their criminal approach seems more refined. They grabbed mostly pieces from well-known artists.
A display case full of art was untouched, except for one empty shelf formerly filled with popular Hummel figurines, and Thomas Kinkade paintings were the top target.
"Look at that. That's not a Kinkade. It's a Chinese painting and they left that," Patterson said. "So evidently they had some discrimination."
40 Kinkade paintings are gone, and local art dealers are on alert for limited edition prints.
The thieves also took some more unusual art, and burn marks next to an empty space show where they tried to burn open an art safe, then decided to just carry it away.
Fresno Police are looking under different rocks than the ones they normally check after burglaries.
Sgt. Mark Hudson said, "Art dealers, maybe other people out there who deal in stolen property that other people might alert us, Craigslist."
Patterson is a former Clovis Police officer himself, and he collected some evidence he hopes will help solve the crime -- like an energy drink left in the building. But he's afraid, like many burglars, the accidental art thieves who stole from him will go unpunished.
"It appears to me the thieves have a free rein," Patterson said. "They can come through and victimize honest, hard-working citizens."
That may not be the case, though. Fresno Police investigators tell me they're closing in on some potential suspects and the case could be solved soon.
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Security Architecture and Design
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What is a Risk ? (11:59)
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Difference between Third Edition and Fourth Editiom
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Skylight Services
Skylight Training and Certification
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Performance sensors: control
Performance sensors: on-prem & cloud
Collect and Analyze
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By Mae Kowalke
How to Solve Pesky LTE-A Performance Problems, Using Big Data Analytics
Sometimes, a seemingly small or isolated action can have far-reaching consequences—for good or ill. When discovered through analysis, the butterfly effect tends to be startling, whether you’re talking about a natural ecosystem or an LTE Advanced mobile network.
Take the “trophic cascade” that occurred in Yellowstone National Park when wolves were reintroduced to the ecosystem in 1995, after being absent for 70 years. Through a series of interdependencies, the presence of the wolves actually changed the course of rivers in the park!
That’s a top-down sort of butterfly effect example. A more isolated one, and perhaps more relevant for the telecom industry because it involves technology, would be a single broken stop light or accident on a particular city street bringing everything to a halt because of the way traffic patterns are set up.
Even more relevant are some of the surprising correlations that distributed, virtualized network assurance testing, combined with big data analytics, are turning up in LTE-A networks. Light Reading’s senior editor for test & measurement, Brian Santo, explored some of those in a recent article, using examples from Scott Sumner, Accedian VP of Strategic Marketing.
Time for an upgrade?
First example: An operator in India had almost half its VoLTE calls in entire city sectors drop every 14 minutes. Every metric being measured was well below the threshold for triggering alarms (e.g. packet loss was at less than 0.2%, where alarm trigger was set to 2%). Yet, there was a 95% correlation between packet loss, delay ‘bursts’, and call drops.
The carrier took all metrics available from Accedian instrumentation—more than 20 billion records in total, comprising statistical variation of jitter, class of service, MOS, packet loss and VoLTE QoE scores—and correlated them against each other using their big data analytics platform.
That comparison revealed:
MOS problems correlated only to packet loss
Packet loss correlated 100% to loss burst—loss of packets in a row
Delay did not correlate with MOS, but “Max Delay” over the span between call drops did—indicating a possible spike in delay at the time of failure
This data was combined with information from routers and network switch CPUs, and run through a big data analysis system.
This revealed that the loss bursts correlated 100% with particular routers’ loss during ring switching—switching from one side of a ring to the other. This operation, which should normally take less than 50ms to be transparent to VoLTE calls, was taking more than twice that long. The operator went on to correlate this with the firmware versions of impacting vs properly performing routers: all failure points had an outdated firmware installed. With the upgrades performed, the network was back to normal, and callers were back in business.
The problem in this case could never have been solved without analytics, because it involved crunching hundreds of billions of records, and revealed a relationship that would have been nearly impossible to detect. Detecting 100ms of packet loss is hard enough to do, but correlating it with voice QoE, network topology, and network elements and their software version is a ‘needle in a haystack scenario’.
Strange new correlations
Very fine-grained metrics, crunched by big data analytics, are turning up some other, surprising, correlations in LTE-A networks between previously unrelated performance factors. A few other examples from the Light Reading article:
Mobile backhaul – SK Telecom’s network was experiencing packet loss, leading to performance degradation and dropped calls. But, the network had capacity to spare—it was running at only 20% average utilization. The operator started measuring backhaul network utilization every tenth of a second, rolled into 1-second samples. This granularity revealed microbursts only in financial networks. Inter-cell communication was causing 1ms microbursts that exceeded the network’s total capacity, leading to packet loss.
<click image to enlarge>
Antennas again – A Tier-1 operator in Japan was experiencing call throughput oscillations swinging from 200Mbit/sec to almost none and back in the space of a second. They figured out the cause by charting latency against throughput performance, at microsecond scale. This revealed 20-microsecond delays correlated 100% with throughput loss. It turned out the issue was caused by the way antennas were configured in MIMO mode. Spikes in delay resulted in signaling message transmissions getting skewed, causing packets to interfere with each other.
Packet loss = outage – An operator found that losing five packets in a minute was no problem, but losing five packets in a row would cause a 1-second outage on data throughput. This meant that a mere 2% of packet loss could potentially knock down throughput by 80%.
These examples illustrate that LTE-A can be unexpectedly finicky, and that big data analytics can help solve baffling problems in these networks. In particular, big data is useful for identifying LTE-A network characteristics that previously were thought to have little or no relationship to each other.
Analytics systems themselves, however, are no good without the right data to analyze. Virtualized network instrumentation, especially that which is capable of capturing metrics in a very precise and granular manner (think microsecond precision and subsecond granularity) can contribute significantly toward the troubleshooting effort when analytics are put to work solving performance and customer experience issues.
We need a better microscope
In a way, the correlations that can be uncovered using such granular data in an analytics system is not unlike the way the germ theory was validated, transforming modern medicine. Its discovery can be credited in part to precise microscope technology, proving that sometimes, until the right tools are available, you don’t even know what to look for or would be unable to see and definitively prove a hypothesis.
In the mid-1800s, the work of scientists like Edward Jenner and doctors like Ignaz Philipp Semmelweiss gave rise to the idea that diseases might be caused by infectious agents, or germs. But, it was the later development of microscopic techniques that enabled people to actually see those germs, and therefore for Louis Pasteur and others to prove the theory correct.
Proving the germ theory also validated conclusions made by British doctor John Snow about how cholera spread and the sources of infection. (He faced an uphill battle getting officials to take action based on his pioneering public health research; a microscope allowing cholera bacteria to be seen, invented later, would surely have helped.)
Back to modern day: because LTE-A networks tend to be unpredictable, and because capacity demands continue to increase, a more powerful microscope is needed, so to speak, to see what’s going on and understand how metrics are correlating in new ways. Without knowing the cause, it’s hard or impossible to solve a problem.
Microbursts Hit Mobile Backhaul, Impact QoE
Overcoming Mobile Network Backhaul Challenges Posed by 5G
Analytics for Virtualized Networks: Strategies and Challenges
Q and A: Virtualized VoLTE
Mae Kowalke
In her role as Senior Marketing Editor at Accedian, Mae has blogged, managed social media strategy, and produced a variety of collateral focused on thought leadership around telecom industry news and trends. She has more than 15 years of journalism and marketing experience, covering business-to-business technology, including telecom, for a variety of organizations including TMCnet.com and Ziff Davis. Mae holds a B.A. in communications from Thomas Edison State College.
Stay up to date with the latest industry trends and best practices.
Trending: Network Performance News This Week, July 3-9, 2016
Mirror, mirror, what lies ahead for network functions virtualization?
Industrial IoT and Manufacturing set to be one of the biggest 5G markets
Next generation performance for xHaul mobile network expansion and 5G small cells
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Convergence Leadership Project
Worship Matters (Convergence Leadership Project)
Creating Liturgical Alignment
Enroll in Course for $49/m
Many of our churches treat our liturgies (or orders of worship) as checklists … as if God would get a headache or break out in the hives if we didn’t “treat” God with a prelude, invocation, sermon, offertory, and benediction at least once every seven days.
What if, instead, we could see liturgy as a revolutionary act, not because God needs it, but because we do? What if we maximized liturgy for spiritual formation in the way of Christ, infusing people with a transformative identity, equipping people for a robust way of life, deepening people’s sense of belonging, and preparing them for mission? What if your public worship gathering became like a spiritual gym or yoga class - “the workout of the people” - where people exercised their souls in love for God, neighbor, self, other, and the earth?
In this eight-week intensive, you’ll assess your current liturgy and imagine how it could be adapted and energized, so that your people started counting the days until next Sunday (or whatever day you meet).
What is the Convergence Leadership Project?
The Convergence Leadership Project (CLP) is an online, on-demand continuing education program for clergy and laity who want to strengthen their church while preparing them for the cultural changes that impact ministry. We work together to build a church that is deeply aligned and moving forward on a path of just, joyful, generous, and regenerative Christian faith. A church that is welcoming in new people and younger generations to become spiritual activists to care for the planet, seek justice for the poor, welcome vulnerable people, and work for peace across racial, religious, political, and cultural divides. CLP provides self-guided intensives to equip and inspire you and your congregation to be long-term contributors in a vital spiritual movement taking shape around the world. CLP. Participants are eligible to receive a Certificate in Convergence Leadership with the purchase and successful completion of the full online course package. We know that today’s political and social reality needs a new kind of faith leader. The Convergence Leadership Project (CLP) trains congregational leaders, lay and ordained, as spiritual activists in a growing, multi-denominational movement of just and generous Christianity. When you join, you will be part of a growing regional and national movement of contemplative Christian activism that spans denominations and traditions.
Brian D. McLaren is an author, speaker, activist, and public theologian. A former college English teacher and pastor, he is a passionate advocate for “a new kind of Christianity” – just, generous, and working with people of all faiths for the common good.
Available in days
days after you enroll
Monthly Live Video Calls
1. What's Liturgy Got to Do With It?
What Good Does It Do?
The R Word
Evolutionary Roots
Theological Roots (9:02)
An American Christian History Lesson (64:04)
So, What Does Liturgy Have To Do With It?
A Thought Experiment
What Would It Mean?
2. What Is Liturgical Alignment?
What is Liturgy? What is Liturgical Leadership? (9:05)
What is Alignment? (8:16)
Seeking Alignment (26:23)
3. Liturgy and Rituals: Bonding to Meaning
Liturgy and Meaning (3:34)
Imagine...
Unintended Consequences (5:12)
The Null Curriculum
Codes of Silence (4:49)
4. The Checklist Mentality vs. the Workout Mentality
Checklist Mentality (6:23)
Workout Mentality (1:30)
Liturgist as Personal Trainer (1:55)
Workout Specifics (11:22)
5. Joy and Thanksgiving
The Spirit of Jewish Prayer (Abraham Joshua Heschel)
Liturgy as Organized Joy (1:30)
Joy, Praise, and Thanksgiving
She Wrote the Book on Gratitude (48:04)
6. Music and the Worship Wars
Music and Singing (35:15)
Music Matters (4:31)
7. Alignment and Music
Meet David Lundsford from Eastlake Church (Seattle, WA)
Thank God (7:12)
Keep Us All Close (3:36)
One More Thing (12:56)
8. Liturgy, Welcome, Place, and Respect
R-E-S-P-E-C-T- For Our Home (15:21)
Cultural Welcome and Respect (23:54)
A Little Help
9. Liturgical Renaissance
A Short Rant (or maybe a sermon?) on a Matter of Life and Death
Catastrophic Failure
We Need Liturgical Renaissance! (4:29)
10. Praxis Completion Project
Liturgical Creation or Liturgical Audit
Are you finished with this CLP unit?
Courageous Faith Summit
How To Reignite Stewardship In Your Church
Rev. Rodrick Echols
Boundary Training for Clergy
Use the code BOUNDARY to receive %50 off!
CPR Staff
© Center for Progressive Renewal 2020
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The new Carpenters recording with the Royal Philharmonic Orchestra is now available. Use this link to order, and help us out at the same time. Thank you!
A Song For You: The Carpenters Forum
Official Review [Single]: 6. "RAINY DAYS AND MONDAYS"/"SATURDAY" (1260-S)
Thread starter Chris May
Which side is your favorite?
Side A: "RAINY DAYS AND MONDAYS"
Side B: "SATURDAY"
Rainy Days and Mondays..Chart facts.
Australia.35
Canada.3
New zealand.19
Singapore.2
USA.2
Rainy Days and Mondays - Brilliant performance, brilliant arrangement, brilliant production, brilliant matching of melody to lyrics... What else can you say? Well, Paul Gambaccini, of Rolling Stone magazine, steered clear of being as ecstatic, but at least he didn't bag the single outright in his 1971 mention, (Page 47, Rolling Stone, July 8th, 1971):- "The Carpenters are at, or near, the top of the chart of whatever Top 40 station is in your town. That sentence is appropriate every three months; the song that makes it ring true this June is "Rainy Days and Mondays", (A&M 1260). I refuse to knock the Carpenters. This is their fourth gold single, which is four more than I have. "Rainy Days and Mondays" is not the only duo-level easy-listening / teenybop 45 to assault our ears lately. Bobby Sherman sounds more nightclubby than ever on "The Drum", (Metromedia 217)"....(etc).
First time I've heard it implied that "Rainy Days and Mondays" is a teenybopper tune. Also, just thinking over his inference about the assault on the ears.....
Reactions: Tapdancer, Geographer and David A
Proudofyou
God bless Paul Williams.
Reactions: David A
David A
Brian said:
Rainy Days and Mondays has always meant a lot to me, and is never off my top 3 most-listened to Carpenters songs. I know many of us have heard the hits so many times we get "sick" of them; I never seem to get sick of this one. One of their best.
Reactions: Geographer, Mark-T, NowhereMan and 4 others
CraigGA
I also like the one tied with Superstar in the Rainy Days medley from the First Television Special that is also on the list for As Time Goes By CD.
newvillefan said:
That aside, the song is one of my favourites and I love the story Paul Williams told about his mother in Little Girl Blue. He'd coined the line "talkin' to myself and feeling old" from her and the day they first heard it on the radio in the car, she began to cry. When Paul said the lyric was inspired by her, she denied she ever talked to herself, exclaiming "you're crazy!". Very sweet story.
This reminded me of this clip of Paul Williams recounting much the same back story to "Rainy Days and Mondays." For me, it adds an even deeper dimension to a song that has always resounded with me.
Reactions: Song4uman
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Flash Art uses cookies strictly necessary for the proper functioning of the website, for its legitimate interest to enhance your online experience and to enable or facilitate communication by electronic means. To learn more about cookies please see Terms & conditions
Dance Office
SPECIAL PERFORMA19
Game State
#328 Nov 2019–Jan 2020
Fantasies and Dissonance: A Conversation with Anne Bean by Maria Elena Buszek
14 January 2020, 10:00 am CET
Since the late 1960s, British artist Anne Bean has been singularly dedicated to performance and relational art that exists in…
“I’m nothing, I’m no one, I’m everyone, I’m dead!” Aria Dean by Andrea Bellini
9 January 2020, 10:00 am CET
Crises of language dominated the last years of both theoretical and artistic research of Aria Dean (b. Los Angeles, 1993).…
Negative Space, Objects in the Absence of Performance by Brendan Fernandes , Ryan Josey
As art institutions adopt performance-based practices, artists, curators, and archivists are faced with new considerations about how to classify and…
Kara Walker Sprüth Magers / London by Henry Broome
13 December 2019, 11:44 am CET
Coinciding with the artist’s Tate Modern Turbine Hall commission, Sprüth Magers London presents the first retrospective of Kara Walker’s films.…
The (In)Animate World of Rebecca Horn by Lynette Roth
12 December 2019, 3:22 pm CET
Between 1968 and 1972, German artist Rebecca Horn created a series of performances titled “Personal Art.” Not unlike Joseph Beuys,…
Michael E. Smith Modern Art / London by William Kherbek
9 December 2019, 5:00 pm CET
Writing in “The Spirit of Things,” the critic Barbara M. Benedict considers the rise of consumer society in relation to…
Nayland Blake Institute of Contemporary Art / Los Angeles by Andrew Greene
Since the mid-1980s, Nayland Blake has engaged the politics and aesthetics of identity in America. Biracial, queer, and gender nonconforming,…
Nora Turato Serralves Museum / Porto by Pedro Alfacinha
For her first solo exhibition in Portugal, Nora Turato drove her two greyhounds, Taco and Tuna, all the way from…
Jimmy Robert: Reworking Performativity by Eleonora Milani
The work of Berlin-based artist Jimmy Robert (b. Guadeloupe (FR) 1975) is situated in the interstices between the art object,…
Sidsel Meineche Hansen Chisenhale gallery / London by Alex Bennett
“Welcome to End-Used City” continues Sidsel Meineche Hansen’s ongoing consideration of techno-capitalism’s stranglehold on biopolitics. The focus here is the…
Apertures of Queer Prophecy. Alex Baczyński-Jenkins’s Such Feeling by Sam Dolbear
2 December 2019, 12:38 pm CET
At the center of Alex Baczyński-Jenkins’s Until a thousand roses bloom (with Warsaw in the background) (2018) are two plots…
When You Mix Something, It’s Good to Know Your Ingredients: Modes of Addressing and Economies of Attention in the Visual and Performing Arts by Dorothea von Hantelmann
19 November 2019, 3:58 pm CET
The event-oriented neo-avant-gardes of the 1950s and ’60s were very much driven by an oppositional stance to the conventions of…
Image, performance, protest by Isobel Harbison
Over the past decade, much has been written about the rise of performance in contemporary art’s institutions, with gargantuan architectures…
Vincent Fecteau CCA Wattis Institute / San Francisco by Michele D'Aurizio
8 November 2019, 6:25 pm CET
In Vincent Fecteau’s most recent solo exhibition at the CCA Wattis Institute — his first show in San Francisco, his…
Luke Ching Chin Wai | South Ho Siu Nam Blindingspot / Hong Kong by Jeppe Ugelvig
The past eight months of political protest have left the administration of Hong Kong speechless. In failing to acknowledge its…
FALSE SPACES TOKAS Project / Tokyo by Maki Nishida
For its second edition, TOKAS Project invited Hong Kong Arts Centre and independent curator Yuk-Yiu Ip to present a media…
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Modern Economy
Vol.5 No.5(2014), Article ID:45801,7 pages DOI:10.4236/me.2014.55044
Financial Analysis of the Access to Pharmacotherapy for Rare Diseases in Bulgaria
Albena Zlatareva1, Konstantin Tachkov1, Milena Stoicheva2, Svetla Georgieva3, Georgi Momekov1, Guenka Petrova2
1Faculty of Pharmacy, Medical University of Sofia, Sofia, Bulgaria
2Faculty of Public Health, Medical University of Sofia, Sofia, Bulgaria
3“Alexandrovska” Hospital, Medical University of Sofia, Sofia, Bulgaria
Email: gpetrova@pharmfac.net
Received 10 March 2014; revised 10 April 2014; accepted 20 April 2014
The absence of adequate national strategies for rare diseases (RD), high medicines prices and insufficient experts’ knowledge creates to the barriers in therapy, as well as the added factors of inappropriate diagnostics and difficulties in peoples’ access to health care. A heavier burden is placed on patients’ physical, mental, psychological and intellectual wellbeing as well as on the financial capabilities of the third party payers. This study aims to analyze the financial flow for RD therapy as part of the health insurance budget and regional differences in their financing. The point of view is that of the third party payer for a 4-year period. The study is a macro costing top down financial analysis of the expenditures for medicines for rare diseases spent by the 3rd party payer, in Bulgaria that is the national health insurance fund (NHIF). Applied were financial and statistical analyses towards the budget data for expenditures for pharmaceuticals at national and regional level. Results show a constant rise in healthcare medicines expenditures, including those for rare diseases therapy from 20 to 27 million EUR for a three-year period but it is not above 10% from the budget for medicines due to regulatory restrictions. A variety of deviations exist among regional counties, accounting for more than 50% differences in payment per diagnosis. This could be explained with insufficient knowledge and lack of therapeutic standards. There is a need for collaboration on a European level and the creation of a global fund to be able to satisfy therapeutic needs. A closer look at national differences and regional therapy is necessary, as well as standardization of health care services for better health care expenditures management.
Keywords:Healthcare Budget, Medicines Budget, Rare Diseases, Orphan Medicines
Rare diseases (RD) have a potentially lethal exit, or are chronic highly debilitating diseases with limited spread and high degree of complexity [1] -[4] . Approximately between 5000 and 8000 different rare diseases affect near 6% of the European population according to the current state of the art scientific knowledge [4] . In Europe it is estimated that 15 million of the inhabitants are suffering or will suffer from RD. As chronic, progressive and degenerative states, they leave patients handicapped for their entire life. Without therapy patients are destined to remain severely injured. In 2008 the European patients’ platform (EURORDIS) started an initiative to increase awareness in the society to the problem of RD, their late diagnosis and insufficient therapy information [4] . In June 2000 the same organization established significant discrepancies in the financial and physical access to medicines. The latter was supported by other scientific works, especially in Central and East European Countries showing that the access to orphan medicines for rare diseases therapy is hampered [5] -[7] .
The absence of adequate national strategies for RD, high medicines prices and insufficient experts creates to the barriers in therapy, inappropriate diagnostics and difficulties in peoples’ access to health care [8] [9] . A heavier burden is placed on patients’ physical, mental, psychological and intellectual wellbeing as well as to the financial capabilities of the third party payers.
This study aims to analyze the financial flow for RD therapy as part of the health insurance budget and regional differences in their financing. The point of view is that of the third party payer for 4-year period.
2.1. Financial Analysis
The study is a macro costing top down financial analysis of the expenditures for medicines for rare diseases spent by the 3rd party payer. In Bulgaria that is the national health insurance fund (NHIF). The analysis covers the period 2010-2013 year.
The information analyzed was collected from the national yearly financial reports of the healthcare budget. The expenditures for rare diseases and pharmaceuticals paid by the NHIF were systematized per diagnosis, per patient and per region. The international classification of diseases (ICD) 10 was used.
Regional cost differences and index changes were calculated. The cost structure was analyzed by diseases, average on patient and by country regions.
Descriptive statistic and t-test was performed towards the data for the average cost per disease, per patient, and for regional cost differences were. ANOVA analysis was performed to test the statistically significant differences and influencing factors.
3.1. Results of the Financial Analysis
Since 2011 the pharmacotherapy cost of rare diseases is paid by the Ministry of health through a national program for RD with the exception of the therapy for 3 diseases—acromegaly, pulmonary hypertension, and phosphorus metabolism disturbances.
During 2012 the expenditures for pharmacotherapy of rare diseases were reported separately within the health care budget. The financial limit of 10% was imposed on their increase and thus the access to medicines was limited not only clinically, but also financially. Due to these limitations, a decrease in expenditures for medicines was observed as an absolute value in 2012 in comparison to 2011 [10] (Table 1).
In 2013 the expenditures for pharmaceuticals for RD were included into the total health care budget and were not reported separately. The expenditures for oncology medicines were added, due to the fact that their financial responsibility was transferred to the NHIF from the Ministry of health.
It is evident that there is a substantial growth in the health care expenditures for pharmaceuticals, including the RD therapy and all the changes in expenditures are statistically significant (p < 0.05). The increase in the expenditures is a consequence of not only the changes in budget policy, but also of the changes in the number of the reimbursed diagnoses and medicines which are constantly increasing (Figure 1).
Table 1. The structure of the NHIF medicines expenditures during 2010-2013 (EUR).
Figure 1. Number of reimbursed diagnoses and medicines in 2010-2013.
The transfer of the cost of pharmacotherapy of rare diseases from the Ministry of Health to the NHIF budget in 2011 gave rise to lots of concerns for budget failure due to the fact that there were no planned expenditures in the previously used financial programs. At the same time, it was observed, an increase in the number of covered diagnoses and eligible patients (Figure 2).
The inherited deficiencies in blood clotting factors, thalassemia, pulmonary hypertension, diseases of Gaucher, Fabry, and cystic fibrosis consume the highest part of health care budget spending and affects the biggest part of all patients suffering from RDs Table 2.
According to the anatomy therapeutic classification (ATC) in 2013 the most often reimbursed medicines fell into almost all codes as ATC А (alimentary tract)—n = 1, ATC В (blood and blood formulating organs)—n = 2, ATC С (cardiovascular)—n = 1, ATC G (genito urinary)—n = 1, ATC J (anti-infective)—n = 2, ATC L (oncology)—n = 4,varia V—n = 1 (Table 3).
Out of the medicines with orphan drug designation for the therapy of rare diseases are reimbursed medicines with expired orphan drug designation or withdrawn such as shown on Table 4 and Table 5.
3.2. Regional Differences
Regional differences are extremely high. The highest number of patients with thalassemia is in the capital Sofia (region 22; patients n = 29), followed by Plovdiv (region 16, patients n = 25) the second largest city in the country, but the highest expenditures are paid in Rousse (n = 6), and Varna (n = 3), where the number of patients is not significant—Figure 3. On average the cost per patient paid by the NHIF at regional level is 17,910 EUR, but differences are between +/− 14,000 Euro among all 28 regions and those differences are statistically significant.
For hemophilia patients the average cost per patients is 41,108 EUR and the regional differences vary among −16,000 and + 38,000 EUR. The highest is the value in region 05 where only 2 patients with hemophilia are treated. Again the morbidity prevails in the two major cities—Sofia (region 22; patients n = 34) and Plovdiv (region 16; patients n = 24) Gaucher, Fabry and Neyman diseases are classified in one financial group and are the most resource consuming with only 21 patients. The average cost per patient per year of 163,438.29 EUR and variations are among +120584 and −87700 EUR (Figures 3-5).
Similar are the results for the other rare diseases expenditures with great variations among the regions and with higher deviations in small regions.
Statistically significant are the differences among the number of patients per disease, reimbursed expenditures per region, and per patient—Table 6.
The budget and regional differences analyses confirm that the therapy of rare diseases consumes a lot of finan-
Figure 2. Number of rare disease diagnoses and patients subsidized by NHIF.
Table 2. Number of patients with RD and subsidized sum (EUR) for their therapy.
cial resources and requires detailed observations and analyses of the medical, humanistic and social reasons for the differences [11] -[13] . Regional differences could be explained with the lack of well-trained personal and specific knowledge for some rare diagnoses [10] . Evidently the lack of medical resources leads to high financial discrepancies which pose a heavy burden on the third party payer. The insufficiency of the well trained staff is also supported by the fact that the discrepancies in financial flows are mainly at regional level. The assumption is that with no knowledge for specific rare diseases the physicians tend to over prescribe unnecessary medica
Table 3. Most often reimbursed orphan medicines in 2013.
Table 4. Reimbursed medicines with expired orphan designation in 2013.
Table 5. Reimbursed medicines with withdrawn orphan designation in 2013.
Figure 3. Regional cost differences for patients with thalassemia.
Figure 4. Regional cost differences for patients with hemophilia.
Figure 5. Regional cost differences for patients with Gaucher, Fabry and Neyman diseases.
Table 6. One way ANOVA analysis of statistical differences among the expenditures.
tions and thus exceed the financial limits [1] . This is in contrast with other studies revealing that in small cities the prescribing of medicines is usually more restrictive and less costly [8] .
Regional differences in financial resources support the need for revision and reasoning of their medical basis. The patients with rare diseases are extremely limited in number but they consume huge amount of the scarce health insurance budget [5] . Every deviation in their therapy should be precisely revised and timely corrected not only to guarantee the necessary medical results, but also to control budget spending. The high expenditures in this group of patients could not always mean better therapeutic results.
Within the framework of the very dynamic regulatory environment and extensive scientific work in the field of rare diseases therapy, the financial resources remain extremely limited to ensure appropriate therapy and scientifically based treatment. There is a need of collaboration on a European level and the creation of a global fund to be able to satisfy therapeutic needs.
A closer look at national differences and regional therapy is necessary, as well as standardization of health care services for better health care expenditures management.
EC (2007) Rare Diseases Challenge for the Society. www.ec.europa.eu/health/archive/ph_threats/non_com/docs/raredis_comm_bg.pdf
European Parliament and EC. Decision No. 1295/1999/ЕU from 29 April 1999 for the Acceptance of Actions of the Community for Rare Diseases Prophylactics within the Context of the Public Health Activities; ОВ L 155, 22.6.1999, page 1; Changed with Decision No. 1786/2002/ЕU (ОВ L 271, 9.10.2002).
Orphanet (2010) Prevalence of Rare Diseases in Bulgaria. http://www.medicine.bg/novini/nad-polovin-milion-balgari-stradat-ot-redki-bolesti
Ministry of Health National Program for Rare Diseases (2012) www.rare-bg.com/wp-content/uploads/2013/01/NPRD_2009-20131.doc
Schey, C., Milanova, T. and Hutchings, A. (2011) Estimating the Budget Impact of Orphan Medicines in Europe: 2010-2020. Orphanet Journal of Rare Diseases, 27, 62. http://dx.doi.org/10.1186/1750-1172-6-62
Kamusheva, M., Stoimenova, A., Doneva, M., Zlatareva, A. and Petrova, G. (2013) A Cross Country Comparison of Reimbursed Orphan Medicines in Bulgaria, Greece, Macedonia. Biotechnology and Biotechnology Equipment, 27, 4186-4193. http://dx.doi.org/10.5504/BBEQ.2013.0066
Zlatareva, A., Lakic, D., Kamusheva, M., Spaskov, D., Georgi, M. and Guenka, P. (2013) Analysis of Access to Orphan Drugs in Five Neighboring European Countries—Bulgaria, Greece, Macedonia, Romania and Serbia. World Journal of Pharmacy and Pharmaceutical Sciences, 2, 4415-4434.
Savova, A., Kamusheva, M., Georgieva, S., Stoimenova, A. and Petrova, G. (2013) Budget Impact Analysis of Chronic Myeloid Leukemia Treatment in Bulgaria. Biotechnology and Biotechnology Equipment, 27, 3595-3598. http://dx.doi.org/10.5504/BBEQ.2012.0075
Inotai, A., Petrova, G., Vitezic, D. and Kaló, Z. (2014) Benefits of Investment into Modern Medicines in CentralEastern European Countries. Experts Review of Pharmacoeconomics and Outcomes Research, 14, 71-79. http://dx.doi.org/10.1586/14737167.2014.868314
INFOPACK (2010) Patient Care, a Public Affair. EURORDIS, European Union. http://download.rarediseaseday.org/Rare%20Disease%20Day%20Info%20pack%202009.pdf
MH (2009) National Council for Rare Diseases. National Program for Rare Diseases for the Period. http://www.mh.government.bg/Articles.aspx?lang=bg-BG&
Bignami, F. (2007) Eurordis Survey on Orphan Drugs Availability in Europe. Presented at the 6th Eurordis Round Table of Companies Workshop, Barcelona. http://www.eurordis.org/IMG/pdf/2007ODsurvey-eurordis.pdf
Simoens, S. (2011) Pricing and Reimbursement of Orphan Drugs: The Need for More Transparency. Orphanet Journal of Rare Diseases, 6, 42. http://dx.doi.org/10.1186/1750-1172-6-42
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Advances in Applied Sociology
2014. Vol.4, No.1, 30-35
Published Online January 201 4 in SciRes (http://www.scirp.org/journal/aasoci) http://dx.doi.org/10.4236/aasoci.2014.41006
From Food Desert to Food Mirage: Race, Social Class, and
Food Shopping in a Gentrifying Neighborhood
Daniel Monroe Sullivan
Department of Sociology, Portland State University, Portland, USA
Email: dsulliva@pdx.edu
Received November 14th, 2013; revised December 14th, 2013; accepted December 21st, 2013
Copyright © 2014 Daniel Monroe Sullivan. This is an open access article distributed under the Creative Com-
mons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, pro-
vided the original work is prop erly cited. In accordance of the Creative Commons Attributio n License all Copy-
rights © 2014 are reserved for SCIRP and the owner of the intellectual property Daniel Monroe Sullivan. All
Copyright © 2014 a re guarded by law and by SCIRP as a guardian.
New supermarkets in previous “food deserts” can benefit residents by improving their access to healthful,
affordable food. But in gentrifying neighborhoods characterized by the inflow of middle-class, white res-
idents and the outflow of working class, minorities, who benefits from a new supermarket that emphasizes
organic food and environmental sustainability? This paper contributes to the food access literature by
examining the food shopping behavior of diverse residents by using survey data and probability sampling
in the Alberta neighborhood in Portland, Oregon (USA). Regression results show that college-educated
(62%) and white residents (60%) are much more likely to shop there weekly, regardless of age, gender,
owner-renter status, distance from supermarket, or length of time living in the neighborhood. These find-
ings indicate that supermarkets that promote healthy living and environmental sustainability need to be
sensitive to the racial “symbolic boundaries” and socioeconomic barriers that may create “food mirages”
by limiting food access to poor and minority residents.
Keywords: Food Access; Food Des ert; Food Mirage; Social Exclusion; Gentrification; Neighborhoods;
Race; Social Class
Imagine yourself living in a racially, ethnically, and socio-
economically mixed neighborhood that has been a food desert
for the past seven years. Yes, there were supermarkets in sur-
rounding neighborhoods to which you could drive or take pub-
lic transportation. But there were only small corner stores in
your neighborhood, mostly filled with processed, unhealthful
food. During those seven years a boarded-up former supermar-
ket with a barbed wire fence surrounding it served as a constant
reminder of your food desert condition. Now, fast forward sev-
en years. You walk into a new neighborhood supermarket that
replaces the boarded-up one. It has bright-colored walls and art,
large windows that let in natural light, a knowledgeable staff,
and wide aisles filled with fresh organic fruit, vegetables, fish,
meat, and cheese. There is even a place for you to sit and enjoy
a coffee or sandwich.
Most of us would agree that residents living in neighbor-
hoods with a supermarket have greater food access than those
living in neighborhoods without one. Indeed, scholars from a
range of countries have documented food deserts in poor
neighborhoods (Alwitt & Donley, 1997; Coveney & O’Dwyer,
2009; Paez et al., 2010; Sparkes et al., 2011)—including poor
and minority neighborhoods in the USA (Morland et al., 2002;
Small & McDermott, 2006; Walker et al., 2010), and the re-
sulting limited availability, lower quality, and higher prices of
fruit, vegetables and other healthful food (Wrigley, 2002; White,
2007). Although some studies have found that residents in food
deserts are able to find ways of accessing food sufficiently out-
side their neighborhood (Hallsworth & Wood, 1986; Guy &
David, 2004; White et al., 2004), it is clear that neighborhoods
without supermarkets create an environment that contributes to
residents having a variety of health problems including obesity,
cardiovascular problems, and certain types of cancer (Larson et
al., 2009).
Competing Views of a New Supermarket in a
Gentrifying Neighborhood
Where this agreement usually ends, however, is on the ques-
tion of how many and what type of neighborhood residents
benefit from the new supermarket. Developers, as well as some
local politicians, neighborhood leaders and other “urban revita-
lization/regeneration” advocates (they tend to avoid the term
“gentrification”), would certainly interpret the new supermarket
as an unequivocal positive change. In fact, it fits neatly within
their larger belief that the middle class moving into poor urban
neighborhoods is beneficial to all residents—it deconcentrates
poverty, increases economic diversity, and creates what they
would call urban regeneration, renewal, revitalization, or some
other positive term (Grogan, 2000; Byrne, 2003). As Duany
(2001, p. 36) states, gentrification is “the rising tide that lifts all
boats.” Shaw and Porter (2009), commenting on studies of
“urban regeneration” strategies in many cities throughout the
world, are critical of the near unanimity among advocates and
their unwillingness to consider possible negative consequences
D. M. SULLIVAN
such as how little low-income residents benefit from develop-
ment activities (but see Pascual-Molinas & Ribera-Fumaz,
To be fair, the perspective of development advocates has
some validity. In free-market economies, businesses are more
likely to open in neighborhoods that have sufficient demand for
their products. So higher-income residents moving into poor
neighborhoods will provide market signals to prospective busi-
nesses that there is now sufficient demand for their products.
And there are numerous examples of this happening, including
the opening or upscaling of supermarkets (Bridge & Dowling,
2001; Gonzalez & Waley, 2012). What is missing from the
food access discussion, however, is an analysis of which neigh-
borhood residents shop at the supermarkets and how frequently;
proponents are satisfied by the mere existence of these super-
markets and do not investigate the possibility of social exclu-
Many urban scholars, however, would examine the opening
of this supermarket more critically, questioning whether the
food desert has truly disappeared or whether the neighborhood
has become instead a “food mirage”—i.e., what appears to be
adequate neighborhood food access actually obscures social
exclusion, with some minority residents and those with less
education and income finding the new supermarket to be too
expensive or culturally alien (Short et al., 2007; Everett, 2011;
Breyer & Voss-Andreae, 2013). First, many urban scholars
would not label the general neighborhood changes using posi-
tive terms such as urban regeneration but instead call it gentri-
fication, which Kennedy & Leonard (2001) define as the pro-
cess of wealthier residents moving into poorer neighborhoods
in sufficient numbers to change its social class composition and
neighborhood identity. Second, they would note that research-
ers have found that most new retail in gentrifying neighbor-
hoods caters to newcomers and outside clientele, who are more
likely to be white and have more education and income than
longtime residents. They usually support this claim by using
one or more of the following strategies: 1) describing how the
semiotics of the new retail—e.g., products, prices and cultural
symbols such as music and signage appeal largely to gentrifiers
(Patch, 2008; Zukin, 2008; Zukin et al., 2009), 2) detailing a
qualitative account of the typical gentrifier clientele of the new
retail (Lloyd, 2006; Zukin, 2008; Zukin et al., 2009), or 3) in-
terviewing a small number of non-randomly selected longtime
residents regarding their feelings of social exclusion toward
new retail (Freeman, 2006; Maurrasse, 2006; Deener, 2007;
Sullivan and Shaw, 2011).
I argue that, although these urban scholars’ skepticism may
be justified when referring to retail that sell non-essential retail
goods—e.g., restaurants, bars, and clothing boutiques—it re-
mains unclear whether their skepticism is merited when ana-
lyzing retail that sell essential goods like supermarket food.
Unlike lattes, tattoos, and hand-made purses, everyone needs
food. We need more evidence regarding the extent to which
different types of residents in a gentrifying neighborhood bene-
fit from a supermarket opening in a previous food desert.
I also argue that the evidence needs to be collected in a sys-
tematic way, using probability sampling and surveying a sub-
stantial number of residents. These data will allow researchers
to use regression analysis to measure the salience of resident
characteristics: e.g., race/ethnicity, social class, and years living
in the neighborhood. Like Short et al. (2007) and Breyer &
Voss-Andreae (2013), I also contend that it is vital to under-
stand residents’ actual food shopping behavior rather than just
the presence of a new supermarket, since their usage will most
directly measure how much they benefit from it.
This paper examines resident use of a relatively new super-
market in the Alberta neighborhood in Portland, Oregon, one-
that is a racially and socioeconomically mixed, gentrifying, and
that did not have a supermarket for a number of years until one
opened recently. This study, on the one hand, examines the tacit
assumption of the pro-development advocates by examining the
actual shopping behavior of residents—429 randomly selected
ones using survey data—rather than simply assuming they shop
at the new supermarket. It also, on the other hand, contributes
to the retail gentrification literature by focusing on essential
retail items—food—rather than non-essential ones such as fa-
shion clothes and lattes. The two main research questions are:
How frequently do neighborhood residents shop at the new
supermarket? And, given the diversity among residents, are
there differences in usage based race, social class or other de-
mographic characteristics?
Portland: Example of Environme ntal S u stain ab ility
Portland is known nationally and internationally for its pro-
gressive planning and environmental sustainability (Svoboda,
2008; Zellmer, 2010). Its regional and city government promote
such pro-environmental policies as reducing carbon dioxide
emission (Rutland & Aylett, 2008), recycling, composting,
public transportation (Killingsworth & Lamming, 2001), bi-
cycle commuting (Mirk, 2012), and urban growth boundaries
(Jun, 2004). This last feature minimizes urban sprawl and en-
courages local agriculture. In tandem with local nonprofits, the
Portland region has farm-to-school food programs and a sub-
stantial number of farmers markets and community- supported
agriculture programs (The Diggable City Project Team, 2005).
It should come as no surprise that many Portlanders, including
newcomers, embrace pro-environmental policies and are at-
tracted to such food-related activities as urban farming and
local/region food options. Related to environmental sustainabil-
ity and healthy food initiatives, a substantial number of resi-
dents engage in what Baarts and Pedersen (2009) refer to as
“mind -body” practices—i.e., activities that emphasize an aware-
ness of interrelatedness of the mental, emotional, and physical
components of well-being such as alternative medicine, yoga,
tai chi, meditation, and acupuncture. This set of practices is
supported by Portland’s large Oregon College of Oriental Me-
dicine and other mind- body training institutions.
The Alberta Neighbor ho od
Portland residents who are attracted to environmental sustai-
nability, healthy eating, and mind-body practices are not evenly
distributed spatially throughout the city. One of the areas to
which they are attracted is the Alberta neighborhood. A person
touring through the Alberta neighborhood would immediately
notice the large number of bike lanes, community and private
vegetable and fruit gardens, chicken coops, and dozens of
mind-body businesses.
It should come as no surprise that, as residents attracted to
environmental sustainability and mind-body practices have
moved into the neighborhood, there has been marked gentrifi-
cation. There has been a large increase in residents with a col-
lege degree, professional and managerial occupations, and me-
dian household income. There has been a similar increase in
house prices and rent. Although difficult to measure, there has
also been displacement of longtime residents, many of whom
are low-income (Burk, 2006; Schmidt, 2012). This process of
gentrification has been accompanied by substantial racial
change, with a decline in black residents (from 34% in 1990 to
14% in 2010) and an increase in whites (from 57% to 73%).
The decline in black residents coincides with a decrease in
black businesses and institutions (Beaven, 2005; Fitzgibbon,
2006), although some are managing to maintain their neigh-
borhood presence (Scott, 2012).
The New Supermarket
This area had been a food desert from 1994 onward when the
only supermarket within one mile of its center closed. For sev-
en years, residents had to choose between patronizing the do-
zens of neighborhood corner stores that sold largely unhealthful
food and drink and shopping at a supermarket outside the
neighborhood.
Within this context of residential and retail change, including
more residents and higher incomes, it is not surprising that a
supermarket opened in what had been previously a food desert.
And it is not just a standard supermarket. Mirroring the busi-
nesses that had already opened in the neighborhood in the near
past, the new supermarket sells products and a life-style that
promote a mind-body connection. It specializes in organic fruits
and vegetables, sustainably harvested fish, non-industrially
processed meats, and a wide selection of cheeses, wines and
specialty beers. Many of these products are produced locally/
regionally, with signage next to them alerting the customer to
their environmental sustainability. It also promotes the mind-
body lifestyle by selling such items as BPA-free water bottles,
yoga mats, and books promoting such practices as meditation
and eating raw food. It sponsors “Health and Wellness” classes
that “promote healthy lives and well-being from the inside out.”
It encourages health and environmental sustainability, in addi-
tion, by providing bike racks, recycling bins, a newsstand with
free issues of Green Living magazine, and a free drinking water
refilling station (to discourage buying disposable plastic water
bottles). It even has the dictionary definition of sustainability
painted in large letters on its walls.
New Seasons does make an attempt, however, to increase
food access to neighborhood residents who do not easily fall
into the gentrifier, mind-body category. It sells national brands
of breakfast cereals and other common products, uses “Every-
day Value” signs to signal which products are more affordable,
accepts food stamps and coupons that assist poor women and
children, offers discounts to seniors, and donates money to
organizations that support minority residents.
The main goal of this study is to examine usage of this new
supermarket and, given the neighborhood’s racial/ethnic and
social class diversity, analyze whether particular types of resi-
dents use the store more than others.
Data and Methodology
A research team documented all occupied housing units in
eight census block groups that were close to the New Seasons
supermarket. Then vacant houses and institutionalized housing
(e.g., drug rehabilitation centers) were eliminated from the
sampling frame. 679 housing units were then randomly selected.
Surveyors attempted to maximize the response rate using the
following practices: sending a postcard in advance explaining
the goal of the survey, offering an incentive for participation,
going to the selected households at different times of the day
and evening and different days of the week, and attempting to
make contact up to twelve times. 425 individuals from these
households participated in a face-to-face survey, resulting in a
63.2% response rate. Demographic analysis revealed that par-
ticipants were similar to neighborhood residents in terms of age,
gender, whether they had children living at home, and distance
from their household to the supermarket. As is common with
neighborhood survey research, whites, homeowners, and those
with a college degree were overrepresented in the sample.
The survey was conducted approximately two and a half
years after the New Seasons supermarket opened, giving res-
pondents enough time to become aware of its existence and
change their food shopping habits, if desired. The dependent
variable is ordinal on the survey instrument, measuring the
frequency of shopping at New Seasons during the past twelve
months: never, less than monthly, at least monthly, and at least
weekly. The ordinal variable is used for univariate and bivariate
analyses, but a binary of 1 = at least weekly shopping at New
Seasons, 0 = less than weekly shopping is used for the logistic
regression analysis because it most accurately measures wheth-
er residents use New Seasons as one of their primary food
shopping venues.
The independent variables of theoretical interest are race/
ethnicity, education, tenure status, and years living in the
neighborhood. Race/ethnicity is measured using four categories
for the initial bivariate analyses: white, non-Latino; black, non-
Latino; Latino, and other race/multiracial. Bivariate analysis
with the dependent variable, however, reveals that all three
non-white categories have similar shopping usage; so, for the
sake of parsimony, race/ethnicity is a binary in the logistic re-
gression: 1 = white, non-Lati no ; 0 = minority. Similarly, educa-
tion is originally measured in five categories: less than high
school degree, high school degree, some college/associate’s
degree, college degree, and graduate/professional degree. Biva-
riate analysis with the dependent variable, however, indicates
that the three lowest education categories have similar shopping
usage at New Seasons and the two highest education categories
also have similar usage patterns to each other but distinct from
the lower education categories. So, for the sake of parsimony,
education is a binary in the logistic regression: 1 = college de-
gree or higher; 0 = less than college degree. Tenure status is a
binary: 1 = homeowner; 0 = renter. Years living in the neigh-
borhood is a scale variable. Other independent variables are
included as control variables. Gender is binary: 1 = male; 0 =
female. Age and distance from the New Seasons supermarket
are scale.
Multicollinearity diagnostics show no collinearity problems
with the most parsimonious model presented here. Interaction
terms were tested but none were statistically significant and,
hence, they were not included in the regression.
Table 1 illustrates the descriptive statistics, including for the
whole sample and stratified by race. As is common in gentrify-
ing neighborhoods that are going through racial change, whites
are more likely to own their home (69% v. 55%) and have a
college degree (62% v. 21%). Whites also tend to live slightly
closer to the new grocery store (10 blocks v. 11 blocks). Black
residents tend to be older (45 years old v. 40 years) and have
lived longer in the neighborhood (12 years v. 7 years).
The vast majority of residents (90%) have shopped at least
once at the new supermarket during the past twelve months, but
with varying levels of frequency. Fifteen percent shop there less
than monthly, 25% shop there at least monthly but less than
weekly and about 50% shop there at least weekly. This last
category—shopping there at least weekly—suggests that these
residents use the new store as one of their main food shopping
venues.
The Importance of Race
Table 1 also illustrates the usage of the new supermarket by
race. Supporting the race hypothesis at the bi-variate level,
white residents are nearly three times as likely to shop at least
weekly at the new supermarket as non-whites. There is some
variation among racial minorities—black residents (15%) are
less likely than “other race/multiracial” (33%) and Latinos
(38%)—but white weekly usage clearly surpasses all of these
minority groups. On the other extreme, non-whites are nearly
four times as likely to never have shopped there within the last
twelve months.
Given that race is correlated with three other important di-
mensions of living in gentrifying neighborhoods that are un-
dergoing racial change—whites are more likely to be home-
owners, college educated, and newcomers—I use regression
analysis to examine if race has an independent and nonspurious
effect on shopping behavior. Logistic regression results from
Table 2 further support the race hypothesis. In this racially
diverse neighborhood, the odds that a white resident shops there
weekly are over 3.5 times as likely as non-whites, after control-
ling for variables that are directly related to gentrification: so-
cial class, tenure status, and years living in the neighborhood.
These findings support qualitative gentrification research that
have found race/ethnicity to be an important factor in under-
standing social exclusion in regards to retail venues, which
researchers suggest is due in part to potential shoppers perceiv-
ing racialized symbolic boundaries (Maly, 2005; Deener, 2007;
Patch, 2008; Zukin et al., 2009; Sullivan & Shaw, 2011).
Descriptive statistics of variables, stratified by race.
Overall Mean Whites Non-whites
Dependent Variables
Shop at New Supermarket at Least Weekly 49.9%** 60.3% 21.2%
Shop at New Supermarket at Least Monthly 74.4%
Shop at New Supermarket at Least Yearly 89.2%
Never Shop at New Supermarket 10.8%
Independent Variables
College Degree 50.8%** 61.6% 21.2%
Homeowner 65.2%
Years Livi ng i n the Neighb or hood 8.5** 7.4 11.7
Age 41.5
Gender (Male) 42.1% 44.6% 35.4%
Distance to New Supermarket (blocks) 10.0
N 425 312 113
Note: C h i-square test of proportional d ifferences. * = p < 0.05; ** = p < 0.01.
Logistic regression results factors influencing weekly use of new supermarket.
B Significance Standard error
Race (Whites) 1.265 ** 0.281
College degree 1.159 ** 0.242
Homeowner (reference = renter) 0.017 0.264
Years Livi ng i n the Neighb or hood −0.017 0.015
Gender (Male) −0.477 * 0.212
Age −0.003 0.011
Distance from supermarket (blocks) −0.066 * 0.021
Constant −0.434 0.484
NagelkerkeR2 0.271
* = p < 0.05; ** = p < 0.01.
My findings also contribute to the retail gentrification litera-
ture by showing that the racial differences are not limited to
stores selling non-essential goods (e.g., restaurants and bouti-
ques), but also include those that sell basic goods. Some Amer-
ican scholars help explain these racial boundaries by arguing
that alternative food practices in the U.S. are dominated by
whites, associated with whiteness, and are perpetuated by white
privilege (Slocom, 2007; Guthman, 2008; Alkon, 2012). Al-
though white businesses, workers, and customers may assume a
position of “colorblindness” when discussing such topics as
organic food, local produce, and “healthy living,” these scho-
lars argue that racial minorities often feel excluded.
The Social Class Hypothesis: Education, Not
One dimension of social class—education—also is important.
The odds that someone with a college degree shops there
weekly are over three times as high as those without a degree.
Among the different education categories, those with a college
degree or an advanced degree are about twice as likely to shop
there weekly as those with some college/two-year associate’s
degree (38%) or a high school degree (31%) and about five
times as likely as those with less than a high school degree
(17%). The weekly usage of those with a college degree or
higher (67%), however, is far higher than all of these less edu-
cated groups. These findings support the work of previous re-
searchers who find that the college-educated middle class are
more likely to have a taste for “mind-body” products and ser-
vices such as yoga, alternative medicine, and organic food
(Bridge & Dowling, 2001; Su & Li, 2011). Doel & Segrott
(2003), in addition, suggest that “mind-body” clients are well
informed about health issues, which suggests that those with
more education tend to know more about nutrition and about
the health and environmental impacts of highly processed, in-
dustrially produced, and nonlocal food.
However, another dimension of social class—tenure status
—is not significantly associated with shopping at the new su-
permarket; renters and homeowners have similar usage patterns.
Future research should examine whether income—a dimension
of social class that is not available in this data set—is correlated
with usage. The higher prices of many of New Seasons prod-
ucts, in comparison to more mainstream supermarkets in adja-
cent neighborhoods, suggests that those with more income
would be more likely to shop there regularly.
Surprisingly, once race and social class are taken into ac-
count in the regression analysis, there are no significant differ-
ences in weekly usage between newcomers and longtime resi-
dents. This suggests that the typical “newcomer” characteristics
in racially/ethnically diverse, gentrifying neighborhoods of
being white and college educated are the most salient, and that
food shopping routines that longtime residents have established
over the years are not as important.
Among the control variables, women and those living closer
to the store are more likely to shop there weekly, but age is not
significant.
Food deserts can be detrimental to neighborhood residents’
health. So it would seem intuitive that the opening of a super-
market, especially one that emphasizes healthful food and life-
style, would result in positive health effects. You would get no
argument from “urban regeneration” advocates, who espouse
the virtues of middle-class residents moving into previously
poor neighborhoods (i.e., gentrification). These virtues include
a larger retail sector, including supermarkets, from which they
assume all residents benefit. But is their assumption accurate?
Certainly urban scholars who study retail gentrification would
be skeptical, arguing that new retail cater largely to newcomers
and marginalize longtime residents, especially the poor and
minorities. But their skepticism is based largely on analyses of
non-essential retail such as boutique clothing stores and bars.
Further, their qualitative approaches, although providing rich
detail, do not systematically measure shopping behavior.
My study examines supermarket shopping behavior in a ra-
cially and socioeconomically diverse neighborhood in Portland
that is in the process of gentrifying. Does the opening of a su-
permarket eliminate the food desert or does it instead create a
food mirage, whereby minority and lower-class residents do not
find it to be a viable option for their regular food shopping?
Using probability sampling and regression analysis, my survey
of 425 randomly selected individuals supports the skepticism of
retail gentrification scholars. Although most residents have
shopped at the new supermarket at least once in the past twelve
months, only about half of them use it regularly. White and
college-educated residents—characteristics closely aligned with
gentrifiers—are much more likely to shop there weekly than are
minority and less educated residents. These findings support the
work of Breyers & Voss-Andreae (2013) who find that none of
Portland’s racially diverse and gentrifying neighborhoods are
food deserts, but rather food mirages.
Future research should examine the reasons for these racial
and social class differences in usage. Sullivan & Shaw (2011)
use in-depth interviews to understand residents’ opinions of
new retail in this neighborhood and find significant symbolic
boundaries based on race: blacks feel excluded and are resent-
ful of the new retail, which includes a substantial number of
mind-body businesses that are similar to New Seasons. In ad di-
tion, the work of Bridge & Dowling (2001) and Su & Li (2011)
in other cities suggests that there may be symbolic boundaries
based on social class. Clearly New Seasons attempts to appeal
to a particular “mind-body” facet of the middle class— through
its food and non-food products and its other retail semiotics
—but it also makes some effort to attract other kinds of neigh-
borhood residents. Future research needs to explore further the
salience of social class by examining which facet—its cultural
or economic dimension—is most salient. Do less educated and
minority residents shop there, less mostly due to higher prices,
symbolic boundaries, and/or some other reasons?
It is clear that the mind-body lifestyle espoused by much of
the new retail in the Alberta neighborhood, including the New
Seasons supermarket, continues to grow in Portland (Gunder-
son, 2013); in fact, it is a trend that is likely to increase in other
cities throughout the US and the world. And with a growing
number of racially and ethnically diverse neighborhoods in
cities throughout the world, due to increasing immigration
(Pemberton, 2008; Bretherton & Pleace, 2011), the challenge
for supermarkets is to avoid creating a “food mirage” by con-
structing spaces that, on the one hand, promote healthy living
and environmental sustainability and, on the other hand, in-
crease food access to a range of racial, ethnic, and socioeco-
nomic groups.
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Disney Bucket List
Fangirls Are We
Fanboy / Fangirl / Movie
December 16, 2014 December 16, 2014 nataliecaileenLeave a comment
I watched one of the best documentaries I’ve ever seen this week, Fangirls. It instantly became a favorite. It’s about a brilliant idea of a live show, what it ends up delivering, and what it means. Mortified Nation tells the story of adults, and the ghosts of their hilarious childhood selves.
Mortified is a show founded by a handful of lovely and insightful people. It asks adults to come up on stage, armed with their childhood journals, and read stories & excerpts from their lives. Out of this, comes some of the funniest stuff I’ve heard in a long time. But what really makes it grand, is its relatability.
Everyone has been in the places these readers delve into. Or at least most of them. Stories of lust & “love”, angst, dreams, and what you ate for dinner that day. They discuss struggle in all of its different shades. Secret aspirations, denial of sexuality, abuse, and running a house cleaning service with your mom. These readers put so much out their for this whole crowd to discover. It’s an incredibly vulnerable place to put yourself in. On a stage, in front of a large audience, reading the most embarrassing & outrageous moments from your childhood. But there is a real sense of comradery that comes out of it. There’s an understanding feeling on everyone’s mind that knows exactly what they’re talking about, exactly how it felt to be there. It’s funny because it’s all too real.
One man had an alter ego gangster rap persona that he tried on through his journal.
Another had created a rock band and a second life in which he toured the country in search of drugs & “loose women”, though he didn’t even play any instruments. One woman drew detailed story boards of her “future” relationship with the most popular guy in school. Showing all the activities they’d partake in, their love making, the engagement, and the wedding. One expressed her unwavering desire for a first kiss. One trialed her experiences with an abusive mother, and her undying love for a waitress at Chi-Chi’s. Though the stories are their own and uniquely hilarious, everyone can relate to all the feelings behind them, and what they have in common.
It puts an inspiring stress on journaling. These people were able to go back to their wild childhoods and grow from it. Be charmed by themselves, maybe even inspired to do something. It makes you feel a sense of growing up to look back at them, and points how what you’ve learned, but in what hilarious ways you haven’t really changed. After watching this documentary, I went on a hunt for some of my own old diaries. I didn’t have wild success, but definitely found enough worth giggling over. I urge you to do the same, Fangirls, it does the soul good to do some reflecting. Even if it is a little mortifying.
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GUEST POST: Writing A Good Villain by Gerrard Cowa...
Interview with C. T. Phipps (Interviewed by Mihir ...
Interview with C. T. Phipps (Interviewed by Mihir Wanchoo)
Q] Welcome to Fantasy Book Critic. To start with, could you tell us what inspired you to be a writer in the first place, what experience you went through in finding a publisher, how you ended up with Ragnarok Publications, and anything else you’d like to share about yourself?
CTP: Oh, I think I’ve always wanted to be a writer. I wrote my first (terrible) book when I was six-years-old and I’ve been inspired to try to do it ever since. I didn’t make a serious attempt until I was done with college and I made quite a few mistakes on my way to finding a publisher. If I were to give any recommendations to fledgling authors, it’s to seek out other authors for their advice and attend seminars.
Don’t try to do this on your own but learn from the voices of experiences. I owe a lot to finding very helpful friends amongst already-published authors who helped me refine my craft before they introduced me to Permuted Press, Ragnarok Publications, and Jim Bernheimer (owner of Amber Cove Publishing and writer of Confessions of a D-List Supervillain).
Q] “The Rules Of Supervillainy” is a straightforward comedic urban fantasy book, while “Esoterrorism”, is a much darker urban fantasy-thriller hybrid. Can you tell us how & why there was such drastic shift between books?
CTP: I think the difference between the books is a good illustration of the nature of the writing process and how it can be more than you expect it to be. When I set down to write Esoterrorism after several other attempts at writing the Great American Fantasy Novel TM, I had the idea it would be my big epic work. It was the one I was focused on making it my “signature” piece.
While doing so, I became mentally drained and decided to write something just for fun. You know, just to clear my brain so I could work on Esoterrorism some more. The Rules of Supervillainy was the result, being, essentially, a love-letter to everything I loved about superhero comics and a sort of madcap comedic romp.
It was written before the Avengers movie which makes someone’s early comment on the manuscript (It’s like superheroes written by Joss Whedon) all the more funny. It was just pure entertainment and nothing I really expected to be a big success. Still, every time I shared it with someone, people loved it and told me I should publish it so I decided to give it a try alongside Esoterrorism.
Much to my surprise, I found out it was every bit as popular, if not more so, than Esoterrorism now I have two very different but awesome groups of fans. It’s given me encouragement to follow my instincts and write whatever genres I feel inspired to try my hand at. Next year, I’m going to be releasing my dark fantasy novel, Wraith Knight, for example, which is going to be entirely different from both.
Q] Esoterrorism is the first volume in the Red Room series. Could you give us a progress report on the next book, offer any details about the sequel and outline your plans for the series as a whole?
CTP: The sequel to Esoterrorism, Eldritch Ops, is done and already set for publication in 2016. It follows series protagonist, Derek Hawthorne, as he (badly) adjusts to being one of the House’s Committee. It’s a bit like being a board member of the Illuminati and he’s less than pleased by the moral compromises and ruthless decisions he has to make. Given an opportunity to do some fieldwork after discovering his ex-partner is still alive (albeit as a vampire), he leaps at the opportunity to determine if there's a conspiracy within the world's most powerful conspiracy.
Derek has to determine whether it’s possible to reform the House as a force for good or whether the organization has become so obsessed with power that the only option is to try and tear it down. I have a lot of fun examining the politics and world-building of my setting as well as Derek’s past as an operative. We also get some good developments on fan favorites Shannon, Lucy, and Penny.
I have the third volume of the book, Operation: Otherworld, in manuscript form and that will be the focus for all of the major events in the series to come to a head. After that? Who knows. It may be a trilogy or it may turn into an ongoing series. I’m still undecided.
Q] You also have a sort of comedic superhero book out called The Rules Of Supervillainy. What was the inception for this story and what was it about this idea that you HAD to write it?
CTP: I like to think of The Rules of Supervillainy as part of an emerging genre called "capepunk." Capepunk books are those prose superhero books which attempt to seriously examine the underpinnings of superhero worlds both silly and serious. Because book series tend to be finite creator-owned content, they can have serious changes and developments which comic books don't have as serialized corporate-owned IP.
The first capepunk book was, IMHO, Soon I Will Be Invincible by Austin Grossman and it’s gone on to inspire many other similar works. I, myself, was inspired by works like Marion G. Harmon's Wearing the Cape, Confessions of a D-List Supervillain by Jim Bernheimer, and Peter Clines' Ex-Heroes.
What actually inspired The Rules of Supervillainy and the Supervillainy Saga as a whole was my thinking about the mechanics of a comic book world from the person on the ground. One thing I loved about the early seasons of Buffy: The Vampire Slayer is they took an irreverant post-modern look at what it would be like to live in a world where every horror movie was true. Being an ardent lover of comic books and superheroes, I had the idea of sticking a character who was as familiar with superhero tropes and comic book geekery as the average fan into a world where he was one.
Gary was born and raised in a world where men can fly, women can punch through walls, and a guy stalking the streets in a black cape is "normal." Analyzing what sort of place that it is and how this came to be seemed like it would be really fun to right. I also decided to make him a (reluctant) supervillain rather than a superhero since we'd seen everymen become heroes in the Marvel movie franchise. I was interested in seeing how the reverse would be true, basically Scarface meets Spiderman. Gary is a little nicer than Tony Montana, though.
Wittier too.
Q] In the preface for The Rules Of Supervillainy, you very clearly wonder about the world of superheroes and as to why anyone would want to be a villain? Yet you then explore how Gary Karkofsky decides to become one? What made you choose Gary to explore this dichotomy?
CTP: To go with my earlier Spiderman example, Peter Parker's initial reaction to being bitten by a radioactive spider wasn't to fight crime. No, his initial reaction in the comics was to decide to use his newfound powers to get rich. It took the death of his Uncle Ben to become devoted to the principles of "with great power comes great responsibility."
For me, I'm cynical enough to believe the majority of people in the world would be interested in using their abilities for self-interest before anything resembling the Batman's heroic resolve to rid the world of crime. I love crime fiction and over-the-top stories of colorful gangsters so it was interesting to see if I could combine those to do a "supervillain" origin story the same way so many superhero movies are hero origins.
The thing is, I play with the concept a bit as while Gary is evil enough to be a wannabe bank-robber and thief, he's not quite bad enough to be a monster like so many of his world's villains. More Catwoman than Joker.
Q] What are your plans for Gary and rest of the cast of TROSV? Can you tell us about the The Games Of Supervillainy and the series beyond?
CTP: Well, I'm pleased to say The Rules of Supervillainy audio book is coming out this month and The Games of Supervillainy is coming out early this November. I have plans for two books a year at present. The Supervillainy Saga books are extremely easy to write since I’ve got my entire childhood and seventy years of comics to draw from.
As for The Games of Supervillainy’s plot, it picks up immediately after the events of Rules, dealing with the fact Falconcrest City has become overrun with zombies and an evil cult. Gary’s wife, Mandy, has since gone on to become a superhero in her own right and the tensions between the couple will be a focus of the book as they try to figure out if a marriage can survive being on opposite sides of the superhero/villain divide.
Further books will get into showing the world going through a transition as the setting’s people try to figure out just what sort of world they want to live in. Do they want idealistic superheroes like Ultragod (the setting’s resident Superman) or something more vicious and brutal (like the Extreme). Gary as the outsider to all of this will serve as a wildcard and we get to see him develop fully into his role as a supervillain in a world which is well and truly sick of them.
We’re also going to get some fun character development from Cindy (a.k.a Red Riding Hood), Gabrielle (a.k.a Ultragoddess), and Diabloman—people who have been effected by Gary’s good-natured antiheroism. Some will get better and some will get worse. Some will even fall in love.
Q] You have used this quote by R. Chandler in one of your articles: “Down these mean streets a man must go who is not himself mean, who is neither tarnished nor afraid. He is the hero; he is everything. He must be a complete man and a common man and yet an unusual man.” Please tell us what about it struck you and how did you utilize it in your writing (if any?)
CTP: I think, for me, Raymond Chandler's quote encapsulates something I love about my writing, which is the fact my (anti)heroes journey into gritty and dark worlds not of their own making. Gary, Derek, and my upcoming Wraith Knight hero Jacob are all flawed protagonists with qualities that would make them villains in other series. However, at the end of the day, we're walking through their shoes and we understand where they're coming from. The world around them is also far more corrupt and entrenched in its troubles than anything they bring to it.
For me, I like to write about heroes who don't necessarily have the ability to slay the dragon and rescue the Princess. In Esoterrorism, the House is a ruthless and corrupt institution which is still (arguably) a necessary evil to protect society from the supernatural. In The Rules of Supervillainy, we have genuine superheroes but they seem to be overwhelmed by the endless numbers of bad guys who just keep popping up. In Wraith Knight, we have a world which is full of all the corrupt institutions of real-life Medieval history AND supernatural evils akin to orcs and Ringwraiths.
My heroes are never cowardly but they're sometimes self-serving and rarely have the answers to solving problems. They muddle their way through the complex social and moral ills of their setting as best they can. What they do which separates them from the rest of us is they meet it head on and that makes them heroes, whether they're bad or good.
Q] When you start out writing, do you have an overall plan for the book? How much of the plot do you plan out? Or to quote George R.R. Martin, “are you a Gardener or an Architect” when it comes to your writing?
CTP: It depends, really, on the work. I am definitely a fly-by-the-seat-of-my-pants author when I write Gary and that results in quite a few rewrites as I have to herd the cats my main characters turn out to be. Wraith Knight is a very structured sort of story and I know exactly where each little piece goes. Esoterrorism is more of a mixture of the two, conversations being freeform and the general story being carefully plotted out.
In general, I like to think that I am more of a Gamemaster (to reference Dungeons and Dragons). I create the set up for my characters and then I imagine how they would react to it. When you have characters that are really well-developed in your mind, I believe they tend to take the initiative with plotting and interaction.
Q] Please tell us about the books and authors who have captured your imagination and inspired you to become a wordsmith in your own right. Similarly, are there any current authors you would like to give a shout out to?
CTP: If I had to thank any particular author for setting me on my present path, it would definitely be Jim Butcher for the fact The Dresden Files were the first books which made me think, "I could do this." I just loved the blender of sticking together snark, a hodge-podge of mythology, 1st person narration, oddball characters, and humor with a very serious world. Esoterrorism also owes a bit to Charles Stross as he created a semi-serious take on spies with The Laundry Files which included more than a few "take that" shots at James Bond-style superspies. I wrote Esoterrorism as a counterpoint to TLF as a result, saying, essentially, "What's wrong with James Bond-style superspies?"
In terms of local influences, I would like to, again, give a shout-out to Tim Marquitz (Demon Squad, The Blood War Trilogy), Jim Bernheimer (Prime Suspects: A Clone Detective Mystery, Confessions of a D-List Supervillain), Rob J. Hayes (The Ties That Bind trilogy), Kenny Soward (GnomeSaga), and Seth Skorkowsky (Tales of the Black Raven, Valducan). These authors have not only been influences in me and good friends but I enjoy they’re work too.
Q] I believe you have a fantasy series coming out later this year or early next year as well. Can you talk to us about it and what will be your elevator pitch for it?
CTP: Wraith Knight follows Jacob Riverson, an epic hero of the past, who wakes up two-hundred-years later after his death and discovers he’s a Wraith Knight. A sort of legendary monster created by the King Below to be generals to his armies of monsters and created from the enslaved souls of heroes. The King Below is dead, albeit not exactly gone either, and his armies are scattered.
The heroes who defeated him have since used their defeat of the King Below to justify building an empire which is attempting to instill the values they hold into all of the formerly enslaved followers of the King Below as well as other “heathens.” Jacob gets roped into assisting a rebel against their reign, Regina Whitetremor, despite the fact it’s not exactly a straight contest between good and evil. It also may be a road to hell as the King Below’s ghost encourages him to take up the mantle of Dark Lord.
Maybe fantasy peoples need a Devil to blame everything on.
Q] Amidst all your writing, you also actively review books, movies and more on your blog page. How do you find the time to do all of it? Which recent reads have caught your eye that you would like to spotlight for our readers?
CTP: I find a lot of reviewers make the mistake of trying to take on too much at a time. It's understandable if your blog or review site is your life but if it's a hobby, it's important to pace yourself. One of the more interesting criticisms I received was someone mentioning I didn't do very many reviews of stuff I didn't like and that caused them to question my integrity. My response was, "Well, I tend to review stuff I like since I don't really want to waste my time writing about stuff I think stinks."
If I had to recommend some recent reads, aside from those authors I thanked above, then I could be here all day. I would, however, like to recommend Devan Sagliani and Shana Festa if you like horror and zombies. If you love dark fantasy, like I do, then check out Mark Lawrence and Scott Lynch. If you want a fun urban fantasy romp then I would be remiss if I didn’t suggest you check out Craig Schaefer. I won’t lie to you, I also go to Fantasy Book Critic to get a lot of reviews about stuff I want to check out too.
CTP: Read what you love, write what you love, and make no apologies.
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Black rag dolls meant to be abused are pulled from stores
NEWARK, N.J. (AP) — Black rag dolls that came with instructions to “find a wall” and slam the toy against it have been pulled from three stores after customers and a lawmaker said they were offensive.
The “Feel Better Doll” featured instructions to “whack” the doll “whenever things don’t go well and you want to hit the wall and yell.”
The president of One Dollar Zone said roughly 1,000 dolls were pulled this week from its store in Bayonne and two others also in New Jersey.
The dolls were made of black fabric with yarn hair of red, green, black and yellow in the style of dreadlocks, and featured large white eyes and a white smile.
State Assemblywoman Angela McKnight, a Democrat whose district includes Bayonne, called the dolls “offensive” and “inappropriate” after seeing a post on social media.
Bayonne Mayor Jimmy Davis said in a Facebook post that the dolls were “insensitive” and “can certainly be considered racist.”
One Dollar Zone President Ricky Shah apologized for the dolls’ appearance in the stores and said they were pulled Monday after someone posted images online. The Paterson-based company didn’t adequately check a large lot of items it had received before distributing them to stores, he said.
“This somehow slipped through the cracks,” he said.
The dolls were included in a shipment of about 35,000 pieces of closeout merchandise, Shah said, mostly with an “I Love NY” theme, including mugs and picture frames.
The supplier that shipped the order offered to credit One Dollar Zone for the cost of the dolls, Shah said.
The dolls’ manufacturer, the Harvey Hutter Co., couldn’t be reached at several phone numbers and email addresses at its location just north of New York City. Shah forwarded an email from supplier Global Souvenir Marketing stating that the company is no longer in business. Global Souvenir Marketing did not respond to an email seeking comment Friday.
One Dollar Zone operates more than two dozen stores in the northeastern U.S. from Massachusetts to Pennsylvania.
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На главную » Rolland A. Lynden » Of Breakable Things.
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A. Lynden Rolland
Of Breakable Things
For you who are breakable too.
The foolish trust their eyes,
Those left behind.
When the living, having died
Leave footprints
Only in the mind.
Abigail Frank, “The Manual of Sight”
When your hourglass trickles sand three times faster than a normal life, you don’t have time to dwell.
No matter how often Alex Ash reminded herself of this, she continued to dwell. A lot. Especially about death. Maybe that was why she took it so well.
She figured that she’d be able to hover over her casket listening to the harmony of sobs echoing off the walls of a church before she moved on to … well, wherever she was supposed to go. This, however, was certainly the last place Alex had expected to be once her life ended.
Familiarity saturated the cinderblock walls splashed with tones of citrus yellow and apple green. Invitingly squishy bean bag chairs sat like distorted gumdrops. Bookcases overflowed with picture books and preteen novels under motivational posters of stranded kittens and toothless children. Utterly confused, she spun in her plastic seat to face the front of the room. A shock of recognition struck her to find her third grade teacher sitting at the desk. The corners of Miss Petra’s soulful brown eyes turned down sadly, but she tried to smile.
Alex raised an eyebrow. “I guess this means you’re dead, too?”
Her smile became genuine. “That isn’t usually the reaction I get.”
“Should I start crying or something?”
“No, thank you. This is a nice change of pace.” She clasped her hands in a professional manner. “How do you feel?”
Alex leaned forward, and her once beautiful hair coiled in greasy clumps on the desk in front of her. She gripped two fistfuls of the faded pastel hospital gown that plagued her frail body. “Is there anything we can do about this ?”
Miss Petra looked amused. “You can take it off if you want, but I have nothing for you to replace it with.”
Pastel gown it was.
“Now that we’ve established you are not in shock, do you have any immediate questions?”
Alex shifted uncomfortably in the pint-sized chair. Despite the fact that the person whose tears mattered most to her was already rotting under the ground, she was still eager to witness one thing. “Will I be able to go to my funeral?”
“Would you mind telling me why you’d want to witness something so emotionally stressful?”
Actually, Alex did mind. Her reason was personal: she wanted to spy on her father. Would he show any hint of feeling or love, some indication that he missed her, that he blamed genetics and not Alex for killing her mother?
“It’s no matter. I think by the time of your funeral, you’ll be long gone from this place.”
Where would she be going? Alex felt tingles of anxiety beginning to seep through her, but then, they released into the air like puffs of smog against a clear blue sky, replaced by a blissful calm.
“What’s wrong?”
“I think my emotions are out of whack.”
Miss Petra’s eyes flickered to a door adjacent to the chalkboard, the one with an iridescent light trying to creep out from under. “What do you mean?”
“I just died. I don’t have a reason to feel so … ” Alex's tongue stuck to the roof of her mouth. “Happy .”
Alex had long forgotten how it felt to be so buoyant, to have a heart that pumped for something other than mere survival. Granted, she’d been waiting anxiously to die for some time, so in theory she should have been pleased. But one essential variable had not changed. The only thing—the only person—who had ever made her happy was not there.
“Death is not such a terrible thing,” Miss Petra murmured, sweeping her hair into a bun. Loose ends hung at her face. She hadn’t changed much since Alex had seen her last. She seemed shorter, probably because Alex was taller. But her effortless grace still had the ability to take Alex’s breath away. “You don’t seem too upset about being here.”
“Well, neither do you.”
“Sometimes joy and sorrow enter through the same door.”
“And that door just so happens to lead to my third grade classroom, huh?”
Miss Petra winked and pushed herself to a stand behind her desk.
“Why am I here?” Alex asked. No matter how much she’d enjoyed the third grade, no heaven should include a school classroom.
“You’re seeing something that is comforting and peaceful for you. Two people hardly ever see the same thing.” Miss Petra’s heels click-clacked as she crossed the room and rested her hand on a shelf clustered with models of Mt. Fuji. “But I can see why this room would be an exception. I suppose I can pat myself on the back for that one.”
Alex offered a tight-lipped grin and followed Miss Petra’s gaze to the twenty-six plump green caterpillars marching across the wall. Each one had the name of a student printed on its chubby green belly. Alex found her name and noticed that her caterpillar’s little red shoes seemed to be touching those of its neighbor. The caterpillar adjoined to hers had perfectly printed letters that spelled out CHASE.
Alex’s heart began to thud in her chest, fueling a body that no longer needed it. She stared at his name numbly, watching the letters bleed together until they meant nothing. Somehow she found her voice. “Is he here?”
Miss Petra didn’t answer.
Alex didn’t dare look at her while she forced herself to choke out the next question. “Or is Chase really gone?” The unexpected haze of comfort overcame her again. It smelled a bit like chocolate chip cookies, and although the scent was favorable, she swatted the air around her. “Why does that keep happening?” she grumbled.
“You would rather be miserable?”
If she didn’t have Chase, yes, she would rather be miserable. Not that she had ever had a choice in the matter. Joy would never accompany that sorrow. “Is he gone?” she repeated.
Miss Petra crossed her arms. “Let’s just leave it open-ended for now.”
Hope spread through Alex’s body like a sleeping limb awakening in a prickling of pins and needles. Painful but promising. She waited for this emotion to be swallowed up by the room, but strangely, it remained. Clearly, hope was allowed here.
“I am dead, right?”
“The idea of death is a state of mind. But then again, so is life. Most of what we are is mental.”
“You didn’t used to be so wishy-washy with your answers,” Alex remarked.
“This is a little more complicated than long division.”
So it seemed. “You said you thought I’d be gone from here soon.”
“Most people find death to be difficult. I don’t think you’re one of those people.”
“So why are you still here?”
Miss Petra’s eyes flickered again to the caterpillars. “We all find our purpose eventually. I made a choice, just like you will.”
“I’m not very good at making choices.”
“Of course not. Because others have always made them for you.”
“What’s left to choose if I’m dead?”
Miss Petra smoothed out her silky blouse. “Even in death we are still very much alive.”
The ambiguity of her answers was maddening.
“We have some things to discuss before you can leave. That’s why I’m here. So you can talk, laugh, cry, whatever you need to do to prepare yourself to make your decision.”
“I’m not going to cry.” Alex said.
The corner of Miss Petra’s bright red lips turned up in a smug smile. “Of course not. You were always so much stronger than you looked. ‘Tough as nails,’ your father once told me. When I learned you were coming, that was the second thing I bet on.”
Tough as nails. Yeah, Alex was sure her father would say something like that. She was a product of her environment. If Alex was a nail, her father was the iron that strengthened the steel. “What was the first thing you bet on?” Alex asked.
“That you would ask about Chase.” Miss Petra inched closer to Alex, her face twisted in awe. “I never saw two children, two people ,” she corrected herself, “who were so immersed in one another. Everything about you, your behavior, your feelings, your desires, they were all braided together.”
Alex stared at Miss Petra accusingly. “You didn’t think it was so wonderful back then.”
“I don’t think I ever truly understood your relationship.”
“Back then I didn’t think it was possible for an eight-year-old to have found the love of her life.”
Chase Lasalle was the youngest of four brothers. Even when they were in diapers, the Lasalle boys had been infamous in the town of Parrish. They looked like baby models with their innocently cherubic faces framed by halos of blonde hair. At a closer glance, their eyes gave them away, windows to their mischievous souls, though it was nearly impossible to witness any of the boys immobile long enough to notice. As preschoolers, they ruled the playground with a plastic fist. The power was in their effortless ability to turn life into a riveting game.
Their mother was friends with Alex’s mom long before the two shared a mat space at prenatal yoga. With three boys already, Danya Lasalle longed for a contrast from testosterone. Erin Ash just wished for health and happiness. Unfortunately, neither woman was granted her wish. Danya counted her blessings, nevertheless, when the doctors handed her another blue-blanketed bundle of joy, because she rested in a warm bed while Erin rested in a body bag. In a roundabout way, Danya got her wish, because Chase and Alex never left each other’s sight.
The Lasalle boys were less than thrilled when Alex tagged along during their adventurous excursions, especially since her fragile condition was often a buzzkill. But Chase was their weakness, and Alex was Chase’s weakness, so her presence was tolerated. Alex and Chase did everything together. At the circus, he’d pass her wads of cotton candy, waiting to take his share until she’d eaten hers. During baseball games, he punched his oversized mitt, hoping to catch a stray ball just for her. On trips to the beach, he held the bucket while Alex collected shells. Chase was her childhood, her partner in crime, and her saving grace.
“Chase saw this room too, didn’t he?”
“Why do you assume that?” Miss Petra asked. The window warped her reflection as raindrops collided with the glass, merging together into streams.
Chase’s presence was the lingering perfume of a candle long after burning out. “I can feel him. Like a ghost in the room.”
Miss Petra stiffened. “Yes, he was here. A long time. Longer than you will be, I think. He wasn’t as accepting of death. I think his choice was more difficult than yours will be.”
“Again, what’s left to choose? I thought after I died, my fate was kind of set in stone.”
“Freedom of choice doesn’t refute the idea of fate. Choices lead you to various paths, but some lives are intended to cross with others. It’s just in their design; some magnetically attract, and some also repel. So in that sense, there may be reasons why the universe pulls a person in a certain direction. But it’s impossible to control the decisions that a human makes.”
Alex only partially agreed. After all, no matter her choices, she would have ended up dead anyway. That was in her design. She’d been sick since day one. But not Chase. Not his family. They hadn’t been born with a death sentence like hers.
Miss Petra forced open one of the dingy windows, overwhelming Alex with deliciously fresh air. “How does a dead person still have a sense of smell?”
Miss Petra closed her eyes, breathing deeply. “Actually, your senses are much keener now.”
“That doesn’t seem logical.”
“Are your eyes still working?”
“Although your eyes were part of your former body, which is ninety percent gone, your brain did most of the work to allow you to see, and your brain is still very much intact, working much harder, actually. Physical death is an awakening for your mind.”
This seemed rather oxymoronic to Alex. “How is that possible?”
Miss Petra held up three fingers. “In the physical life, you have to exercise mind, body, and spirit. In cognitive life, commonly known as the afterlife”—she took a finger away—“it’s just mind and spirit. Basically, the body is no longer inhibiting the other two.”
Alex was pleased to be getting some sort of explanation, even if it wasn’t completely clear. Confusing answers were better than no answers at all.
Miss Petra wrote the word SOUL on the blackboard in a large bubble. She then drew two lines, attaching two smaller bubbles, labeled MIND and BODY. It was like a pre-write for an English essay.
“All barriers break down once your fragile body is out of the picture. And the other two aspects, the ones that essentially make you who you are, are more vulnerable without the armor of the body.” Miss Petra lifted the chalk and wrote PHYSICAL next to BODY. “This world is over for you.”
“I think we’ve established that.”
She glanced over her shoulder with an expression of reprimand before writing MENTAL next to MIND. “In a nutshell, this is your afterlife. But the mind is a living thing, and it can’t live forever.”
“Some just get old. Some aren’t stimulated enough. Some are beaten down.”
The idea of beating down a mind seemed silly. Alex pictured a geeky school competition with two debate teams of nerdy opponents in horrendous blue blazers, thick-rimmed glasses, and bad acne. “So you’re saying I’m not dead?”
“It’s all in how you choose to look at it. Your body is dead, but that doesn’t mean you don’t have options. Socrates said that death may be the greatest of all human blessings. Maybe he knew even more than we thought.”
“A blessing?”
The creases in Miss Petra’s youthful forehead deepened. “You don’t agree?”
Alex crossed her arms. Of course not. Death had been knocking on her decrepit door since the moment she was born, and then it arrived early to toy with her, to steal the only people who mattered to her. It wasn’t a blessing. It was cruel. “Why would I?”
“Considering your history … ”
“You know to what I’m referring.” Miss Petra placed the chalk in a mug and began to straighten the objects on her desk. “Did you not consider taking your own life?”
Alex hadn’t realized her teacher would be privy to that information. Her arms were still crisscrossed protectively over her chest, but she peeked down nonetheless to be sure the scars were not exposed. “Something else happens to suicides. I’d have no chance of seeing Chase again.”
“Oh?” Miss Petra’s dark eyes grew wide. “And why would you think that?”
“Liv Frank told me.”
Miss Petra turned to the caterpillars. The capital letters spelling out Olivia’s name were slightly distorted. Kind of like Liv herself. “How would she know that?”
“Beats me. That’s just Liv.”
“And why would you take her of all people seriously?”
“If a Frank gives you advice, you listen,” Alex said.
For generations, the Franks had held the honor of being the strangest family in Parrish. Olivia Frank did not deviate from her ancestry. Like her relatives, she frequently spoke to herself in public, doubled over in laugher in a silent room, burst into tears for no reason, and saw no fault in any of it. But Alex liked her. She understood what it was like to be different.
“Remember the time she told us to bring umbrellas to class?” It was an incident difficult to forget. On the morning after Liv’s warning, a pipe burst in the ceiling, drenching anyone who had not believed her.
Miss Petra pointed to the chair that had once belonged to Liv. “In the midst of the chaos, she popped open her umbrella and grinned at me.”
“Liv knows things. So when she told me suicide would ruin everything, I listened, even though I didn’t agree.”
“Didn’t agree with what?”
“With her argument. She said I was lucky.” Alex exhaled loudly through her lips.
“She had a point.”
Alex shook her head. “I lived in a house with a man who never spoke to me. I used to think that one day it would change.” She’d thought perhaps the hatred would subside, but instead it resiliently clung to the stale reek of his whiskey-soaked existence. It grew each time he noticed her and glared at her, and it gathered in corners of the house like dust until it became visible, tangible, and sickening. “One time I knocked over a glass vase trying to make my own breakfast. I was maybe six or seven. He came into the kitchen, noticed me on a chair surrounded by a sea of glass, and just turned around and walked away. Oh, he threw the broom at me, though.”
“I’m sure Liv was referring to a luckier aspect of your life.”
Chase? If luck was so manipulative, she didn’t want it. Luck had allowed her to dance in circles around Chase for sixteen years, ignoring the feelings that clouded their air like pollen in the spring. Luck would not have allowed Chase to leave the traces of his feelings behind him after death in the form of tiny white papers. Luck would not create more pieces for Alex to pick up.
If she had been truly lucky, Alex never would have found the confessions strewn across her bedroom like confetti. In the eye of the snowstorm of paper, there was an open note that read:
A long time ago you told me that you would never make plans for your life because it would be like breaking promises to yourself. So I’ll make them for you. We’ll do everything in the world together. And you know I never break a promise.
P.S. We need to talk about what happened the other night.
What was all this? Alex had lowered her body to the floor, surrounded by what she momentarily presumed to be a sick joke. Maybe the notes were left by one of Chase’s brothers. Probably Jonas. He was mean enough to do it.
But on an old concert ticket, she recognized Chase’s handwriting:
This ticket seemed symbolic since this concert was entitled “Love and Memories.” My favorite part of the concert was definitely watching you push your way to the front of the stage only to be escorted back to our dinky lawn seats by security. The disappointment on your face was adorably cute. I promise in the future, I’ll get you backstage somehow.
She found the next note attached to a photograph taken when she and Chase were six, grinning so widely their eyes were mere slits while they sat on a porch of a Cracker Barrel:
Ah, the Lasalle family vacations. I remember rocking in those chairs with you and the only thought going through my head was, “I hope the tooth fairy can find me in Virginia.” So simple. So happy.
I promise in the future, we will grow old enough that sitting in rocking chairs is actually cool. You can trip me with your walking stick and I’ll hide your dentures. We’ll laugh for another seventy years together.
Attached to a baseball memento:
The Baseball Hall of Fame. We were nine. It was the last place you wanted to be, but you sucked it up and smiled all day. I was so proud of you until I found out that my mother bribed you with a trip to New York to visit the American Girl store if you behaved during the trip. You’re such a brat. You may not want to visit American Girl anymore, but you never did get your trip to NYC. I promise I’ll take you there and we’ll go ice skating, and see the huge Christmas tree from Home Alone 2, and stay at the Plaza Hotel, “New York’s most exciting hotel experience.”
And a driver’s ed brochure:
Remember when I tried to teach you how to drive a stick shift in the parking lot of the Parrish Park Shopping Center? You stalled out, grinded gears, gave me whiplash, and made me laugh harder than I ever thought possible. And then the cops found us and took us home because we were only twelve. You still cannot drive stick to save your life. I promise you I will help you to perfect those skills.
Attached to a figurine of Cinderella’s castle:
My favorite moment in Florida was probably when you jumped into my lap during the Jaws ride at Universal Studios … or seeing Jonas throw up after riding the Teacups. It’s a tie. You said that one day you’d live in Cinderella’s castle. I told you that I would buy it for you. Somehow I promise to find a way.
The notes went on and on. So many promises attached to so many memories. They were dreams she’d never dared to imagine for herself because she wouldn’t live long enough for them to come true. Her body was too frail. But Chase was always true to his word, so when he said something, she believed it. She even believed the note that said he loved her.
That was luck? Hardly.
Because reading and believing Chase’s promises, the highest point in her pitiful life, was immediately followed by the lowest. Because she was wiping tears of happiness from her face at the same moment the Lasalle family van was smashed into a highway barrier by a Mack truck.
There were many adjectives people used to describe Alex Ash’s life. Lucky was never one of them.
Alex gestured to the word under which Miss Petra had drawn several emphatic lines. MIND. “If the life I have left is mental, what happens if my mind isn’t all there?” She searched for the right words. She’d spent the last year of her pathetic life in a drug-induced haze. “My mind is more than a little bit cracked.”
Miss Petra wiped the chalk from her hands. “Well, my dear, that’s kind of the purpose of our meeting here. You can leave it all behind you, you know.”
“Leave what?”
“Everything. Including the things that made your mind so fragile. Your mind can’t be damaged if it doesn’t exist, and thus you can’t feel pain.”
Alex mulled over the idea. No more sadness. No more regret. The offer was certainly tempting. She studied the door at the front of the room. It practically bulged from the force of the light behind it. Was it that easy?
“On the flip side,” Miss Petra added, “to be rid of pain is to be rid of its source as well.”
The source?
“What made you feel that life was no longer worth living?”
Alex suddenly understood. Her losses hovered around her, expanding into the air like smoke rings. “I wouldn’t remember any of it?”
“You can’t have a memory without a mind.”
“None of my life? Nothing about him .”
Another head shake.
“No,” Alex replied softly, “I would rather live without Chase than lose what I remember of him.”
“You’re sure?”
“You know, most people would consider you to be rather lucky to have something to make this decision so easy. You need to look deeper than the surface. You might not have been able to keep your body forever, or to keep Chase, but the things that exist forever are never in tangible form.”
Miss Petra walked swiftly to the back of the room and stood next to a door with an EXIT sign above it, a door Alex hadn’t noticed until now. There was no bright light behind this one. “Let me be clear. If what you said is true, then you are making the choice to keep living as who you are. You aren’t ready to give up your memories or, ultimately, the life you had. Therefore, you live as Alex Ash, with whatever life you have left in your mind.”
“That’s the choice? That’s it?”
“Yes. To remain here or not. And please be advised that the easy way out is literally right in front of you.”
Miss Petra pointed to the door at the front of the classroom. Trying to tempt Alex, the air from underneath the door rose like the scent of sweet sugar, calling her home.
“You and I both know how ugly the world can be. I’m sure you can imagine the possibilities when boundaries are broken. But you’ve never been one to take the easy road, have you?”
Alex rubbed her forehead, glancing at the door ahead through her fingers. The light behind it brightened. “Where does the shiny one lead? If I’m not really me anymore, who do I become there?”
“I wouldn’t know. I’ve never been through that door, but comfort hums through the cracks, so there’s no doubt in my mind what lies behind it is much easier than the alternative.”
Door number one was a mystery. Alex hated surprises. She twisted in her seat and looked again at the door in the back. “But what about that one? Can you tell me what I’ll become if I make that choice?”
The difficult one.
“Since the mind you had in the previous life still exists in the form of energy, the essence, or the spirit, of your former body is still intact.”
Alex leaned toward her teacher. Hope fluttered inside of her. “Ghosts ?”
Miss Petra face contorted into disappointment. “Society has made that word so belittling.”
“But that’s what you meant? That’s what I’d become?”
“I realize it’s rather hard to conceive of the possibility.”
“Miss Petra, do you remember where I grew up?”
Like in most old towns, ghost stories in Parrish were a dime a dozen. Alex had had her fair share of paranormal experiences, so the possibility of ghosts was never something she questioned. Chase had been here in this room, too. Why would he have been here if he had not been asked to make this same decision? If any two paths were meant to collide, it would certainly be theirs. Alex’s heart continued to pump happiness through her useless veins in beautiful iambic beats, ba-bum, ba-bum, ba-bum. He’s here, he’s here, he’s here.
“The ones who find themselves here have the strongest of spirits.”
Alex’s hands trembled, so she clasped them in her lap to hide it. Wrists down, of course. “How is one soul stronger than another?”
“Sometimes nature. Design. Heredity.”
Alex’s mind was clicking away a mile a minute. “And Chase? What did he choose?”
“I think you already know the answer.”
Alex took another good look at the door in the back, the one with darkness on the other side. Could death, which had toyed with Alex all her life, become her beginning again? Was Chase out there now, waiting? The thought of it made her spin around and turn her back on the light.
Miss Petra moved to the bookcase against the back wall and lifted a gray blazer draped over a stack of books. She slid into the jacket one arm at a time. “Sometimes you have to turn around to move forward.”
Something tugged at Alex, urging her from the chair. Desire? Optimism? “You aren’t exactly trying to convince me to stay.”
“Do you want me to?”
Instead of replying, Alex took a deep breath, stood up, and walked determinedly to the back of the room.
“Go ahead and open it,” Miss Petra instructed.
“You aren’t coming?”
She shook her head, gesturing to both doors. “I’m neither here nor there.”
Miss Petra smiled slightly. “You don’t think these are the only two possibilities, do you?”
That’s exactly what Alex had thought, but she didn’t want to confuse herself any more, so she took one last look at her teacher and pushed open the door.
At first she couldn’t see or hear anything. And then it was like shaking water from her ears. She could hear the voice clearer than anything in her entire life.
She heard a loud gasp and a boy’s voice say, “My God, you look just like her.”
Alex never met her mother, never heard her voice. But she could probably pick it out of a lineup. There were many times as a child when she’d woken in the night to the soft whispers of a lullaby. Her mother had had the voice of an angel.
Parrish was a small town, and everyone knew Erin Ash. They knew about her unfortunate condition, the one she’d regrettably passed on to her daughter. Old ladies would cluck their tongues like they might scold a misbehaving child when Erin walked by with her swollen belly.
People always said Alex looked just like her mother. Some people even stopped on the street to gawk at her, no doubt wondering if they could add another ghost story to those that gave Parrish its fame.
You look just like her , the boy had said.
“You know my mom?” Alex hadn’t even considered that her mother might be here. She had only thought of Chase.
The boy’s voice was low. “She isn’t here. Not anymore.”
Alex blinked her eyes several times until her vision cleared. She stood face to face with a child, a boy whose smile faltered.
“Sometimes we don’t last very long,” the boy replied, taking a step forward. “Come on out.”
Alex’s shoulders slumped. Once again she was too late to know her mother. She abandoned the cover of the doorway, and was surprised when her foot touched the ground. She had shoes. And real clothes. She ran her manicured nails through the waves of her honey-colored hair. “How did that happen?” she asked, hugging herself. “Not that I’m complaining.”
“Dead or alive, we all create a small version of our own reality in our minds. Here you can just project it more effectively. I take it you recognize your clothes.”
Of course she recognized her favorite jeans, her favorite shirt, and even the bracelet she’d worn every day since Chase had given it to her.
“How did you know my mom?”
“She was my friend.”
Alex ignored the pang of jealousy. “What happened to her?”
The boy tilted his head up at the sky and blinked through the raindrops. “Let’s save that for another time. Please. We have to get going now.”
She held her palms upward. The rain sent tiny electric pings through her skin, but didn’t leave it moist. She rubbed her fingers together. “Why can’t I feel the rain?”
He grinned. “You’re thinking of how the rain felt before.”
“You’ll get used to it. Your senses are just different now, that’s all.”
He jabbed his thumb in the direction of a path and began to walk. She stole a look back at the doorway, surprised to find a moss-covered bunker with only darkness behind its open door. Miss Petra was gone, and the safety and familiarity of her classroom had vanished with her. Maybe Alex shouldn’t have been in such a hurry to leave. She had no choice now but to follow the boy.
Despite the overcast sky, their glittery green surroundings sparkled as though the trees were comprised of emeralds. Everything around her was adorned in shades of color so much more brilliant than she’d ever seen before.
“Beautiful, isn’t it?” the boy called over his shoulder.
“Yes,” Alex said, watching the rain around her jumping like colorful flashes of heaven. “Where are we?”
He chuckled. “California.”
“No, I’m serious. It’s the same old Earth. You can just see it better now.”
Crayola would have a field day with this place. The colors embellished everything, even the dreary canopy of clouds twinkling like a gray diamond. “It doesn’t seem fair that everyone can’t see this way.”
“Hmm. You wouldn’t appreciate it so much if your eyes had always been so open. Sometimes things only become clear when they don’t exist anymore.”
Alex listened to the trees whispering a song that sounded like her name. The trunks were so large it was like weaving through the legs of giants. Branches of the smaller, twig-like trees curled their fingertips in hello.
“They like you. I can tell.”
Alex caught up and fell into step next to her tiny companion, who carried an aura of comfort. She stole glances at him while they sloshed through the kaleidoscope of colors. His baby-fine hair fell over his chocolate-brown eyes and pale skin.
“Who are you?” she finally asked.
He kicked his feet up slightly while treading down the muddy pathway shining radiantly like a river of dark gold. “My name is Ellington Reynes.”
An inappropriate name. It was much too grown up for a boy who was doomed to look like a cub scout for the rest of his life.
“I’m the one who saw your arrival,” he informed her proudly.
“Saw it?”
“In my head. I’ve been seeing arrivals now for decades.”
Alex took in his babyish features. “How old are you?”
“Don’t be fooled by the bowl cut. I’m much older than you.”
“How old were you when you died?”
“Twelve.”
“You don’t even look ten.”
“I was short for my age.” he said, leading her to the bank of a torrential river.
Alex skidded to a halt. “Is there a bridge?”
Ellington stepped right onto the rolling tide and swung his arms playfully as he strode across. “We are the bridge!” The water acted as a crooked treadmill, carrying him downstream, but he remained unfazed and leaped casually onto the opposite bank.
“Your turn,” he called, spinning back around to face Alex.
She froze at the water’s edge. She couldn’t do this.
“Are you just going to stand there?” Laughter rose from the splashing current, and Ellington lifted his finger to his lips to hush it. “Go on,” he urged her, crouching down to watch with the expression of a father seeing his child taking a first step.
Alex bent to touch the water. Her outstretched fingers shook, making contact with the gelatinous surface. The shock of electricity from the river stung much more than the rain, and buzzed like a headache. She straightened up and stepped gingerly onto the water. Her body jerked to the left. She flailed her arms to steady herself, shuffling the rest of the way without lifting her feet.
“You made that look way too easy,” she said, tumbling to Ellington’s side.
“I’ve had more practice.”
Alex watched the water lapping and splashing the shore. “Could I still go in the water?”
She pressed her fingers against the surface, which yielded somewhat but did not allow her to breach it. She raised her palms. Now what?
“Think a little harder about breaking the plane,” Ellington offered. “You need to use your mind. You’re weightless now, so you are going to have to use a little willpower.”
Alex nudged the water, but it was like pushing on putty.
She concentrated harder. Finally her hand shot through the static goo, which felt like a breeze. She raked her fingers through the wonderfully unsettling energy. “Wow,” she breathed.
Ellington crouched down. “You’ll like it here.” He patted the water like a pet. “If you don’t mind me asking, what makes someone like you choose this alternative?”
“Someone like me?”
“Well, you weren’t exactly in love with life.”
Chase , Alex thought to herself. Even now, without knowing where Chase was or how long it would be before she saw him again, merely the idea of knowing it would happen was enough. If he existed in his world, they’d find each other.
Ellington pushed himself to a stand. “Besides the obvious reason.”
“When I saw you arrive, I saw a few other things, too. It’s just something I’ve always been able to do. It’s kind of like watching a trailer for a movie. As the images appear, I get little bits and pieces of the person arriving, and then I wait for them.”
“Do they always show up?”
“What did you see about me?”
“Chase.” He sighed. “All I saw was Chase.”
As a child, Chase couldn’t fathom the idea that his best friend was sick. Alex had too much energy. When he stood next to her, he could feel it like the static electricity he learned about in science class. So then how could she somehow have less life than he did?
He knew it was called Ehlers-Danlos syndrome, and he’d heard Alex’s doctor say things like type four and vascular and dangerous . He knew Alex’s mother had been sick with it, too. And her mother was dead.
“They don’t look any different to me,” Chase whispered to his mother. That morning they had driven into the city so Alex could attend some sort of meeting. There was a huge banner outside the Baltimore Convention Center that read Learning Conference: Living with EDS . Jonas had snorted and told Alex she was going to a freak show. Chase had punched him in the belly, and to his shock and amazement, his mother turned her head and didn’t scold him. And now, sitting outside the convention center, the people walking inside didn’t look strange at all.
“There are different kinds of EDS,” Danya explained to him, ruffling his hair. “Some are worse than others.”
“Worse than Alex’s?”
Danya shifted on the bench. “No. Alex has the worst kind.”
“She doesn’t look sick.”
“That’s because most of it is inside her body.” She pointed to his arm. “You have tissues in there. Don’t scrunch your face like that! They aren’t the same kind that you blow your nose with. Your tissues hold your body together. Alex’s tissues don’t work quite as well as yours.”
No kidding. One time he’d pulled on her arm to get her attention and her shoulder fell out of its socket. He’d cried the entire way to the hospital because he’d hurt her.
“In our tissues, we have something called collagen. And if collagen is like the glue of body, the normal person has liquid cement while Alex has cheap Elmer’s glue.”
“Is that why Jonas says that Alex was assembled at Kmart?”
His mother rolled her eyes. “Probably, but Jonas really shouldn’t say that. I’ll speak to him.”
Chase fiddled with the Velcro on the pocket of his shorts. “I still don’t get it.”
“Why is it such a big a deal?”
“Tissues support your skin, which is why Alex bruises easily. And they hold your bones together, which is why hers are more likely to break.”
“But broken bones don’t kill you,” he argued. “Why did her mom die?”
His mother’s face crumbled, and he felt that pang in his chest that told him he’d said something wrong. “I’m sorry.”
“No, don’t be sorry. I just miss her.” Between her han
ds, she rolled a pamphlet she’d picked up that morning at the convention. “Tissues also support your organs. Like your heart. That’s an organ. The things inside you that keep you alive, and if they aren’t supported properly, you could bleed inside your body. That’s what happened to Alex’s mommy when Alex was born. They couldn’t stop the bleeding.”
“Is that why her dad hates her?”
“He doesn’t hate her.”
Chase looked at his mom doubtfully, but quickly shifted his attention to several people exiting the convention center. His heart fluttered in hope, but his friend wasn’t among them. He couldn’t believe his mother had made him stay out here instead of letting him go in with Alex. This was all Miss Petra’s fault. Their teacher was the one to suggest that Alex’s friendship with the Lasalles might be detrimental to her health. She was always trying to put them in separate groups during class or encouraging Alex to hang out with the other girls during recess. Thankfully, Alex ignored the suggestions. But within the past few months, Alex had broken three different bones during their adventures with his brothers. So her dumb doctor recommended she meet other kids who were “limited” too.
A selfish part of Chase wanted Alex to come screaming out of that door. Usually they joked about her illness. They would look at the bruises on her arms and laugh about what they saw … like lying in the grass and finding images in the clouds, only these clouds were stormy. She was going to be sick no matter what, so what good would it do to sit around and talk about it? Alex didn’t like to think she was different, so he was sure she wouldn’t enjoy this experience. Or at least that’s what he hoped. After all, he needed her as much as she needed him.
She just never understood that.
“It wasn’t so bad,” Alex told him later that day. The convention had dampened their spirits, and they sat dejectedly on a log by the beach. “They had doughnuts. That was cool.”
Chase picked up a stick and pressed it into the sand. He drew a weaving line from his feet to hers and then traced an identical one beside it, tying them together.
“It was kind of depressing, though,” she added. “Sitting around and talking about death isn’t exactly my idea of a good time.”
Was it bad that he was relieved to hear that?
“It just sucks to know I’m not normal and it will only get worse.”
“Who said you weren’t normal?”
Alex laughed. “Wasn’t that the whole point of going today?”
He threw the stick across the beach. “Those people are stupid, Alex, and so is your doctor. You are normal.”
Alex bent her hand backwards so that her finger practically tickled her forearm. “That’s normal?”
“Lots of people are double-jointed.”
“I can’t do half the things other kids can do.”
“I can’t participate in gym.”
“And most of the other girls wish they could sit out, too.”
She pointed out her collection of bruises. “I can’t wakeboard with you guys. I have to sit in the boat like a baby. I can’t ski. I can’t even go sledding.”
To top off her argument, Alex pulled at the collar of her shirt, revealing the maze of veins branching across her chest like blue coral. Evidence of her vulnerability.
Chase shrugged. “It just looks like a really cool tattoo,” he said, and when Alex’s face broke into a huge smile, he felt light enough to fly.
“I never thought about it like that!” She glanced down into her shirt. “You’re right!”
Apparently, fate overheard their foolish conversation, because that night Alex broke her ankle simply rolling over in bed.
Chase presented her with a teddy bear in the ER, patted her back and said, “Who wants to be normal, anyway?”
Alex stared at Ellington while they walked, but he didn’t seem to mind. “Do you see much about the lives of the people you meet?”
“Not a whole lot. Just fragments of the important parts.”
The wind picked up, dancing through the gargantuan trees. Their voices reminded her of the woods at home. They had stories to tell.
“So, there are ghosts all over the world?”
Ellington nodded. “Some more civilized than others.”
Alex watched her feet trudging through the muddy path, but she noticed only one set of footprints trailed behind them. Those belonged to Ellington. “How did I end up back there? And how did you know where I would be?”
“Because everyone I see shows up there.”
Every answer fed her curiosity. “Can I keep asking questions?”
“Please. That’s why I’m here.”
“Why don’t I have any footprints?”
“Because you aren’t thinking about making them. You’ve chosen to be in a mental world, but you really don’t know what that means yet. You will, though.”
“Why do you think people choose to be like this?”
Ellington cocked his head. “I suppose some people have trouble letting go of who they are, or who they were . Some, I think, are merely curious about omnipresence, knowing what people are doing without their awareness. Most don’t realize how much they hate it until they taste it. Others do it for the clout.”
Alex dodged a bird flying by. It flashed with light like a crystal in the sun. “Clout?”
“Power. You’d be surprised what your mind is capable of.”
“I don’t get it. What does a spirit do ? Hover around and watch people?”
“Maybe once upon a time that’s how it was, but now there’s much more to it,” he explained. “You’ll learn more about this soon, but a while back spirits became a problem.”
“Exactly what you said. All they did was hover, observe. Mischief is the product of an idle mind. A life without walls opens a Pandora’s box of new temptations. Just because a soul is spirited enough to come here doesn’t mean it is good . Therefore, a solution was created. Much like in the physical world, once our numbers grew, someone had to step up and take control. The result is about fifty feet ahead of us.”
They reached a fortress of black, leafless trees with branches intertwined from the ground up. Nature had weaved the bark so intricately that Alex doubted she could find a hole large enough to fit an arm through. The branches continuously twisted into a word she’d never heard before. “Eidolon.” The term tasted magical, and she licked her lips to savor it.
“Eidolon,” Ellington echoed with a content sigh.
More colossal redwoods waited through the gate. There were no buildings, no signs. There was no one there to greet them. She reached out her hands, but could only grasp the “bars” like any normal person.
“How do we get through?”
You’re here?
Alex gasped. The melody of Chase’s voice soared through her mind like a tranquilizer, engulfing her with a happiness she’d long forgotten. Distracted, Alex failed to notice Ellington reaching for her hand. The electric pressure of his grasp startled her, but the prickles of electricity preceded something much worse. Stepping through the branches was like passing through a cookie cutter of needles. Alex attempted to pull away from the pain embedded in the bark, but Ellington wouldn’t allow it. A scream exploded silently within her, deepening with the pressure of the punctures. With a lurch, she reached the other side. The torment left no traces but white sparks of shock erupting from all around her.
“Allow the discomfort to remind you that you exist. It’s alarming, I know, but I promise you’ll get used to it,” Ellington assured her. He brushed his hair from his forehead. “I hate to rush you, because I know how distressing the experience is for the first time, but unfortunately, we need to hurry.”
She felt vulnerable and frightened, but the echo of Chase’s voice motivated her. Stiffly, she followed Ellington, each step easier than the last. They ascended a hill and reached a wall composed of mossy stones with palettes of tired blue and smoky gray. A small archway stood crookedly off center, etched with the words Ab Vitam .
For Life , Alex translated in her head. The Latin had been inscribed on her great uncle’s tombstone. He died during World War II, and she had often passed his tombstone when she visited her mother’s grave. Alex had thought during those visits how ironic it was to carve those two words on a stone that marks the existence of death.
As they stepped through the archway, Alex noticed that they were venturing through a series of walls, each one tilting at a different angle. She shuffled through one disorienting arc after another, feeling like the rotating hand of a clock.
Darkness shrouded the sky when they finally reached a courtyard framed by two black L-shaped buildings. They towered in size, and thus Alex realized the purpose of the mammoth trees. Crossbreeds between skyscrapers and medieval churches, the epic structures stood blatantly out of place in the middle of the forest. Crookedly placed gothic stones comprised the misshapen framework, each block cracked into a unique form. It was imperfection at its best.
“This is it?” Alex whispered.
Ellington’s shoulders relaxed. “It’s a small part of Eidolon, but it’s a good place to start.”
A rippling of fog lapped at her ankles like an airborne stream. Outlining the rickety, stone pathways through the courtyard, hazy streetlights stood at attention allowing ivy to coil around their bases. This is exactly what she’d expected a ghost town to look like. The scene was daunting and exquisite in a fabulously eerie kind of way.
One was thing missing. “Where are all the people?”
“I’m not sure of the time,” Ellington said. “But I assume the sessions are still in progress.”
“Sessions?”
“Like workshops. There’s so much you don’t know about this afterworld.”
“You make it sound like school ,” she said with a grimace.
“The actual city is farther that way.” Ellington pointed through a gap between the two buildings. “But where we stand now is Eidolon’s Brigitta Square, a campus where the newly buried must stay.”
“A few years.”
“And I have to take sessions here? Or workshops, whatever they’re called.”
“I think you’ll appreciate all there is to learn.”
“Learn about what?”
“Being a spirit.”
Alex looked down at herself. “But I already am a spirit.”
“Were you not a person when you were born? And yet you still had a lot to learn, right?”
Alex had no counterargument, so she merely crossed her arms.
Ellington smirked. “Remember when you asked how I was able to cross the river so gracefully? It wasn’t because I’ve crossed it so many times before, although I’m sure that helps. It’s because I was able to calculate how quickly I needed to walk based on the speed of the moving water.”
She recalled that he hadn’t even hesitated at the riverbank. “How did you do that?”
“My mind. You can do it too. You just don’t know how yet.”
“I hate math.”
“You won’t hate it when you realize how good you are at it. You need to learn to use the new capacity of your intellect. Why do you think a learning center was built inside the city? And besides, you can’t just be thrown into a world without knowing the rules.”
Spirits had rules?
“People have difficulty dealing with the concept of death. The learning, the people, the campus—they help the newly dead to cope.”
“And I would live here?”
He stretched his hand towards a door that stood poised in its elegance with Brigitta carved above the frame. “Right there, but we’re waiting on someone.”
Alex felt a pounding in her chest. Her mind hadn’t forgotten what anticipation felt like.
“I have no idea what’s keeping her. She’s usually very punctual.”
Alex’s heart sank. Her . Not Chase.
Ellington stood tapping his foot, checking the sky, and fidgeting with a button on the cuff of his shirt.
“I wish I knew what time it was.”
She reached out for his wrist. “Why don’t you just use that watch?”
His mouth popped open in surprise. “I hadn’t even realized I had one.” He rubbed his head. “It still gets me sometimes.”
“What does?”
“You’ll find out soon enough. And, oh, it’s later than I thought. It’s going to be very crowded here soon.” He lifted a hand and began to nibble on his nails. “Stay here. I’m going to see if I can find her.”
“Can’t I go with you?”
“You won’t be able to get in.”
Alex inspected the door for a lock but realized it didn’t even have a knob. “But you can?”
“I used to live here. A long time ago.” Ellington approached the monstrosity of a door, and it swung open with a groan of welcome. “I’ll be right back. It will only take me a minute.” The door slammed immediately behind him, reinforcing the idea that Alex was uninvited.
Before a minute passed, Alex heard the creaking of another door, and a boy emerged from the fog. He darted through the archway connecting the two buildings and disappeared without noticing her. The way her anxiety began to rise, Alex could have been standing in a room at the bottom of the ocean and hearing the first drip of water seeping through the cracks.
The door opened again. Drip. And again. Drip, drip. It leaked out spirit after spirit. They were very diversely dressed, to say the least. Their attire ranged from sundresses to prom dresses, rainy day sweats to runway chic. No one else seemed to think this was strange. Despite their differences, they swam together, immersed in the same air of excitement, like it was the last day before a holiday.
Some of them noticed Alex and began giggling or elbowing one another. How ironic, Alex thought, that a girl in a bathrobe was eying her like she was the oddball. And then came the flood.
The doors of the building burst open, releasing dozens of spirits who spilled out into the square. Alex had to move with the tide to avoid being trampled. As she treaded among the crowd, she couldn’t be sure if they were staring because of her frail appearance—her size had always generated attention—or because in a small setting like this one, a new face stood out.
The attention only increased when Alex broke away from the current to stand alone in the corner of the square. The whispers and the pointing didn’t bother her, but the paranoia did. Kids stood on tiptoe, scanning the perimeter, and some covered their heads with their books. Alex tried to ignore them and keep her focus, searching for Chase. Hoping.
She probably wouldn’t have seen it coming if not for the eruption of screams. A dark shadow inched across the crowd. Above it, a stone boulder of a bench arched to the peak of its height and surrendered to gravity.
Ellington had not been lying about the new extent of her mind. Now that she thought about it, she could see the trajectory of the object, as though someone had used a marker to trace it in the air. The bench was set to land on the crown of her head. In that split second, she could even visualize exactly where the pieces would land once the bench was demolished.
Instinctively she thought to run, a logical reaction, but before she could move, an unexplainable energy tugged at her brain. She cried out as her head filled with pressure like a screeching teapot. She feared her skull might burst, and prayed for the pain to release her. It aptly obeyed, shooting from her, detonating like a bomb, forcing her to her knees. The granite bench halted above her, colliding with an invisible barrier. It fell to the ground and landed with five simultaneous claps of thunder.
Alex remained on her knees, head in her hands, arms shaking like she had just bench-pressed three hundred pounds, and all the weight had landed on her throbbing head. The whispers commenced, but in shock now instead of curiosity. Everyone turned to gawk at her.
As the dust cleared, there was a figure walking towards her, his shoulders thrown back in a familiar stance of confidence. A moment later, his arms were around her. But something didn’t feel right. His grip was too tight, and his build was too bulky. Alex realized then that it was Jonas Lasalle, and not his brother, who was burying his face in her hair.
Jonas Lasalle had never been speechless in his life. He was actually quite proud of his big mouth. But when he saw Alex, it took him a few moments to find his voice. He had known she would join them eventually; the girl had been a walking corpse since birth, but it still didn’t prepare him. There she was. Alive. Prettier than ever. Alone. Without Chase around to distract her, to hover over her like a canopy, hell-bent on preventing her from having any fun in life.
Who the hell had thrown that bench? Usually when new kids arrived someone would throw a rock or a book at them. It was a barbaric form of initiation, but it was also hilarious. Most boys ran away while the girls screamed like their lives were ending all over again. But not Alex.
He smirked, listening to the kids around him.
“Who did that?”
“How did it explode?”
“Forget that, who threw it?”
“How did she do that?”
He strutted forward, blinded by the dust that stubbornly hung in the air alongside his anticipation. When she saw him, her face twisted into such an expression of joy that Jonas supposed Chase had appeared right behind him. But that was impossible. Chase was gone. For the time being, at least.
He forgot himself and wrapped his arms around her. Her shock was tangible. He could feel it emanate from her. The fact that he was hugging her was certainly uncharacteristic. Of all the Lasalles, Jonas knew he was considered to be the least likeable, especially in Alex’s eyes. As a child he had ridiculed her. He’d kicked her shins, pulled her hair, hid her belongings, and once even locked her in an old trunk. Now he was hugging her. This PDA went against the image he’d tried so hard to maintain his whole life. He was a desperado of a boy who was acting like he needed a place to rest his reckless head, and he knew it.
He hated to admit it, but he could get used to it.
Alex’s arms hung stiff at her sides until Jonas finally let go.
“You look like you’ve seen a ghost.”
Bad joke , he thought to himself, cursing loudly in his head. None of this was funny. But Alex’s face broke into a smile, and they both began to laugh. And they kept on laughing until they were practically holding each other for support.
It felt good.
Alex composed herself. “And your brothers? Are they here too?”
Annoyance tasted like a mouthful of salt. Jonas tried to keep it from showing on his face. Before he could answer, the door of the Brigitta building swung open. Ellington Reynes emerged, looking antsy.
Oh, not this guy , Jonas thought with a roll of his eyes. Ellington was way too serious for his liking.
“I’m so sorry, Alex,” Ellington said, nodding to acknowledge Jonas. He didn’t seem surprised at all to see Jonas standing there.
Ellington had been the one to greet him at the gates of Eidolon, and he had access to various milestones in Jonas’s former life. How did Ell
ington interpret his odd history with Alex? Judging by the knowing look on his face, he’d seen enough. Damn it .
“I’m afraid the Brigitta director is detained at the moment.”
“That means you can’t get in the building,” Jonas informed Alex before turning to Ellington. “I’m willing to bet that Romey will be gone the rest of the day. She had to take care of my brother.”
Ellington groaned. “Not again.”
“Which brother?” Alex demanded, interrupting them.
“Your favorite one.” Jonas tried to wipe the salty taste from his lips. He watched Ellington begin to bite his nails. “At least Chase didn’t get anywhere this time. He was caught pretty early.”
“Any other newbury would have been expelled by now.”
“Newbury?” Alex cut in.
“Newly buried, like you.” Ellington paused, noticing the large slabs of granite scattered throughout the courtyard. He cringed at what was left of the bench. “Is this what I think it is?”
“If you’re thinking that a bench the size of a standard midsized sedan came flying at Alex’s head, then yes,” Jonas replied.
Ellington huffed. “They didn’t waste any time, did they? I take it you were forced to run for your life?”
“Actually,” Jonas said, “she diverted it.”
“She what?”
Ellington closed his eyes tightly, as if some secret was out of the bag. “She can’t just stay out here until Romey returns.”
Jonas sensed the opportunity. “I’ll just take her with me. I’m heading to Lazuli Street now, and then we’ll be back for curfew.”
Ellington looked wary. “That is probably the last thing she should be subjected to on her first day here. It will probably scare her a bit.”
“Might as well rip off the Band-Aid.” He glanced at Alex, satisfied to see that she was stepping closer to him.
“What’s Lazuli Street?”
“If you come along, I’ll show you.”
Ellington didn’t look convinced. “I’d feel better if I could join you.”
A chaperone was the last thing Jonas wanted.
“But I have a meeting in the city at the Dual Tower.”
Score.
“You’ll probably find Romey there,” Jonas said eagerly. “I think that’s where they took Chase.”
Alex opened her mouth, but Jonas held up a hand to shush her. “Cool it,” he warned. Alex crossed her arms in frustration, and the way she stuck out her lower lip was kind of adorable. He did his best to ignore it. “It’s a masque. She’ll be fine.”
“That’s true. I’ll meet you back here before curfew, just in case,” Ellington said. “Alex, will you be okay?”
“Don’t worry,” Jonas said. “She’s tougher than she looks.” He took Alex’s arm and she followed obediently.
As they departed, Jonas heard Ellington mutter under his breath, “She’ll need to be.”
Wrong , Jonas thought. Alex would finally be able to make her own choices. She wasn’t made of glass anymore.
Alex didn’t care where Jonas led her. He was a piece of home. She’d rather be in the company of familiarity than be left alone.
They crossed through the courtyard, and Alex thought the scene was like something out of a dream. The rain had stopped, but several spirits formed circles around the dark puddles. They held their hands above the water, which rose and fell like a solid object, morphing like putty. Near them, a mob chanted for what appeared to be an unorthodox race. Two spirits sprinted towards each other until, in the split second before collision, one disappeared, like a game of invisible chicken. Jonas called it “child’s play.”
Though the sun had not decided to show itself at all that day, it appeared the moon was much more curious as to what was going on below. As the day died, the sky darkened in mourning, and the clouds parted for the moon to peek through.
“Jonas,” Alex began. “Was that normal?”
“That bench?”
Jonas let out a little laugh. “It’s normal when you’re new. I’m not sure when the tradition started, but it’s like a rite of passage around here.”
“It isn’t very nice.”
“You’re dead, Alex. Don’t be so sensitive.”
She glared at him. “What’s the point of it?”
“I guess to see the reaction. To see the new kids squirm.” He stepped over a dimple in the stone walkway. “That dent is from Kaleb’s initiation. He had a tree nearly fall on him. Newburies don’t usually demolish the object like you did.”
“I have no idea what happened,” Alex admitted. How could she even be sure she’d been the one who caused the explosion? The only thing she’d done was wish for the pain to cease.
“It would be weird if you did.”
The wind flitted through Alex’s hair. It reminded her of childhood bike rides, or cruising in Kaleb’s jeep with Chase at her side, and she wished for him. “Jonas, what did Chase do? Why is he in so much trouble?” A shadow flashed across Jonas’s face, but it happened too quickly for Alex to identify the sentiment. For a moment, the air was filled with the sharp reek of salty bay water.
“He got a taste for breaking the rules, and I guess he liked it.”
Not likely. Chase was never one to stray from order, but to Alex’s exasperation, Jonas didn’t seem willing to offer more of an explanation.
Jonas looked back haughtily over his shoulder. “There’s a festival tonight.”
“A festival. Like a party.”
She doubted this day could become any stranger. Death, third grade, California, and now a party? A part of her would prefer to curl into a ball and take time to process this unbelievable world, but Jonas wasn’t the type to sit at her side and pat her hand. If she needed to go to this festival in order to keep him around, she’d do it.
“Feel that charge around us? Spirits like to let loose. You’ll learn that pretty quickly.” He skirted around some loose bricks. “One of the perks of being dead. With all the time in the world, why not have a little fun?”
She understood what he meant about the charge. The air around them began to tremble. “Is that why you’re dressed up?”
Jonas hurriedly rolled the sleeves of his button-down shirt. “I hadn’t noticed.”
“How could you not know what you’re wearing?”
“Because it changes according to my mood.”
“Is everyone that way?”
That explained the eccentrically dressed kids in the courtyard. Ellington had said the mind created its own version of reality. She just hadn’t realized how public it would be.
“You look nice,” Alex noted. “Is there an occasion for this party?”
“Actually, yes. Autumn is like Christmas around here. Best time of the year. A small piece of the world dies for a bit, just like us. Spirits celebrate all over the world. One of these days I’m going to travel to one of the larger festivals. I hear it’s insane in other countries because they aren’t confined to the city like we are.”
Jonas always used his hands for emphasis when he spoke, and she noticed he had something clutched in one of his fists. “What’s that?”
“My mask for the festival. It’s a masquerade.”
This kept getting worse. “I have to dream up a costume?”
“Or maybe we can just find a sheet to throw over your head.”
Alex bit her lip. How ironic that after everything she’d been through in the past few hours, her biggest concern was a costume.
“I’m kidding,” Jonas said with a roll of his eyes. “Can’t you hear it yet? The music? It’s already started.”
They crossed through a guard of gnarled trees and emerged onto a dark cobblestone road. Knobby lampposts with orange lights bathed the throngs of people who flooded the streets. Alex glanced up at the signpost. They stood on Lazuli Street, but she could not read the name of the adjacent road because the sign itself wore a feathered, birdlike mask.
“If you can’t dream up a costume, here you go.” Jonas stopped next to a table that was littered with disguises and nodded at the vendor. He took a blue mask with peacock feathers, and fastened it gently around Alex’s head. “Now you don’t have to be the new girl until tomorrow.”
Alex liked this idea. No one would be staring at her tonight; she could be the one doing the watching. Since when did Jonas understand her so well? “What’s the purpose of the masks?”
“It’s tradition. Like I said, some festivals are outside of our own cities. If everyone wears masks, no one can distinguish the living from the dead.”
The party was like Mardi Gras. People hung over the distorted iron balconies of the shops, toasting with stemmed glasses in their hands and shouting merrily to the people who danced and sang below. Games with dice and wheels, bands, tables of books, and holograms of advertisements lined the streets. Vendors smiled and offered vials, stones, or odd-looking gadgets. Some tables were even clustered with steaming cups, from which Alex shied away. What could a spirit possibly drink?
Was Chase somewhere in this mess? Would she even recognize him if he was? Yes, she thought without doubt. Even if she were blind, she could find Chase.
Alex watched a girl peel off Jonas’s mask and hand him an alternative, this one more like a headdress of a great black bear. Jonas laughed loudly, his face engulfed by the fangs of the beast. The girl thrust a champagne glass in his hand, filled with a gray swirling mist, and he tipped back his head to empty it.
The exchanging of masks seemed to be the custom. The first person who tore off Alex’s mask surprised her so greatly that she cried out in shock, though the noises around her drowned it out. The girl narrowed her eyes at Alex and opened her mouth to speak, but Alex quickly snatched her cardinal red mask in return.
The horde of hidden faces and maniacal laughter disoriented her. Alex clung tightly to Jonas’s arm. He stiffened, and through the fangs of the bear, Alex could see uneasiness flicker in his eyes. In that same instant, Alex was jostled by the crowd. Jonas had no choice but to catch her fall. He helped her find her feet again, his expression unreadable.
“Crazy, huh?” he whispered into her ear. “You should see this place on All Soul’s Day. It’s twice as nuts.”
An invisible wave herded them to the right, out of the street and up the sidewalk. The crowd sliced itself in half cleanly, making way for something Alex could only see on tiptoe. It resembled an approaching fog the way it drifted above the heads of the partygoers who clapped and cheered in excitement. Alex jumped and swayed from left to right to get a better view, but she was too small.
Jonas watched her with amusement. “Come on,” he said, grabbing her hand and elbowing his way to the edge of the crowd.
And then Alex could see that it wasn’t a fog at all, but dancers. They moved like nothing she’d ever seen before. Weightless and wispy like rolling clouds, they moved so rapidly that their black and white costumes created a gray haze to shroud them. She stood dumbstruck and mesmerized until something she feared was blood began to splash out into the crowd. These dancing storm clouds produced a horrific rain. She stepped even closer to Jonas.
“Don’t worry. They’re poppy flowers.”
A red drop landed on her forearm. He was right. It was only a petal.
As the dancers continued on their path, trickling by in perfect cadence, their porcelain masks hid all the emotion their movements so sublimely portrayed. Behind them, the crowd spilled back into the street, a confluence of the two masses.
Just as quickly as the dancers arrived, they were gone. Alex realized she hadn’t been breathing this entire time, not that it mattered. She exhaled, and her cold breath became visible. All that was frozen burst back to life with new vigor.
A jazz band kicked into gear above them. Alex felt a zap of energy and noticed a hand resting lightly on her shoulder. “Care for a reading, young one?”
The cat-like mask only covered the eyes of the woman who spoke, and Alex watched the corners of her lips curl upward in an appropriately feline sort of way.
“No thanks.” Jonas yanked Alex’s hand and pulled her back into the street. “Stay away from those,” he hissed, jerking his head in the direction of the shop.
“Those what?”
“Aura readers. They’re like fortune tellers.”
“Oh.” She glimpsed back over her shoulder with interest.
“Don’t even think about it. They’re unreliable.”
The street forked, and Jonas steered Alex to the left, where the noise was less deafening. Puffy lollipop trees lined the road, their color fading in and out like blinking Christmas lights.
“How are they doing that?” Alex asked. Another spirit stole her mask, leaving her with shimmery feathers resembling angel wings.
“Too many feelings,” Jonas said. “They can’t decide.”
“This place is really confusing.”
“It’s kind of like how spirits are dressed around here. It’s just their mood affecting their appearance.” He waved his hand at the trees. “They have feelings too. Who would’ve guessed?”
He led her to a top of a hill where they found a clearer view of the fireworks popping in the sky around the moon, which sat idly like an eye without a pupil, a neglectful babysitter. A mob of spirits gathered on the hill, dancing underneath the bright colors, but Jonas didn’t stop. He continued through the crowd until they stood overlooking a valley.
The first thing Alex noticed was a ring of lights that circled the lower grounds like a halo. “What is that?”
Jonas grinned. “That’s the real field of dreams.”
It was a park with several playing fields, each one congested with spirits. Alex heard childish laughter rising from the fields like a vapor, and a glow emanated around it.
“Ballparks?” Alex asked, shaking her head in disbelief. “Really?”
“Why do you look so surprised?”
The scent of hot dogs and spring grass permeated the night. “You didn’t think this was crazy the first time you saw it?”
“Eh. Maybe just that court made of trampolines. What did you expect? Tombstones? We’re kids here. It’s like a giant playground. There’s even a skate park. Kids dream about something like this.”
“This isn’t a dream, though.”
“No, you’re right. It isn’t. It was made into reality.”
She studied the face behind his mask, baffled by how content he seemed, how un-Jonas-like. “What is that cloudy light down there?”
“Happiness.”
“I can see happiness?” she asked without hiding her skepticism.
“Yes,” he said matter-of-factly. “Since there’s nothing to contain it out here in the open. What would have been the point of choosing this”—he motioned to the world around them—“if there wasn’t some enjoyment?”
As she watched the spirits flickering across the fields like fireflies, innocently free like children at play, Alex felt her throat tighten. A decade ago these spirits were probably still curled in the laps of their mothers, listening to bedtime stories and dreaming about what they’d grow up to be. She’d wager none of them would have said ghosts.
“It just seems so silly. Parties and … ” She fidgeted with her mask and kicked a stray ball back down the hill before muttering, “games.”
“Everything we do is a game. Life is a game. Death is a game.” He moved to allow several kids with skulls for masks to flip past them. Above, spirits released brightly lit balloons from the rooftops. The balloons fell like stars to the earth, only to be thrown back into the sky where they belonged. “This is just a different sort of play, although I guess I understand why Ellington thought it would scare you. Did it?” His eyes went to his arm, where Alex had been holding on to him, like she’d left traces there. He seemed to smile at it for a moment.
“It was just a little crazy. Unexpected.”
“Was it worth it?”
His voice dropped. “To get to them?” Jonas moved aside so she could see a group of spirits leaving the fields. Alex scanned the faces of the crowd, but they were each hidden behind a disguise. To whom was he referring?
“Where have you been?” one of them shouted to Jonas.
The familiarity of the voice warmed Alex’s heart. He was masked, sure, but he was unmistakably Kaleb Lasalle, and the curly-haired blonde next to him had to be Gabe. The square jawlines, the defined cheekbones, the roguish mouths that didn’t look right if they weren’t laughing. Their masks were simple and black, like two boys playing Zorro, like the games from her childhood, and Alex was suddenly filled with an overwhelming surge of nostalgia.
Chase’s brothers were here. Happy. In typical Lasalle fashion, they had defied death’s attempt to break their spirits and used their own tragedy to their advantage.
In life, the Lasalles did their best to protect her, but Alex’s illness was always a fascination for other children, another Parrish legend to explore. When she was young, Alex hardly minded the attention. It filled the void at home. To other little girls, she was a walking, talking porcelain doll with her large eyes, heart-shaped mouth, and snowy skin. But the years went by, and the attention developed as much as she did, which is to say, not at all. She was always classified as the sick girl. Perhaps this explained why she allied with Liv Frank, who had also been born into a predetermined stigma. During adolescence, images are as malleable as cement.
By the time she reached middle school, the constant company of the Lasalles was often torturous. They could effortlessly turn heads in their direction. Guys wanted to be them and girls wanted to be with them. They allowed their power to roll off their backs, while Alex was sentenced to the sidelines, where she felt stifled by it. The Lasalles became more mesmerizing the older they grew. On the contrary, as Alex aged, she only seemed smaller and weaker in comparison.
Parrish Day was the most important event of the year in their little town. While the Fourth of July meant family fun, fireworks, and corn on the cob, the eleventh of July was a day of guilty pleasures. It was a hazy, scorching mess of barbecue, beer bottles, beaches, and boat races. Every adult in the community drank too much, smoked too much, and laughed too hard to notice what the kids were doing, particularly at night during the beach bonfires.
On her thirteenth birthday, Alex sat sifting her toes through the cool sand, watching the tide stealing the grains like it was the world’s hourglass. She was finally old enough to recognize that her differences were hindrances. And she was becoming jealous of other girls, and not in the petty ways she always had—this wasn’t about playing sports or riding water slides. The other girls would get to grow up, and they would have children and grandchildren. They would get to live in ways she couldn’t.
The Lasalles dominated the volleyball sand, and the shimmering flames of the bonfire lit the scene, accentuating the definition of their muscles. They stood like four Adonises while their opponents were mutts, panting pathetically opposite them.
“Come on, guys, make this a little difficult for us!” Jonas taunted them.
“Alex, what’s the score?” Kaleb called, fanning himself with the footbal
l jersey he’d draped around his neck. “And don’t lie just because you feel sorry for those guys.”
“We only need one more point to win.” Chase turned and winked at Alex, and she felt her stomach flutter.
Jonas continued his bantering. “Do you think you guys might be able to score at least one point? Or are you too distracted by the girls?” His gibe was followed by a tittering of high-pitched giggles from their female audience.
“Stop being so obnoxious,” Gabe ordered.
Kaleb threw the ball into the air, but he didn’t direct it over the net. Instead, he aimed it at Jonas’s head. It ricocheted off Jonas and spiraled right to the hands of Gabe, who bumped the ball to Chase. Alex watched him spike it as easily as dribbling a basketball.
Kaleb pumped his fist, and the girls next to Alex began to whoop and holler like a bunch of drunken cowgirls. She scooted away from them, embarrassed. A redhead leaned in close to her. She reeked of seaweed.
“Your boyfriend is adorable,” she said with a slight slur, holding her cup out towards Chase.
“Oh. No. He’s not my boyfriend.”
“Really? But I always see you with him.”
Another girl leaned forward. “They’ve been inseparable since kindergarten,” she said to her friend. Alex recognized Posey Freebelanger. She had always been rather annoying, but boys liked her because she was curvy and she had a pretty face. Looks were about all she had to offer, because her name was enough to make her a social outcast, and her IQ wasn’t much higher than the SPF on her sunscreen. She’d once invited Alex to a sleepover and convinced her parents to take them to a bounce zone. A bounce zone! Alex had sat on a bench for two hours watching the other kids jump and scream and laugh, and Posey’s mom had complained she’d wasted money paying for Alex.
The redhead stood up to get a better view of the game, sloshing her drink and staining the sand. She peered down her long nose at Alex and flipped her hair over her shoulder. “You are such a tiny little thing. You must be freezing.” Her comment could have been an attempt to be friendly, but it didn’t properly mask the scorn.
Alex recoiled from the girl’s grubby fingers. “I’m okay.”
“Seriously, do you ever eat?”
One of the girls sitting with Posey could barely keep her eyes open. Sticks and leaves stuck out from her bleached blonde hair. She lifted a shaky finger at Alex. “Wait, you’re that girl. Aren’t you the one who is like … dying?” Posey tried to shush her friend, but Alex had heard the question loud and clear. She eyed the girl’s disheveled hair and wished she was callous enough to say, But somehow I’m not the one who looks like she just crawled out of a grave.
Redhead pointed to Jonas. “I used to sit next to him in health class,” she said in a scornful voice. “He’s cute, but he’s an ass.”
Usually Alex reprimanded Jonas for his behavior, but this girl seemed like she deserved it.
“Chase is better looking anyway. How do you stand having such a gorgeous best friend?”
Alex wasn’t quite sure if the question was rhetorical.
Bleach Blonde was swaying in rhythm with the cattails by the water’s edge. “So what will he do when you die?”
Posey jumped in. “Sorry, Alex. She’s drunk.”
Alex hated girls like this, ones who used excuses like drinking to defend their candidness when really they were just mean.
“I’m just saying maybe you shouldn’t keep him all to yourself,” Bleach Blonde retorted.
Chase appeared beside them. “What are you talking about?”
Posey began to speak, but Alex cut her off, finding courage in Chase’s presence. “Oh, these girls were wondering what you’ll do with yourself after I drop dead.”
Anger plagued his gorgeous face. “How did that topic come up?”
Redhead shrugged a shoulder. “My friend has had a little too much to drink.” She helped Bleach Blonde to her feet, but their legs tangled, and they both tumbled back into the sand.
Chase looked disgusted. “Maybe you should get them home.”
Redhead and Posey were already pulling Bleach Blonde away into the shadows. “I’m starving,” Alex heard Bleach Blonde wail, but they didn’t even make it off the beach before she fell to all fours and began to vomit.
“That’s really gross,” Chase said.
Alex was quiet.
“Hey.” He lowered himself to his knees in front of her and tucked a strand of hair behind her ear. He followed her gaze to the trio of girls who were still on the outskirts of the beach. “Forget them.”
Alex nodded halfheartedly. Chase snatched her cup from her hands and tossed it into the sand, then squeezed her fingers. “Look at me.” She surrendered, and the corner of his beautiful mouth lifted slightly. “You are perfect.”
There was silence for several moments before Chase whispered, “Are you okay?”
His brothers came bounding over.
“What’s wrong?” Kaleb demanded, seeing Chase kneeling in front of Alex. Jonas started towards the girls in the distance, but Gabe grabbed his shirt. They huddled around Alex, and she realized that yes, she was okay. Despite her limitations, she wouldn’t trade her small slice of life for anyone else’s. She couldn’t be resentful of who she was, because unlike any other girl in the world, she had Chase, and she had the Lasalles. And they were worth it.
“Well, Jonas, where have you been?” Kaleb demanded, tossing a ball from hand to hand.
“Jonas shrugged in response. “I had to play tour guide. You know.”
Kaleb caught the ball and stepped forward. “No, we don’t know. Since when are you helpful?”
Alex stood in silence, her eagerness creeping higher than the redwoods. They weren’t Chase, no, but they were pretty close. Her mask hindered her peripheral vision, but Jonas must have gestured to her because Kaleb suddenly dropped the ball, and Gabe’s mouth fell to the pavement with it. “Is that who I think it is?”
“Have you ever met anyone else that small?” Jonas said scornfully.
Kaleb let out a low whoop, ripping the mask from his face. He lifted her off her feet and swung her around like a child. “You aren’t fragile anymore!”
Gabe shook his head in disbelief. “Thank goodness,” he said, looking at his brothers meaningfully before wrapping his arms around Alex. He gently lifted the mask from her face with hope in his eyes. He seemed afraid that it wouldn’t really be her underneath.
“See, I always told you there was a perk to being the sick girl,” Kaleb laughed.
“Do you think that’s why … ?” Gabe’s uneasiness transferred to Kaleb, who gave one sharp nod of his head.
“Why what?” Alex pressed him.
“Nothing,” Kaleb said hastily, flashing his charming smile. “What a day to arrive!” He took Alex’s mask from Gabe and refastened it to her head.
And suddenly they were hugging her again, passing her back and forth like a lucky charm. And she didn’t mind whatsoever. Seeing the Lasalles was like finding the missing pieces of her heart. But it would be Chase, she knew, who would be the adhesive to hold it together. Before she could ask about him, Kaleb spun around with a wicked gleam in his eye.
“Wow, Jonas, that was really nice of you to escort Alex through the festival.”
Jonas studied the crowd indifferently. “I figured Alex always followed us around like a stray dog anyway. I gave her a break since it’s her first day after dying.” His posture, his tone, his expression—it was all back to the Jonas of old. Bored. Uncaring. Acerbic.
“We were actually coming up to find you because we needed you in order to win a little wager.”
“With who?”
Gabe groaned. “Do you have to ask?”
“Legacy kids?” Jonas flattened his mouth like a toad, disdainfully.
“The Darwins, of course. Who else?”
Alex raised her brows, but Jonas shook his head as if to say, You don’t want to know.
“What did you wager?” he asked, snatching a new mask. “Nothing of mine, I hope.”
Kaleb responded with a humorless laugh, leading Alex to believe that probably, yes, he’d risked something that belonged to his brother. “Doesn’t matter. Who cares about the Darwins now? This is a party! And now we really have something to celebrate!” Kaleb swung an arm around Alex and pulled her towards the commotion on Lazuli Street. His features were so similar to Chase’s that Alex could barely stand to look at him.
He led the group, with Gabe and Jonas flanking his sides, just as they’d done as children entering the playground. Alex and Chase had always hung back together, and she was painfully aware of his absence now. She wanted to know why they were avoiding the topic. “Kaleb?”
But her voice dissolved in the noisy ruckus. Kaleb took the hands of random girls, swinging them around, dipping them low, and kissing them on the cheeks. He traded masks and accepted a cup from a vendor, thrusting it at Alex.
“What is it?” she asked, scrunching her nose. Yet another question no one could hear. It drowned in the sea of faceless color.
Gabe mimicked drinking and urged her with a thumbs-up. Alex swirled the glass and a mist rose, carrying with it the scent of popsicles, chlorine, and sun-kissed skin. She sipped the weightless vapor, and it swaddled her in comfort. It was liquid summer.
Kaleb and Gabe joined in the merriment, singing loudly and climbing the podiums to high-five the party-goers. They lifted Alex on their shoulders and made the disarray fun because they took charge of the chaos and made it their own. Jonas lagged, grumbling about how embarrassing his brothers were. It didn’t take long for him to disappear, a typical move once the shadows of his brothers were cast over him, so Alex was surprised when Gabe felt bothered enough to stop the group.
While they waited for Gabe to locate Jonas, Alex tried to ask about Chase again. But Kaleb, who found it hard to remain sedentary for any long period of time, darted away and climbed a balcony to join a band singing “Only the Good Die Young.”
Alex took a seat on a table of gold masks and watched the show.
Two women approached. “They must be newburies,” one of them remarked with a grandmotherly tone of reprimand.
“Music isn’t what it used to be,” the other woman agreed, examining the masks. “And in my day, costumes were much more elaborate. Now it’s all just plastic and feathers.”
“Remember the year everyone impersonated the French royals?”
The other woman chuckled. “Josepha and Johanna didn’t like that too much, did they?”
“Not when the faux revolution began.”
Even behind their masks, misleadingly, these ladies didn’t seem to look a day over twenty, and yet they sounded like finicky old women.
“Why did you want to come over here with the newburies?” the first woman asked.
“I was curious.”
“Change is in the air. Don’t you feel it?”
“Then you haven’t been paying much attention. The trees have been talking, warning us that change is coming. And Maori told me that all of his sunflowers have been following the sun east to west. It’s a sign to keep an eye on our youth.”
“You spend too much time gossiping.”
“It isn’t just gossip! What about the incidents?”
“Paranoia,” the woman scoffed. “We’ve been around long enough. We’ve seen it and heard it all before.”
“I tell you, something foul is brewing around here, and I’m not talking about the stench wafting from Duvall’s chimney.”
The other spirit sighed loudly in disapproval.
“I just want to catch a peek at some of the new ones. I hear there are siblings.”
“They’re masked, or haven’t you noticed the theme of the party?”
“You of all people know that it takes more than a mask to hide a face.”
Alex jumped when Gabe appeared beside her. She glanced at the other side of the table, but the two women disappeared behind a curtain. “Did you find Jonas?”
“Yeah. In there.” Gabe twirled a scepter in his hand before using it to point to the store beneath the balcony, where Kaleb held court. Jonas appeared in the crowd and stood with his hands on his hips, staring coldly at the line of noisy celebrants. “Always a scowl on his face,” Gabe said.
“Actually, I thought he seemed different this afternoon.”
“Did he? Hmm. Maybe that’s the mask he was wearing today. Who really knows what’s going on underneath that façade?”
“He seems pretty happy to me.”
“Ha! Have you ever known Jonas to be happy?”
It was a legitimate argument. And now, no, Jonas didn’t seem happy at all. “You’re worried about him,” she noted.
“I always worry about him. He’s so quick tempered. So offended by us. I’m trying to fix that.”
What else was new? Jonas had always been the resentful one. He always tried to make the most noise while complaining that he was never heard. Maybe she’d imagined his cheerfulness earlier.
Kaleb, on the other hand, had confiscated a set of drum sticks and was putting on a show, grinning widely in Alex’s direction. The girls directly in front of Alex practically fell over themselves. They huddled together, whispering excitedly, until one of them peeked back over her shoulder. The girl must have said something to her friends, because one by one, they each turned to sneak a peek at Alex and Gabe.
“Some things don’t change,” Alex said. The Lasalles seemed to be just as regal here as they had been in Parrish. But one member of the royal court was still missing. She peeked sideways at Gabe. “Or maybe they do. What happened to Chase?”
“I know you’re probably anxious to know about him, but I don’t know much about the situation.” Gabe rubbed his forehead. “Kaleb was with Chase this morning, but he’s kept quiet about it all day. I don’t think he understood Chase’s actions until a few minutes ago. Our baby brother hasn’t been himself since we arrived here. He’s wanted nothing to do with us or this place. He’s done everything he can to get himself kicked out. Sweet charming little Chase, the juvenile delinquent. After the last time, I thought we’d gotten through to him. He promised he wouldn’t do it again.”
“Do what again?”
“Break the rules. Newburies can’t leave the campus unsupervised.”
“This isn’t summer camp, Alex.”
“It isn’t prison, either.”
Gabe shook his head. “Newburies don’t know anything about the world out there anymore. It would be like sending a nine-year-old loose in the world. How long do you think he would last?”
“Okay. Then why would Chase want to leave?” she asked.
“Until today,” Gabe said with a sigh, “the only thing Chase has wanted since he died was not here.”
When Chase appeared to Liv Frank after his death, she felt relieved. She’d hoped he would show up on her doorstep sooner rather than later. But she’d been told that the young spirits, the ones who still stunk of fresh earth, rarely got out much. All spirits wanted something or they wouldn’t have stuck around. Many of the ones she spoke with didn’t have a clue what they were looking for, but Chase would surely be searching for Alex. She took one look at his heartbroken face, and she knew he’d already found what was left of her.
As a child, Liv Frank thought the people she saw were invisible friends. It was entertaining at first. She thought she was special, because the other kids with imaginary friends only had one, and she had dozens! The invisible people were nice to her. They didn’t call her fat like the kids at school. Sometimes they would even give her answers to a test or help her win a board game. But eventually, their presence became a nuisance. They never left her alone. They would show up in her bedroom or in the bathroom. They would scare her. Liv began to ignore the faces that others couldn’t see, the ones that belonged to the dead. After a while, the faces turned into mere shadows. They became irrelevant, and for the most part she led a normal life.
Until Chase died. After the accident, Liv had visited Alex frequently, but each time, she felt more and more helpless. So Liv wouldn’t force her to do anything. If Alex was staring at the wall, she’d sit and stare with her. Sometimes she’d tell her stories, or sing, or stuff food in her chubby cheeks to try to make Alex laugh. Her friend barely responded. Sometimes Alex would be in a panic. She’d cover her ears or pull at her hair or scream. Those were the moments when Liv was afraid of what Alex might do to herself. That frightened part of her must have been willing to let Chase in. He showed up one night, sitting, waiting, and saying he was breaking the rules but didn’t care. He fed Liv the words that Alex needed to hear, because he could no longer say them to her himself.
Liv hadn’t seen Chase since Alex was taken away. Was he angry at her because she’d failed? Alex had been committed to that loony psychological rehab center. A lot of good that did, because she died a short time later. And now Liv was alone with her thoughts, her guilt, and her ghosts. Literally.
Somehow, when she allowed Chase into her mind, the others found their way back in, too. This time, she didn’t fight it, because quite frankly, she was lonely. But a part of her also hoped one day Alex would wander in with the others.
She might finally know that her friends were okay. That Alex and Chase had found each other. Maybe sometimes happy endings had to wait for a different lifetime.
Alex hurried to keep up with the Lasalles, who rushed through the crowds of spirits. Laughing, Kaleb led the group through a small alleyway between two buildings.
“Will we be late?” Gabe asked, flinging his mask like a Frisbee into the crowd.
“Nah,” Kaleb said. He turned to Alex. “Newburies have curfew. One of many restrictions around here. They like to keep tabs on us.”
Alex frowned. First confinement and now curfew. “Why would they need to do that?”
“Ask Chase,” Jonas said loudly. His comment immediately sobered the group.
The ferocity of Kaleb’s glare sliced through the night air. “I guess we won’t have to worry about that anymore, huh?”
“Speaking of,” Alex interjected, “do you know exactly where he is now?”
“No,” Kaleb said, “but I’m sure she does.”
A young woman with somber eyes and Shirley Temple curls was stationed in the entryway of Brigitta, talking to a distraught Ellington.
“What are you doing out here, Romey?” Gabe asked.
Her eyebrows lifted all the way up to her thick bangs. “You were almost late.”
“Almost.” Kaleb grinned, opening his arms toward the other kids still loitering around the courtyard. “It’s a holiday. There are plenty of newburies still out and about.”
“Other newburies typically follow the rules.”
“A little trouble is good for the soul.” Kaleb leaned closer to her. “I bet you were the life of the party in your day. Did you get a chance to enjoy the masque at all?” His face creased in concern. “I’ll volunteer to take over your duties for a few hours.”
Kaleb’s charm was like an anvil on a house of cards, and Alex saw Ellington roll his eyes. He stepped between Alex and the Lasalles and placed a hand on the woman’s back. “Alex, this is Caren Throme, the Brigitta director.”
“Call me Romey.” The woman squinted at Alex in the darkness. “I’m so very sorry about earlier. I—” Romey caught a glimpse of Alex’s face and gasped loudly enough to breathe shock into the air. Pings of
blue light danced around her face like sparks.
“Uncanny, isn’t it?” Ellington asked her. “The resemblance?”
Romey continued to gawk. Resemblance? Had this woman known her mother too? Alex felt a heat of childish rage rising inside her. Why did everyone else in the world get to know Erin Ash besides her? It was hardly fair.
Ellington ducked when a large piece of debris whizzed past them. Several spirits were using the demolished bench to play catch or dodge ball.
“It’s lovely to finally meet you,” the woman managed to choke out. She extended her hand towards Alex. “Again, I apologize. This has been the most unusual of days, I must say. Though I’m very glad you’ve found familiar faces.”
Alex wondered how this stranger would know her familiarity with the boys, but she noticed Ellington ducking his head guiltily. “I always give her as much background as I can before she receives a newly buried spirit.”
Alex cringed as a slab of granite slammed into a boy beside them. It made a loud whooshing sound like the air being punched from a pillow. It hammered the boy into the ground with a force that would have easily knocked out anyone who was actually living. But the boy jumped back to his feet, and Kaleb chuckled appreciatively. “Good one,” he said.
“Why don’t those kids have curfew?” Alex whispered to Gabe.
“They do. They’ve been dead longer though, so their curfew isn’t so early.”
“What happened here?” Romey asked, wagging a finger at the mess in the courtyard.
Jonas stuck a thumb in Alex’s direction. “She did it.”
Ellington lifted his hand to his mouth and began to bite his nails again.
“Wait,” Kaleb laughed. “That was Alex ?” He turned to her with newfound admiration.
“What else can she do?” Romey whispered to Ellington, who responded with a shrug of his shoulders. “You left her here alone?”
“I was searching for you inside the hall. I was gone for maybe three minutes. I figured that once she was finally safe on campus, no one would know who she was. I didn’t think she’d be in any danger.”
They were speaking in low voices, which seemed silly to Alex because she and the Lasalles could hear every single word.
“Know who she was?” Jonas asked loudly. “What do you mean? It’s just Alex.”
Ellington ignored him, continuing the conversation with his voice still hushed. “I thought the campus would conceal her.”
“Concealment didn’t exactly work for her mother either, did it?” Romey murmured.
“Her mother was foolhardy.”
Romey bit her trembling lip and sniffed.
“What does this have to do with my mom?” Alex interjected.
“Nothing,” Ellington and Romey responded in unison.
Pieces of the bench were still flying around like a meteor shower. Gabe intercepted a large slab of stone. “Spirits have been talking about this all night. I can’t believe it was you, Al.”
“Therein lies the problem,” Ellington muttered, but the Lasalles weren’t listening. They were too busy trying to find something else to throw at her.
Kaleb tried to wrestle the piece of stone from Gabe. “We might have to experiment with this, Al.”
Gabe refused to give up the stone but instead tossed it at Alex. She halfheartedly swatted it to the ground with her hand, and he pouted. “Boo.”
“I can’t believe someone threw a whole bench at you. That’s brutal.” Kaleb flicked his chin in Jonas’s direction. “Was he standing next to you or something?”
Jonas placed his hands on his hips. “You act like I’m the bad seed.”
“Speaking of which”—Gabe redirected his attention to Romey—“do you have anything on Chase?”
Alex still didn’t understand how one word could have such an effect on her. As much as his name had pained her after his death, the reverie of possibility was now equally as powerful.
“And I’m not allowed to discuss anything about the events that occurred this morning, I’m afraid. Or the proceedings thereafter.”
“But he is still here,” Alex said. It was more of a statement than a question. His voice that she’d heard earlier—it wasn’t far. Her intuition felt even more accelerated than her new eyesight.
“I think Alex might make your life a little easier, Romey,” Gabe said quietly.
“So I’ve heard. Unfortunately, I’ve done a very poor job of making her feel at home today, which is why I opted to wait here so she could actually gain entrance to Brigitta Hall.” Romey hadn’t taken her eyes away from Alex. She gazed at her fondly, though a bit sadly. “You should be able to get in from now on. We’ll talk more tomorrow, yes? Good. Boys, can you show her to the seventh floor?”
“Seventh, huh? Interesting,” Kaleb remarked, and Alex wondered why.
Before she could ask, Ellington placed a gentle hand on her shoulder. “A word of caution. If I were you, I wouldn’t disclose any information about your mother.”
“I second that,” Romey added. “Oh—the Bonds weren’t with you guys, were they?”
Jonas snorted. “Of course not.”
“Did you see them tonight?” she asked with concern.
“Let me think. No.”
“Oh, bother,” she mumbled.
“They didn’t check in?” Ellington asked.
“They may have just wandered off again.” Romey twirled a finger around one of her tight ringlets in thought. “Or they may be tied to a tree somewhere. I’d better go find out.”
“I’ll go with you,” Ellington offered, following her into the darkness.
“Who are the Bonds?” Alex asked quietly. “And why would they be tied to a tree?”
Kaleb made a face. “Don’t worry about them.”
The doors to the Hall swung open, and Alex stepped inside. A creak escaped from the hinges, apologizing to her for being so unwelcoming earlier. Entrapped within the dark marble flooring, a blue fire waltzed and twirled beneath her feet. She lifted her gaze to avoid stumbling from its dizzying effect. Square columns lined the walls, stretching all the way up to the glass ceiling, with tiers of stone balconies twisting around each floor. The bottom level housed long tables and vacant chairs.
“I didn’t expect it to look so … ”
“Elegant?” Gabe laughed. “I thought the same thing. The outside looks kind of like Hannibal Lector’s prison cell, doesn’t it? And then you walk in and find this palace.”
At the end of the fire walkway stood a peculiar fountain. A bridge crossed its spout, giving it the appearance that a sword had sliced it down the middle. Oddly, the fountain held no water.
“It’s quiet in here,” Gabe noted with a frown.
When they reached a desk, a girl suddenly appeared, rigidly perched like one of the gargoyles outside. Everything about her seemed to be pointy; her sharp nose, her narrow chin, and even her hair rested on her shoulders in perfectly perpendicular edges.
“Oh great,” Jonas grumbled. “What’s Tess doing here?”
Kaleb cupped his hand over his mouth so his words wouldn’t travel far. “That explains the empty room.”
“You guys are late.” Tess’s mouth twitched in an attempt to smile, but the expression never seemed to reach the other features of her face. She was like a stone.
“That’s because we were talking to Romey outside,” Kaleb said. “So you don’t have to worry about blabbing to her, Tess.”
“Romey’s outside? Did she say how long I have to stay here?”
“You weren’t exactly on our minds,” Jonas said. “Besides does it matter? You’ve already missed all the fun tonight.”
Alex didn’t think this girl looked like the type who knew how to have fun.
“There was plenty of commotion to keep me entertained. Did you guys hear about the fountain?”
“What about it?” Gabe asked.
“The contamination? I’m sure you’ve noticed there’s nothing in the fountain. But, oh, I guess your family has been rather preoccupied today.”
“Contaminated, huh? Did you have something to do with it?” Jonas asked.
A corner of her lips jolted upward. “Funny you say that. Weren’t you questioning Romey about the fountain last week?”
Jonas looked uninterested. “What are you getting at, Tess?”
“I don’t know. I just think it’s a little sketchy, especially since you were asking about how it filters our air. My brothers say—”
Jonas cut her off. “I really don’t care.”
“At least my brothers follow the rules.”
“Follow the rules?” Kaleb exclaimed with a loud laugh. “Since when is throwing people in the fountain following rules? Maybe that’s how it got contaminated!”
Jonas was scowling. “And for your information, I asked about the fountain because I had to clean it during detention last week. So maybe you should check your facts before opening your ugly mouth.”
Tess’s rock hard expression didn’t waver. If anything, she seemed pleased. “Maybe you could just inform me of some facts then. What happened to Chase this morning?”
Alex didn’t like the accusatory way she said his name. She hadn’t thought so many people would know about his predicament.
“Why do you care?” Kaleb asked.
Tess shrugged innocently. “Jonas was just saying I should get my facts straight. Who better to ask than his own brother? Did it have something to do with the fountain?”
“Actually, no, it didn’t.”
“Then why is he in trouble?”
“No offense, but that’s really none of your business,” Kaleb said calmly.
Tess let out a small hmph of laughter, and even that was sharp like a spur. “So Alex, do you have any ancestors here?”
Ellington’s advice was fresh in her mind. “I don’t think so,” she said quietly.
“Why are you such a nosy—” Jonas began but Gabe shoved him to shut him up.
Tess smiled. She seemed to like that her spurs were getting under their skin. “You boys wouldn’t understand. You’re first-generation spirits,” she said, indicating this was a stigma. “What is Alex short for?”
“It’s short for shut the hell up,” Jonas interjected.
“That was so clever,” said Tess. “Honestly, Jonas, I cannot leave my seat, which wasn’t such a punishment until you arrived. But if I bother you so much, why are you still here?”
“Excellent point. We were just leaving. It’s been such a pleasure seeing you, Tess.” He spat the words as though the taste of them was wretched.
As the Lasalles pulled her through the vestibule, Alex peeked back over her shoulder at the icy girl. The aggression of the conversation didn’t seem to faze Tess.
“She was charming,” Alex said sarcastically.
Kaleb made a face. “Tess-the-Pest thinks she can say and do whatever she wants.”
Jonas seethed. “Did you hear the scorn in her voice when she called us first-generation spirits? I hate that girl.”
“Why did she ask about my family?”
“Get used to it. Everyone asks about it when newburies arrive.”
“She was trying to see if she should invite you into her little cult,” Gabe explained.
“Legacy kids. They think they’re superior because they have ancestors here.”
“They do get special treatment.” Kaleb led the group to a narrow opening in the far corner of the room where a wavy ramp spiraled around a black pillar like an Archimedes’ screw.
Alex kept a hand on the pillar to support herself while she followed the boys around and around. At each floor, the darkness broke to reveal beautiful stone balconies with chairs and tables overlooking the vestibule. At the seventh floor, the boys stopped.
“It’s interesting that she’s on this level, right?” Jonas asked his brothers, giving Alex a little shove off the ramp. “I guess after what she did to the bench, it shouldn’t be such a surprise.”
Alex shifted unsteadily on her feet. “You know I hate it when people speak about me like I’m not here.”
“The seventh floor newburies tend to be advanced,” Kaleb said.
“Is that a coincidence?”
“There aren’t many coincidences around here. You blew up a bench earlier, so they must have gotten your room assignment right.”
“You might have family here,” Gabe said.
“I don’t think so.” Not anymore, at least.
“You’d be surprised. The longer the lineage, the stronger the spirit. The other day I read about the evolution of—”
“Come on!” Kaleb interrupted. “If you start spouting off, we’ll be standing here all night.” He offered Alex an encouraging nod. “Good luck!”
She hadn’t thought about what would happen next. She didn’t know where she was supposed to go or what she was supposed to do. Taking a tentative step forward, she poked her head around the corner to find a seemingly never-ending corridor. “What now?”
Jonas attempted to take a step out onto the landing, but Kaleb yanked him back. Jonas scowled. “Figure it out,” he snapped, turning back to the ramps. They disappeared, and his voice called down, “We did!”
For the first time since she died, she was alone. And she didn’t like it.
Taking a deep breath, she crept gingerly down the hallway, hoping a door might somehow have her name on it, and noticed something peculiar.
There were no doors.
The hallway contained window and picture frames of varying sizes but with mirrors behind them. Alex couldn’t see her own reflection, just the image of the decor behind her. Each frame displayed a caption underneath. The circular one closest to her read Sonja F. Rellingsworth, Founder of the Modern Periodic Table. The rectangular frame next to it was labeled Kender Federive, Service General. Alex continued down the hall, her eyes drifting over the captions, panes, and mirrors. She stopped beside the large crisscrossed window of Kinza Adel, Eidolon Ambassador from 1843–1986 , and she heard the squeak of hinges.
A piece of the wall swung open like a door. Cautiously, Alex crossed the threshold, and the door clicked shut behind her.
There was no question this room was hers, because it was exactly what she would have wanted. It was a scene she’d seen once in a catalog advertising high-end home goods. The welcoming room smelled of fresh linens and lilacs. French doors grinned at her from the far corner, with tables on either side piled high with worn books, though not nearly as many as those that inhabited the built-in bookshelves. Everything was beautifully aged, yet somehow brand new.
A bizarre ending to a bizarre day , she thought, falling into a great brute of a bed. Like the thick tufts of clouds in a child’s drawing, the layers of blankets cradled her form. Fatigue overcame her as she rearranged herself horizontally, supporting her back against the wooden backboard. It was comforting to have something secure behind her. Security that the world was not going to disappear as she slept. Security that she would not disappear.
She slept like the dead.
Alex’s sleep was not dreamless, but it was like television snow. All power and no programming. That is, until the very last seconds between asleep and awake.
When her mind opened itself, she realized she was lying on her stiff rock of a mattress at the Eskers Psychological Rehabilitation Center, a candy-coated term for “mental institution.” Bullets of fierce raindrops disturbed the darkness, pelting the skylight, her only connection to the outside world. Her mind felt drug-distorted, similarly to when she’d been a resident there, and muffled whispers curled around her from every direction. Through her hazy eyes, she could see movement on the walls. It was like staring at the sun and then closing her eyes to see the shadow that had temporarily imprinted itself in her mind.
Alex . His voice was a vigilant whisper, afraid of startling her.
As if anything could frighten her anymore.
Alex , the wonderful voice echoed again. Are you all right?
Depends, Chase. She answered as though it was perfectly normal to have a conversation in her mind. Am I alive or not?
Alive. But you’re dreaming. There was a smile in his voice.
I’m not at the institution?
No. But that was the last place you heard me. Your mind must have taken you there for that reason.
Why can I hear you?
I don’t have an answer for that.
She tried to blink through her dizziness, but her brain felt like a spinning CD. She used to watch enviously when the Lasalles would hold out their arms in their backyard, twirling like tops until they fell to the ground in heaps of laughter. She was not allowed to do such things, but she imagined this was what it felt like.
I’ve been hearing you for months now, Chase said. Since I died.
Why didn’t you talk to me before?
I tried. I couldn’t get through.
Alex tried to wiggle her fingers, but they refused to cooperate. How could her ears be working so perfectly and her other senses be so useless?
I’ve missed you, Chase whispered.
Rain began to drizzle onto Alex’s bed. You have no idea.
Yes, I do. I just told you I was in your head. I could feel it. Every little bit of it. I’m honestly not sure which was worse, mine or yours.
Then why does it feel better now? Alex asked. You’re still not here.
I’m here, he assured her. Haven’t you learned yet that your eyes are misleading? Don’t be fooled because you can’t see me.
I won’t be long. His voice quieted. Time to wake up now.
In the lingering darkness, Alex could hear the chirping of birds. It was the first indication that her grieving brain hadn’t simply invented the events of yesterday. Birds hadn’t ventured anywhere near to her window since the Lasalles died. Sorrow is contagious, after all.
Reluctantly, Alex opened one eye. She waited for the unfamiliar room to transform, for the image to warp like a painting in a kiln until the colors bled together, melting into her lonely old bedroom in Parrish or the bare walls at the Eskers. Minutes elapsed before she accepted the room as reality.
Wrapping a blanket snugly around her, Alex shuffled to the French doors to gaze out at the town adorned in a gray overcoat of fog, half expecting Chase to be there waiting below her balcony like some paranormal Romeo. The ever-present fog dimmed the pumpkin-orange lights of the street lamps parading down the lane, casting an appropriately spectral glow throughout her literal ghost town.
Even from this distance, her eyes were sharp enough to see the sign on the lamppost that read Lazuli Street. The road slept serenely, clean and quiet. There was no indication that the festival had occurred only hours before. From so high up, she could see past Lazuli, where the road forked. The left side curved toward the ball fields. The other veered right and disappeared under an awning of trees.
She guessed the disappearing road led to the two enormous towers in the distance. They melted into one another like a sculptor’s experiment, twisting near the top like a dip in a dance. Elevated tracery tattooed the stonework in green ringlets and wording. Alex lifted her hand toward the dancing building, and even from such a distance she could actually feel the roughness of the gnarled stone. She pulled back her hand in surprise, wondering how she could possibly know
how something felt to the touch from miles away.
Because your fingers don’t exist anymore , her intuition answered for her. It’s all in your head.
It was jarring nonetheless, so she turned to survey the room, noticing details that she’d overlooked in her fatigue the previous night. A large misshapen clock hung above the wooden desk, its hands indicating the time without ever seeming to move, without ever ticking. It was affirmation that time could stand still in this world, yet somehow keep moving. She found a standard note of greeting and an itinerary so painfully similar to a high school schedule that when Alex picked it up, she grimaced. Today she would be subjected to psychology, intro and history. Tomorrow it would be science, sensory development, and physics. There was also a footnote about periodic general education. The absurdity of death workshops made her laugh aloud, and she could have sworn she saw the walls pulsate, inhaling her merriment.
“Good Lord,” Alex murmured. “I should have brought my backpack.”
She had hours before her first scheduled appointment. It was no use trying to go back to sleep. She was jittery with anticipation for what the day would bring. There was only one source of entertainment in the room: the wall that was corner to corner, ceiling to floor, stuffed with books.
One of these should put me back to sleep , she figured.
She extracted the thickest one: Eidolon Greats: A Compilation of Biographies . This seemed too structured, so she replaced it and ran her fingers along the spines of the others. Introduction to Eidolon and the Surrounding World . Maybe she could skim through it.
Poised in the middle of the room, an arm chair stood like a lone island, out of place. It looked like an antique, thick and heavy, the type of furniture that would usually merit the phrase “They don’t make ’em like this anymore.” Alex pushed it over to the French doors so she could occasionally glance up and feel at ease that her new world was still there. She curled her feet under her legs and propped the book on her lap.
Her brain devoured the text, a paragraph per second, retaining the information easily. She read until her head ached, the anchors of information weighing down her mind, and she was shocked to discover she’d read nearly four hundred pages. No wonder there were so many books in her room. It would probably only take her a week to read them. With a brain like this, school wouldn’t be so bad after all.
She gathered the appropriate books and turned, tripping over a backpack that she was positive had not been there before. It was identical to the one she’d owned in life. Coincidence? According to Kaleb, there were none.
She made her way to the door, which gracefully swung open of its own accord. It seemed to know her hands were full. She even would have thanked it if she hadn’t been distracted by a girl across the hall. Her back was to Alex, covered in a fuzzy lion’s mane of bushy grayish hair.
The girl spun around at that moment to find Alex there and dropped several of her books. “Oh!” she said in surprise.
Alex smiled in greeting, but the girl scooped up her books and scurried down the hall.
That was weird, Alex thought, trailing behind. When she reached the winding ramp, an arm was flung in front of her face, chopping the air like the swing of an ax and preventing her from following.
“You should wait a few more seconds,” Tess-the-Pest advised. “Just in case.”
“Just in case of what?”
Tess didn’t respond. Instead, she made a face like she’d swallowed a mouthful of lemon juice.
“Who is that?” Alex asked.
“Calla Bond. No doubt going to fetch her brother. I have no idea why that girl is on our floor.”
Bond. So she wasn’t tied to a tree outside.
Tess’s lips moved slightly while she eyed the ramp, counting the seconds since Calla had left. “Okay. We should be good now.”
Bewildered, Alex journeyed around the ramp and down to the vestibule. Tess walked a straight path, maintaining her statuesque posture, and spirits scampered out of the way when they saw her coming. The air around her screamed authority so loudly that Alex fought the desire to cover her ears.
They passed the fountain, and Alex noticed it now contained a misty, white substance. Tess held out her arm and wiggled her fingers along the surface of the captive cloud. “I’ll show you to your first class.”
It wasn’t an offer but a command. Alex had been planning to wait in the vestibule until one of the Lasalles appeared. She felt anxious without them, but something told her that disobeying Tess was a bad idea.
They stepped outside into another gray day. Drops of moisture speckled the cool air like water on a camera lens. The spirits occupying the tables littered around the square didn’t seem to mind. Tess passed a bench with two sharp-featured boys with beak-like noses and nodded in greeting. “My brothers,” she explained.
Alex scanned the courtyard, searching for the Lasalles, but the only spirit she recognized was Calla Bond, who tramped up the steps of the school, constantly watching her feet like the ground might crumble beneath her. She bent down to adjust the cuff of her jeans, and someone bumped her shoulder and knocked her sideways onto the ground.
Alex began to voice her disapproval when she nearly tumbled over a jagged slice of the bench that was overlooked during the cleanup.
“The bench was your doing, wasn’t it?” Tess asked, coming to a stop.
Tess glanced in her direction. “I heard you didn’t run. I’d be careful if I were you. Anyone who missed the first display is going to be chucking heavy objects at you to see a live encore.”
Alex hadn’t thought about that and felt a strike of paranoia, but everyone in the courtyard seemed preoccupied. The two girls at the table nearest to Alex and Tess were seated opposite one another. One was holding flashcards of random objects while the other girl had her eyes shut tightly. “Apple, hammer, moon,” she whispered. Alex’s mouth fell open.
“Meditation activity,” Tess explained curtly with a wave of her hand. “So how did you do it?”
Tess took an exaggerated step over the stray mound of rock. She kicked it with her heel and began to walk again. “Control it.”
“I didn’t know what I was doing. I saw the bench coming, and then I just felt a pain in my head.”
“I’m sure you could do it again if you tried.”
“No, I couldn’t.”
“It isn’t typical, you know. Being able to do that on your first day. You must have family here.”
Alex remembered what Jonas had said about Tess and her self-righteous cult. “I have no idea.”
“Hmm.” Tess remained quiet until they reached the stone doors of the school. “What session do you have first?”
The doors lurched open, revealing an entrance hall. Hushed voices of students and loud chirping reflected off the walls, echoing all the way to the tip of the fan vault ceiling. Alex breathed in the smell of fresh paper and pencil lead.
The largest of three staircases greeted them front and center, leading to three levels of balconies, similar to the structure of Brigitta Hall. Two rippling staircases hugged the walls on either side and disappeared under dark archways.
Alex stood closest to the rightmost staircase, where she noticed artistic calligraphy carved into the stone that read “To the Grandiuse.”
Below the writing and at her feet jumped no less than five hundred tiny blue birds, chirping on the shiny black floor. How something so unusual was the last thing she noticed was evidence that she was beginning to expect the unexpected.
“What is this?” Tess lifted her leg and skipped over one of the creatures. The large elaborate tail feathers of the miniature peacocks fanned out behind them.
“These aren’t usually here?” Alex asked. One of the birds pecked at her ankle, but she felt nothing.
“No! Absolutely not!”
And then Alex heard Tess inhale sharply like she’d been stung. Calla Bond had appeared beside them. Tess attempted to move away, but the entryway was much too crowded.
“What’s going on?” Alex heard Calla ask a nearby student.
In response, the boy grabbed his ear and slunk away. Despite the obvious distraction, Alex noticed that every eye in the room had shifted from the flock of blue birds to focus on Calla, but no one waved, smiled, or spoke to her.
Alex couldn’t help but rubberneck at the strange girl too, until a shadow fell over them. A man entered the hall. His long coat billowed behind him, and he waved his burly arms. The force of his motions sent a furious gust through the entryway, impelling each student to the wall like bugs to flypaper, Alex included. She craned her neck to watch the man swish his arms, the conductor of a squawking orchestra. He created a swirling maelstrom to eat up each and every bird. His wild hair strewed erratically across his face, which trembled in concentration.
He filled the vortex and began to march out the door, but stopped abruptly to frown back at the newburies. Alex couldn’t tell if his focus was on her or Tess or Calla—perhaps all three—but the weight of his stare made Alex feel faint. And then he was gone, the chirping tornado following behind him.
Alex released herself from the wall. “Who,” she gasped, “was that?”
“Good question. I’ve never seen him before.” Tess rubbed her head and moved away from Calla. “I need to go find my brothers. Just take that center staircase to the second floor. Hang a left, and it’s the first door. Your doctor will be waiting.”
Alex was confused. “What doctor?”
“For psychology. You have a meeting, right? What were you expecting?” Tess huffed impatiently.
She’d been expecting a class, not therapy! She’d had enough of that when she was alive. Dread crept in and set up camp.
When Alex reached the room labeled psychology, she waited for the door to open, but it didn’t. She wondered if this room wanted her to make the decision for herself.
The circle of white chairs was empty, but she still felt she was disturbing something. The dimly lit space had a life of its own and the lingering aura of something that tasted like stale grief.
She tiptoed past a desk that supported stacks of tattered accordion folders stuffed with yellowed papers. Each folder had the name Crete Reynes stenciled elegantly at the bottom, and they were all labeled the same: Paradise . She lowered herself to a seat and set down her new belongings, feeling haunted. She couldn’t accept the atmosphere of the room. The emotions that lived here were not her own. Someone else had left them behind.
She pulled her feet up onto the chair and hugged her knees tightly, and then she felt him. She closed her eyes and breathed in the same air she’d sensed in Miss Petra’s classroom, like a storm had blown through with Chase saddled on the breeze. Was it his sorrow she could taste?
Sadness or not, she reveled in his presence, so minutes later when someone else overshadowed it, disappointment tapped her on the shoulder. “Hello there.”
The voice belonged to a skinny little boy with limbs that had never quite filled out and an outdated haircut. Her heart lifted when she recognized the adorable face of Ellington Reynes. The walls seemed to sigh and relax, perhaps happy to see him, too.
Ellington beamed. “Some people call me Dr. Reynes, but I would prefer if you continued to call me Ellington.”
“You’re the shrink?”
“There are several of us, but yes, I am one of them. All part of my job description. Who better to analyze the newburies than someone who has already seen their past?”
She liked Ellington, but Alex had never had a positive experience with therapy. She nodded toward the circle of chairs. “You enjoy all this?”
“It’s in my genes,” he explained. “For the most part, I do enjoy it. I like helping the newburies adjust to this world, to find peace with it. I do believe that peace is my purpose.”
Alex rested her chin on her knees, condensing into a tighter ball of vulnerability. “Is this where you met my mother?”
Ellington pulled his mouth tight as though this would keep too many words from escaping. “Yes.”
Alex scooted closer and waited for him to share more.
“We had to spend a great deal of time together. Those who have gifted minds usually need a bit more help.”
“She was gifted?”
“No. But it was expected she would be.”
“You don’t need to understand at this time. We have plenty to discuss, and your mother is a topic for later.”
Alex relented, but the ache didn’t subside. “How is it possible to still feel my heart?”
“Your mind makes it so. Old habits die hard. I still bite my nails.” He held out his little hand to show her and then patted her knee. “You can relax. No need to be afraid here. It’s a safe zone.”
“It doesn’t feel safe at all.”
“Don’t be afraid of the things that have been left here. You can leave things too. Things you don’t want or need anymore.”
Alex surmised he was not talking about tangible things. “I don’t think I belong here, Ellington.”
“Everyone says that at some point. I’ll confess I didn’t expect it from you.”
“No, I don’t mean here , like afterlife here. I don’t belong here in this room.” Alex said in exasperation. “I don’t need therapy. I hate therapy.”
“Everyone needs to talk about their death.”
“That’s just it. I’ve spent an entire lifetime talking about death. You should know that if you saw some ‘movie trailer’ of my life.”
He thumbed through his papers. “Alexandra Ash. Seventeen. Ehlers-Danlos. Resident of Parrish and then the Eskers Rehabilitation Center. When were you diagnosed?”
“With insanity?” Alex was only half kidding.
“No, with Ehlers-Danlos.”
“Hereditary … obviously.” He made a note on his legal pad.
“We’ve already discussed this, Ellington.”
“I know, but it is protocol. My reports must be documented and submitted to the powers that be. Okay,” he said, clapping his hands together. “Where shall we start?”
Alex shrugged. “Life. Death. Whatever.”
“You forget they are one and the same. Remember that spirits are more alive than any of the bodied.”
“The bodied?”
“Those with a body. It sounds silly to say ‘humans’ because are we not humane as well? We are nowhere near dead, though we say it so frequently. After all, the life we have left can still be taken from us. The human body was glass, yes, but glass doesn’t slip through your fingers. Being a spirit is like trying to hold water in your hands. Don’t get me wrong. Fear is healthy for the mind. And your mind is the most powerful thing you have now.”
Alex’s doctors in life had caused her to build a wall, bricks of obstinacy, but Ellington’s soft, melodic tone was enough to chip away at that wall. She was aware of it, and it alarmed her. Alex counted the empty chairs. “Am I really early?” she asked. “Or is everyone else just really late?”
“Oh, the first few sessions are one-on-one.” Ellington continued on. “Let’s chat about your time at the institution. We haven’t explored that topic yet.”
Alex groaned. “I was committed. Rotting away in an asylum. What’s to discuss?”
“You were grieving, yes?”
Alex nodded. “And losing my mind in the process.”
Ellington loosened his bowtie. “Grief would not have existed if your mind had truly broken. You were plainly sane. Look at you now.”
Alex shook her head adamantly. “I wasn’t in my right mind when I was there.”
Chase. That was the plain and simple truth. But no doctor would ever accept that answer. A doctor couldn’t bring a dead boy back to life to solve Alex’s problems. Psychoanalyzing her didn’t work, so they drugged her instead.
“You know the answer, Ellington.”
“I know the one-word answer, but we’ve only begun to scrape the surface. Simply blaming Chase doesn’t help me to understand.”
Alex cringed. Blaming Chase.
“Did I say something wrong?”
“I don’t blame him. There was nothing either of us could do. We never seemed to have a choice in the matter.”
“What matter?”
“If I explain it, it will just sound cheesy.”
Ellington stretched out his short legs, crossing his ankles. “I get to talk about death all day. I could do with a little cheese.”
She made a face. She really despised talking about emotions.
“Go on,” Ellington urged.
“All right, it’s just that most people spend their whole lives waiting to meet a person who puts all others to shame, who makes nothing and no one else in the world matter.”
“Ah. I think I understand,” Ellington said.
“I was born with that person.”
“There was no life that preceded him.”
Alex nodded. She had no memory of how to function without him because she’d never had to. And that had ruined her.
“It wasn’t about choosing to continue on with my life. I just”—she frowned—“couldn’t. There was nothing left.”
“And how did that make you feel?”
“Infuriated.”
Upon saying this, her feelings of helplessness left her body and filled the air around her. The rest of the sentiments inhabiting the room joined in, consuming her. There was something comforting here. Solidarity. Understanding. Just because her sorrow was different from theirs didn’t mean she didn’t belong.
Ellington waited patiently. “May I ask what you did for the involuntary commitment?”
She merely needed to show him her left wrist. She had never gotten the chance to ask Liv Frank how she knew what Alex had planned to do that night, but any idiot could probably have foreseen it after the hell she’d been through. Alex had been sprawled on the tile floor, her fingers toying with a razor blade, waiting for the right moment to show death that she wasn’t playing its sick game anymore. She wasn’t going to wait around until it finally decided to stop tormenting her. Game over. On her call. She just had to wait for the courage to slice in the right place, to make the decision. She’d taken a few preliminary swipes at her arms like playing a bloody tic-tac-toe. She was punishing herself for her cowardice, but it wasn’t until she closed her eyes and pictured Chase’s face that the blade hit the mark. It was then that Liv had burst into the bathroom to save her.
Alex held out her arm to show Ellington what almost took away her chances of being here. She wondered why this one vertical scar on her wrist remained while the dozens of others hadn’t made the cut. No pun intended.
“Ah,” he sighed. “Only one side?”
Alex nodded. “My father came home early that day.”
Like a shark, he’d smelled the blood and entered into the bathroom to find Liv bandaging Alex’s mutilated arm. He’d sensed the opportunity to finally have an excuse to be rid of her. By that time, her body was finished anyway. She could blame the wear and tear of her disease and the lack of nutrition, but something told her that this was her proper destination no matter the path she took. Simply because the world had a tendency to pull her toward Chase.
“I was never whole,” she admitted. “But then again, I never had to be. I was half of a whole, and I lost him. And I’d never known anything different. After he was gone, I was gone. There was no beauty left in the world. It wasn’t hatred or anger. It was worse. It
was nothing. I was nothing. I wasn’t meant to be there anymore. Not without him.”
“But he is here.”
Alex nodded.
“You are whole again. So perhaps the new question is, what do you yearn for now? You’ve been given an incredible gift. You’ve been given life. What will you use it for?”
Alex thought for a moment. “I guess I haven’t figured that out yet. Am I supposed to know the answer now?”
“Of course not,” Ellington said gently. “But it will be your job, yours and mine, to figure it out.” He tapped Alex’s head with his pen. “But I have a feeling the trajectory of your path is a road less traveled.”
In the ninth grade, Chase’s first English assignment was to create a poem following the template of Shakespeare’s sonnets. Well, he thought iambic pentameter was a pain the ass. He hated counting syllables and using the alphabet to find a way to rhyme his words. Shakespeare must have been on drugs to write entire plays in such gibberish, but Chase could at least appreciate the attention to detail. Their English teacher said the poem could be about anything, but she winked and added that usually they were about love. Honestly, it seemed to Chase that Shakespeare ridiculed love, but this teacher seemed like a bit of a sap, so he didn’t share his cynicism with the class. Besides, if he read into it too much, his teacher might bump him up to honors English, and he wanted to stay in the same classes with Alex.
“What’s wrong?” Alex said.
“Why do you think something is wrong?”
“Your face is doing that thing again.” She touched his clenched jaw.
His anxiety spiked, and he wiped a sweaty palm against his jeans and recited the first two stanzas of his sonnet in his head:
Oh may I fine’ly ask you to be mine?
It’s been so long I’ve waited to say it
I’ve thought these words to you time after time
I’m scared to think them ev’n as here I sit
May I hold you close and whisper your name?
Will my heart be truly safe in your hand?
Deep down I believe you do feel the same
But here I am, in complete fear I stand.
Was he seriously about to do this? He’d spent hours creating it, making sure it was perfect, ten syllables per line, four lines per stanza. Before he could talk himself out of it, he slipped his masterpiece into Alex’s copy of Romeo and Juliet . He’d signed it with his name, a heart, and a question mark. Dramatic? Sure, but if he was going to put the time into creating one of these absurd poems, he should use it to his advantage. This was going to be special. Alex deserved that. She deserved the best of everything.
“Well, this is me,” Alex said with a smile, stopping outside the English classroom. Chase didn’t have Ms. Holden’s class until tomorrow. It was the first time in their lives they didn’t have the same schedule.
“See ya in a bit,” he said, trying to ignore the crack in his voice.
This felt like the defining moment of his life. All their time together, his racing heartbeat, the butterflies in his stomach, the warmth he felt when she smiled at him—he was about to find out if she felt it, too. If she always had. It seemed like destiny, just like Shakespeare said. It seemed to be written in the stars somewhere that he and Alex were fated to be together. Hopefully their story was not meant to be a tragedy. But this was real life, not some old play written by a rhyming lunatic, so their ending had to be happy.
Maybe he shouldn’t have tried to be so clever. But Shakespeare didn’t title his sonnets, and so neither did Chase. Maybe if he had entitled it “Alex” there wouldn’t have been the confusion. Maybe then Alex would have received the note instead of the girl who picked it up by accident. So when he made his way frantically down the hallway after class, it was certainly not Alex who came sprinting down the hallway in his direction.
Clutched tightly in Becca Blackman’s fist was his poem, entitled “Sonnet 14” for the fourteen years he’d been in love with Alex. It was Becca who jumped into his arms and pressed her overly glossed lips against his while her friends giggled and clapped.
Where was Alex? What would she think of this? Oh, God.
Finally, he found Alex’s face in the crowd. Her expression wasn’t one of hurt or anger or jealousy. She smiled . Like she was proud of him or something. He couldn’t admit the truth. He wouldn’t, because the moment was ruined. It wouldn’t be perfect. It was a mess.
And so he snatched the note from Becca and shoved it in his pocket. And with it, he tucked away his feelings. He stuffed it deep in his pocket, somewhere down there with his pride.
Pride. Professor Van Hanlin worried it would be his demise.
He was not a teacher by choice. He’d spent the better part of a century highly ranked in the office of the Legem Patrol, a corps of spirits who dedicated their afterlives to maintaining order, justice, and peace. The Patrol was his life, his purpose, and because of one mishap, he’d been demoted to a measly law professor. Granted, it had been a rather costly mishap. That meant he was doomed to spend his time preaching to generations of arrogant teenagers who considered themselves to be above the law simply because their souls were strong enough to exist in the afterworld. What’s worse, the professors rotated the obligation to debrief the latest newburies in a workshop so cleverly named “Intro.” The most recent batch of dead kids had been assigned to him, and although it was safe to say he didn’t look forward to the workshop, the children were less horrid than some newburies he’d encountered in the past.
The only part of his job that he loved was his classroom. Secluded at the far end of the third floor, it was monstrous and impressive, and it made the mere four newburies in attendance seem that much smaller. Chocolate-brown stadium tiers stood proudly on the lovely navy carpet of the circular hall. The layers of seating overlooked the generous podium for the teacher. When he entered the room that morning, he didn’t even bother to greet the students. He set down his briefcase and promptly wrote floccinaucinihilipilification in large letters on the chalkboard. They’d know what to do.
He dusted off his hands, looked up at his newburies and nearly choked noticing a girl in the middle row. His first instinct was to laugh. Someone must have gone to great lengths to pull off such a joke. He swiveled back to the board for a moment. No, if this was a joke, it was a cruel one. Anguish took over. Maybe he’d imagined her sitting there. Maybe he was losing his mind. Was it possible for a ghost to see a ghost? When he faced the class again, there she was, frowning at the word with a face identical to that of the girl who had cost him his previous job.
It wasn’t until Madison Constance started explaining the directions to the girl that Van Hanlin accepted her as real. He’d been just as baffled when Erin Ash arrived nearly two decades ago. This new girl was the spitting image. Anything short of witchcraft would make her appearance impossible. He knew all too well how valuable she was. The entire city had been hysterical after Erin Ash’s arrival, but it was nothing compared to how they’d reacted to her disappearance. They must be keeping quiet about this girl, because he’d heard nothing about her. Or perhaps, considering the circumstances, they only decided to keep him in the dark.
“We have a new student,” he said, trying desperately to stop his hands from shaking. “I’m Professor Van Hanlin.”
He realized his tone wasn’t welcoming at all. It was suspicious. The imp of a girl tried to smile, but likely found it difficult to do so under his surveillance.
“Welcome … ?”
“Alex,” she replied. “Alex Ash.”
Another Ash.
“As your peers are aware, I am the law professor here on campus. In this introductory workshop, we will cover the basics. General questions and such, enough to get you accustomed to life here.” He circled the word on the chalkboard. “Do your best to brainstorm the given term.”
Alex Ash gaped at her classmates when she saw that they were scribbling notes on their papers. Certainly floccinaucinihilipilification was not a term she used in regular conversation. He watched her glance at the word again, and then her expression became one of surprise. “Oh,” she murmured. He imagined the sensation that rippled through her head was much like watching the pages of a flipbook. Such was always the case with him. The images appeared and disappeared so quickly it was like shuffling at warp speed through a card catalog.
“Write what you see,” he advised her. After minutes of drumming his fingers on his pedestal, he invited Alex to share what she’d written.
Mr. Jackson in seventh grade science discussing “‘pili.”
A tree.
Misspelling “purification” as ‘pilification.”
Sitting in church with the Lasalles.
Nihilistic themes in a song?
He was pleased. “I think you were rather successful with the activity. Your brain now has more potential than you could imagine, a fact justified by what you saw in your head when you merely glanced at this word. Your mind conjured up everything you’d ever experienced with the word or pieces of it.”
Or even , he thought to himself, future experiences.
“Can anyone wager a guess as to what the term means?”
Madison Constance raised her hand. Of course. A normal teacher would probably admire her vigilance, but Van Hanlin found her to be bothersome.
“I saw a science classroom just like Alex did,” Madison chirped, perched on the edge of her seat. “Is it something to do with science?”
“No,” Van Hanlin responded curtly. “Pili is plural for pilus , or cellular organelles. Wrong association.”
“What about history?” Joey Rellingsworth asked. “I saw my old history teacher.”
Van Hanlin smiled at Joey. Upon receiving his list of newburies to mentor, he’d been pleased to find the name Rellingsworth. Joey was multigenerational. He came from a long line of spiritual chemists.
“Often the word is used in political circumstances.”
“And nothingness,” chimed in another girl. He didn’t remember her name, and he didn’t care.
“Nihil in Latin means nothing,” he explained. Kind of like your significance , he wanted to add. This girl was a first-generation spirit.
“Why did I see the weather channel?” Joey asked.
“Flocci I’m guessing is the plural of floccus ?” Madison added. She glanced at Van Hanlin for affirmation, but he decided not to give any. It didn’t discourage her. “I was in PSAT prep when I died, and we were learning all sorts of Latin. I don’t even remember learning the word, but for some reason my mind is telling me that a floccus is a small tuft of a cloud.”
“You may not have even realized your brain had filed away that information,” Van Hanlin said, slightly impressed with the brownnosing girl in spite of himself.
Alex appeared to be gobsmacked by the conversation. He wondered what was hiding in that mind of hers. Incontestably something powerful. Yes, he was lucky indeed to have this batch of newburies. He began to consider the possibilities greedily.
Madison lifted her finger to her chin in thought. “A bunch of words that mean small or insignificant. Is that the actual meaning of the word?”
“The meaning is to deny the value of something, so yes, it is the same to regard something as insignificant. Well done.” He took a coin from his shirt pocket, which he flicked over his right shoulder. It ricocheted off an overhead lamp and landed directly on the light switch, brightening the room.
“Now that your brains are warmed up, let us begin. This afternoon, we are going to delve into the topic of travel. If you try hard enough, you can use your mind to see that things travel past you constantly, the most obvious of which being sound. You need only look for it. We are going to focus specifically on transportation. Of course, you can float, walk, or run without tiring easily, but there are much more practical means.”
A hand shot up in the air, and he acknowledged it through gritted teeth. “Yes, Madison?”
“Can we still drive cars or ride on planes?”
“Yes, of course we can, but we do not usually choose to do so. It’s simply unnecessary because it’s so much easier to ride the waves.”
Madison, who was transcribing his words furiously, said, “Huh?”
“Radiofrequency waves,” Van Hanlin said briskly. “Or in layman’s terms, cell phones. How many of you had cell phones in life?”
He watched all five hands rise into the air. Times had certainly changed.
“Ever had a prank call? A hang up? Those were probably quick trips. We don’t need much time to travel, but the further the distance, the longer we need to keep the connection. Ever been called by a telemarketer? Half of them aren’t even selling anything. They are simply working for us.”
Van Hanlin wrote Gramble on the chalkboard. “The founding family of modern day travel. Al Gramble was a man who perfected the method of transportation through electrical wires. Before we gave the idea of cell phones to the bodied—oh, don’t look so shocked! Of course we contribute to the physical world’s technology when it suits us. Anyway, back in the day, we had to travel through landlines. It was quite frustrating because there were so many unnecessary stops to reach one’s destination. Al Gramble’s great-nephew, Will, invented wave travel. Has anyone seen the turn for Gramble Lane off of Lazuli Street?”
Each of their faces displayed identical expressions of bewilderment. He presumed no one had mentioned it to them yet. They wouldn’t see the road until their minds knew to look for it.
“The parapets on the top of the building on Gramble Lane are like cell phone towers. They give us the ability to ride the radiofrequency waves.”
“What are parapets?” the tall girl asked.
“Those things on top of buildings that look like giant swords at attention,” Joey said. “I heard that teachers sometimes take the newburies on a field trip. Can we go?”
Van Hanlin shook his head.
“Is it because of that kid who keeps leaving campus?” Madison groaned.
Alex Ash looked up so abruptly her neck made the sound of a whip cracking.
“Aren’t there emergency exits in the school?” Joey asked, swaying his body to peek out into the hallway.
Now that it was mentioned, his newburies would have the ability to find the secret stairway outside his classroom if they opened their minds to search for it. The parapets on the learning center led to the travel waves. How interesting that the children had not heard of Gramble Station or the road leading to it, but they knew of the emergency travel access in this building. Van Hanlin’s mind began to reel.
“I’m not at liberty to show you how to travel outside of the city. That would be illegal unless warranted.”
“Professor?” Madison interrupted.
He sighed heavily and waved a hand to indicate she should hurry up and ask another of her infernal questions.
“Is it still possible to travel through the electrical wires?”
“Are we ever going to try it?”
Van Hanlin shook his head. “Please turn to chapter four: Traveling Overseas and Enduring the Discomforts of Water in the (Frequency) Waves .”
He watched to make sure Alex had the correct book and allowed his eyes to linger once more. He wondered how much surveillance they’d place on her, bearing in mind what had happened to her mother.
And more importantly, what had happened to those before her.
Kaleb and Gabe sat at the center of the Grandiuse, an unordinary hall impersonating the interior of a grand library. Two poker-faced girls guarded the door, but they each wrote so feverishly in their notebooks that they didn’t bother to address anyone who entered or exited. Millions of multicolored book bindings snugly clustered the walls, which zigzagged and waved magically to make room for all the information. Even the lamps curved over the tables insipidly like fields of drooping flowers.
Kaleb rested his cheek on his fist and picked at his customary football jersey while Gabe thumbed through a book. Upon Alex’s entrance with Jonas, they shifted their eyes to one another, mirroring an expression of suspicion.
“Where’ve you been, Jo?” Kaleb asked without removing his cheek from his hand.
Gabe stood up and tugged at Alex’s elbow, leading her to the opposite end of the table. She could sense Jonas’s annoyance thickening the air.
Jonas tossed his bag to the ground. “I found Alex wandering around like she was lost.”
“How helpful of you.”
Jonas muttered something inappropriate and unnecessary, but Gabe, who was always one step ahead of Jonas, coughed loudly during the comment so Kaleb wouldn’t hear.
Alex sat on the bench and took some time to ogle at the rippling walls. “What is this place?”
Gabe used his finger to hold his place in the book. “It’s just where professors brief newburies on upcoming events and campus concerns. You can come here to ask questions and get help with workshops, too.” He flipped his book upright and continued reading.
The chipped letters of the title read: Notorious Ghost Stories: Legends throughout the Ages .
Alex rested her elbows on the table. “Is Parrish mentioned in there?”
Gabe grinned. “Why else would I be reading it? The only downfall is that now I have that ridiculous song about the Cove Ghost stuck in my head.”
They had grown up in a town obsessed with its legends. The Cove Ghost was the most famous. Some poetic tourist had visited the town in the late 1800s and written lyrics about waiting on the beach for her to appear. The creepy song became a children’s jump rope rhyme. Alex had sung it frequently on the playground in grade school. The SyFy channel had even done a piece on the ghost. For weeks, their vans had popped up around town like wild mushrooms, unwanted nuisances.
Gabe had bookmarked one page, and he pointed to a word that made Alex’s stomach drop. The Jester . She tugged the book closer to get a better look, and Jonas leaned in.
The original Eskers Institution was home to many broken-minded souls, both dead and alive, but due to an arson attack in 1901, the building became condemned. The new Eskers Psychological Rehabilitation Center, constructed at the west end of the Esker woods, adopted softer methods for treatment. Many lingerers and wanderers still rely on the west-end Eskers to provide psychological assistance. While the physical world might consider The Jester to be a mere attraction, the spiritual world knows better. He frequently diverts the bodied from approaching the grounds by frightening them away before they get too close.
“So there really were ghosts in the wood
s?” Alex asked.
“Guess so.”
“What are lingerers and wanderers?”
“Just what you’d suspect them to be. Lingerers linger and hang out in their old towns, and wanderers wander. They move from town to town. Or so I’ve read.”
Van Hanlin called the Hall to order, and Gabe closed the book and hugged it close to him.
The various lecturers droned about the importance of punctuality, methods to alleviate headaches from retaining the overload of information, and improvements in executive function. Jonas seemed to find it as boring as Alex did because he spent the duration of the meeting trying to annoy her by staring and making faces. Gabe kicked him under the table, and Jonas glowered. “Whatever.”
Pleased her first day had gone so well, Alex gladly accepted when Jonas hurried away from his brothers and offered to chaperone a tour of the city before curfew.
They ventured down Lazuli Street to where it forked at the fields. Trees bowed over the ascending path with branches intertwining overhead and creating natural archways. The hill took them to what Jonas called the heart of the city, with intimidating buildings of concrete masonry and brass detail. A combination of Times Square and a Halloween town, the dark shadows of modern architecture obscured the ancient roads and knurled lampposts. The hustle and bustle of spirits skirting past them disturbed the fog, which haughtily puffed its way upward. It traveled over the chaos and past the lights of the city.
The dancing building she’d seen from her window stood guard over everything. Up close, the government Dual Tower, as Jonas termed it, twisted so high it seemed never-ending, attempting to pierce the sky itself. She hadn’t seen the rest of ‘Broderick Square’ until Jonas told her it was there. She gasped each time a building suddenly materialized from the fog. He assured her this was normal because she hadn’t known what to look for.
The road traveled toward the Dual Tower but separated twice, breaking into an endless knot and stopping several feet away from the tower. “What is the point of having a walkway that doesn’t even lead to the front door?”
“Maybe that is the point.” Jonas grinned, and with the removal of his scowl, it was difficult to believe that he was supposed to be the black sheep of his family.
Alex was momentarily stunned by how much a genuine smile transformed his face. “Is it exhausting to be bipolar?”
“I’m just kidding.”
Spirits eyed her as they traveled to and fro, craning their heads to follow her movements. Was insecurity visible to them? Was inexperience? Even the window frames of the gigantic buildings arced high like presumptuous eyebrows. She yearned for refuge and immediately found a new street sign. She tugged at Jonas’s sleeve and tilted her head in the direction of Scalae Lane.
This quiet road was much better. The redwoods neighbored them to the left, facing older buildings that didn’t seem so nosy. Alex noticed several tunnels and spirals of both ascending and descending stone stairways that led to nothingness, or just places still invisible to her apprehensive eyes.
A chirping bird jumped into their path, rippling its indigo feathers. Jonas picked up a stray branch. “This morning was quite the debacle.”
“Were you in the entryway too? I didn’t see you there.”
“Those lure birds were in every hallway, Alex.”
“Oh. I think they’re pretty.”
“You would think that,” Jonas said. “I just can’t figure out how someone got all those birds to flock into the school.”
“What do you mean?” Alex remembered how easily that strange boulder of a man had scooped them up to escort them out.
“Watch this.”
Jonas advanced on the bird, lifting the branch in his hand, ready to swipe it across the road. Abruptly, the bird retreated with a high-pitched hiss. Its feathers spread, along with its talons, which were silver and sleek like six butcher knives.
Alex jumped back in alarm and covered her mouth with her hands. “That’s horrible!”
“You still think they’re pretty?”
Alex studied the bird with new eyes. Oversized teeth glistened under the deceptively beautiful black beak, bared and jagged like the peaks of an ugly little mountain range.
“They live in the rosebushes between the walls surrounding the city. It must have been nearly impossible for someone to get them into the building.”
“Why would they bother?”
“You got me. But whoever the prankster is, I’d like to shake his hand.”
They stopped in front of a tableau of the architects involved in the construction of the city. Alex easily recognized Van Hanlin in a combat uniform. Madame Paleo, her new history teacher, stood front and center, wearing a mantua with elbow-length bell sleeves, a petticoat, and an apron. On the outskirts of the group a man stood scowling, arms folded.
“You don’t know who that is, do you?”
Jonas squinted at the picture. “No. Why?”
“He was the one who rounded up the birds.”
“Really?” Jonas shrugged. “I’ve never seen him before. Maybe he’s some sort of groundskeeper.”
Not likely. The man had been too powerful, like he was built to withstand an earthquake. Alex doubted his time was spent pruning bushes.
“And what about Calla Bond? Do you know her?”
“She was next to me during the bird incident.”
“I know of her. The Bonds are one of the old families. The multigenerational ones. Heredity is a big deal around here.”
Alex traced her finger over the carvings on the tableau. “If it’s such a big deal, why were people treating Calla like … ” She didn’t quite know how to word it.
“They were avoiding her?”
“Afraid of her,” Alex corrected.
“They aren’t afraid of her. They’re afraid of the Darwins. Tess and her brothers hate the Bonds. And around here, whatever the Darwins say, goes.”
“Why would they pick on her?”
“The weak are always the prey, aren’t they? Calla makes herself an easy target.”
“Are they punished?”
“Who? The Darwins? No way. They’re multigenerational, too. They must have some sort of genetic disease, because Eidolon is crawling with them.”
Alex stood quiet in her thoughts. Here, the trees couldn’t block all the light from the sun, as it tucked itself in for the night, swaddled in the comfort of a fluorescent pink sky and periwinkle clouds. Serenity whirled like a lullaby around them.
“I love when the sky shows off.”
Jonas blinked upward. “I heard the sky only changes color because of pollution.”
Alex stared at the multihued heavens, mortified. So this beauty was toxic? “Thanks for ruining it for me.”
“That’s not what I meant to do,” he said. “But one thing you’ve never learned is that appearances can be deceiving.”
“Nice cliché,” she replied. Two could play at that game. “But you also shouldn’t judge a book by its cover. That’s something you never learned.”
He shook his head. “This is a mental world, one that can easily be manipulated. That sort of optimistic thinking will get you killed.” He paused. “Again.”
She crossed her arms and continued to look upward. Polluted or not, she chose to enjoy it. The luxury of choice was just as beautiful as the complexion of the sky at sunset.
It didn’t take long for Alex’s dreams to find her that night. Thankfully, they didn’t carry her to the Eskers, but to somewhere she’d never been before. She was trekking through a hot desert, miles and miles of it. Although she was alone, millions of footprints imprinted the sand, choppy like an ocean current. She saw no end in sight, but kept walking, unfazed.
“Now this is what I expected death to be like,” she said aloud.
She felt Chase’s presence, and it began to snow. You’ve been watching too many movies.
Death isn’t so much different from life, is it?
“I guess we wouldn’t know, since we aren’t really dead, or so I hear.”
The scenery shifted. Her toes were still in the sand, but the grains turned cold. She was back at the beach on Parrish Day when the boys played volleyball for hours and she was subjected to the idiocy of the drunken girls. The scene unfolded like a movie. Finally, Chase came to her rescue before the redhead and Posey dragged the blonde from the beach.
Chase once again fell to his knees in front of her, tucking a strand of hair behind her ear. Suddenly he looked much older than thirteen. His hair was a bit longer than it had been a moment ago, and all boyishness had vanished. Although his eyes maintained the same Caribbean blue, the face around them, if possible, had become even more breathtaking, stronger and sharper. “How is everything?” he asked her.
The people around them continued to act as they had that day years ago. The volleyball game commenced without Chase, and the other kids continued to talk and laugh around the bonfire.
“Where are you?” she asked with a slow smile.
“I’m paying penance.”
“No worries.” He shifted to sit beside her in the sand, resting his forearms on his knees. “It was worth it.”
“For me,” she said guiltily.
“And for me.”
Alex wanted to reach out and touch him, but fear stopped her. She worried her hand would go right through him. “Where were you going the night before I arrived here? Why did you get in trouble? Your brothers haven’t exactly been eager to talk to me about you. In fact, no one seems eager to talk to me about anything.”
The flames reflected in Chase’s eyes. “It’s frowned upon to even discuss rule-breaking. Who would’ve thought death would be so strict? What were you doing the night before you arrived here?”
“Dying, actually. Thanks for asking.”
His voice was soft. “And you actually have to ask where I was going?”
“You were coming to me. So it was my fault.”
“No. It was my choice.”
Alex turned her gaze to the water and watched the tide rise. “Are you really here, or are you just in my head?”
“It’s one and the same.”
“What about when I was alive?”
He pointed to the scar on her wrist. “Who do you think told Liv what you were planning to do to yourself?”
“And now? How do I know what’s a dream and what isn’t?”
“Why do they have to be separate?”
“Is this a dream right now?”
“The images are.”
The waves began to white-cap, spilling relief-scented energy onto the beach. Alex took a deep breath to savor it. “You’re real?”
Chase chuckled. “I hope so.”
“Why did you risk leaving the other night if you knew I was dying and you’d see me anyway?”
All humor left him. “No one deserves to die alone, least of all you. All I wanted to do was be there with you. I didn’t want you to be scared.”
“My mind was gone anyway. They saw to that at the Eskers. I barely remember it, honestly.”
“That doesn’t make it better. And I thought maybe if I was there, I could talk to you, since I couldn’t get through in your head. Your body shielded you. Although I could get in and I could hear you, it kept you from hearing me.”
“But I heard you sometimes. Whispers.”
“I could tell. It was only when your mind let down its defenses.” He lifted his hand and allowed grains of cold sand to run through his fingers. She took the opportunity to stare at him.
“How long are you going to be gone?”
“I’m not sure.”
“Why are they keeping you so long?”
“I’m sure you’ve heard by now we aren’t permitted to leave the city.”
“It’s like house arrest.”
“It’s a rule. I broke it. I’m paying the price.”
“So it’s punishment?”
“At first I wondered if they just thought I was the one responsible for the pranks around campus. Like maybe they thought I was masterminding some plot to encourage other newburies to break the rules.”
“But the pranks are still happening,” she pointed out.
“Exactly. Which works out well for me.”
Alex glanced up when a shadow blocked the flames. Kaleb twirled a beach chair above his head. “Who’s ready to catch a ghost?”
She quickly realized he wasn’t talking about her. The crowd had dwindled. The younger children had been sent to bed, and most of the adults had succumbed to their impending hangovers and headed home.
She turned to Chase, disappointed to find him young again. Jonas appeared, sandwiching a marshmallow between two graham crackers. “No one has ever seen the Parrish Cove Ghost. You actually think she’ll make an exception for you?”
“Most girls do.” Kaleb situated the beach chair with his back to the group. He shouted against the noise of the waves. “It’s Parrish Day. No doubt she’ll be out to play.”
It was a lost cause. Locals and tourists alike were always setting up camp on the beach because they wanted to witness the infamous Parrish Cove Ghost. But even if the ghost-watchers avoided sleep the entire night, they would still claim to see no activity on the beach. And it had been a long time since anyone had seen a trail of fresh footprints along the wet sand in the morning.
“I’ll stay out here with you, Kaleb,” Gabe offered.
“Thanks buddy. Jonas, no one wants you out here anyway.”
Jonas swallowed his s’more with a loud gulp. “If you really wanted to go ghost hunting, you wouldn’t sit on the beach all night.”
Kaleb turned in his chair. “Really? What would I do, oh wise one?”
Jonas shrugged. “You’d go to the Parrish woods. Check out the Eskers in all its nighttime glory.”
“The mental institution? You’re off your rocker.” But Kaleb seemed excited despite his scoff. “Hey, Liv,” he shouted through the flames of the bonfire. “You’re a mental case. Would you go into the Eskers woods at night?”
Liv Frank was staring in the direction of the bay, stone-faced. Usually, she'd retaliate with a clever comeback. Alex envied Liv's wittiness even if she knew it only masked Liv's insecurities about her nutty family and her weight. Even in the dead of summer, Liv wore long pants because she hated her legs, yet now she shivered.
Liv seemed surprised to find Alex sitting there. She nodded and murmured something about footprints.
Jonas shook his head. “I’m just saying … ”
Kaleb leapt to his feet. “Let’s go.”
Alex didn’t need to listen. She knew what would happen. Within minutes, they were packed into Kaleb’s Jeep en route to the Eskers. It intrigued Alex to be a participant in the dream, acting exactly like she had years ago, but she went along with it simply because she enjoyed it. And she was hopeful that Chase would reappear, the real Chase, not the one she was wedged next to. She was so close to him she was practically sitting on his lap, and her heart pounded in the dream no differently than it had in real life. It was invigorating to feel a true heartbeat again, not just the memory her mind created.
They stopped when they reached the middle of the woods, and they weren’t there half an hour before Jonas dared them to get out.
“Are you crazy?” Liv shrieked. “You aren’t supposed to get out of the car. Those are the rules!”
“Who made those rules, Liv? The ghosts?” Jonas snickered. “You just worry about your Weight Watchers rules. I’m going.”
Kaleb pulled the keys from the ignition. He couldn’t be outdone by his little brother. “Me, too.”
Alex hated to admit it, but she was curious.
“You aren’t supposed to turn off the car either,” Liv wailed.
“You turned off the car! And the headlights!”
Kaleb shrugged. “Habit.”
Liv shook in panic.
“You’ll be fine.”
“Leave the keys,” she demanded, holding out a hand.
Kaleb fought a smile. “Are you planning to drive away without us?”
“No,” she said, but she didn’t sound completely sure.
“She's not going anywhere,” Jonas remarked. “There isn’t a McDonald’s around here.”
All participants in the dare needed to separate, and Alex found herself alone. Within seconds the air around her silenced. No movement, no whispers, no animals. It was dauntingly still, like the world after a snowfall. Alex tried to spot one of the others, but she couldn’t see a thing. She began whispering into the darkness, calling each of their names. No one answered. They couldn’t be far, so she called their names a little louder. The darkness swallowed her voice.
She decided to make her way back to the Jeep, but she couldn’t remember which way was which. She set off tentatively, crunching through the leaves. And then she froze.
She turned her head, listening for it again. The logical half of her brain insisted that she was making it up, but she couldn’t ignore the tinkling sound of tiny bells, like those on a clown hat. A jester’s hat. She picked up her pace.
They rang again, echoing in her head, except this time they’d moved to the right. Her fingers and toes grew numb with cold, and she could only warm herself with an overcoat of vulnerability. She heard a whimper escape her throat.
Chase , she thought.
Don’t worry . His voice came instantly, and Alex wondered if he had been there all along. That Jester guy is just messing with us.
Where are you now? In the dream.
Looking for you. He split us up.
He’s bored. We’re entertaining him.
He doesn’t want to hurt us, right?
No. I feel some sort of energy though, so there might be someone else out here with us, dead or alive. He might be trying to keep us away from whoever that is, too. What made you think of this anyway? Your mind must have held the memory for your dreams to carry you here.
I guess maybe because I saw the Jester mentioned in some book that Gabe was reading.
Gabe’s obsessed. But it is kind of cool that some of this world has to do with where we grew up.
The scene played out exactly how she remembered it. Each of them found their way back to the Jeep because they followed the sound of screaming. When they reached Liv, she was hyperventilating because a pair of blinding white lights was slowly traveling towards the car. The high beams grew larger and larger, and to avoid getting slammed by a car of such size, Kaleb quickly started the Jeep and veered sharply left to get out of the way.
It occurred to them on the way home that the road did not go straight ahead. The lights had been shining at them through the trees . And they were accompanied by the ringing of bells.
As the others screamed, Alex could hear giggling. It wasn’t external; it was like the laughter was inside her head.
And it sounded completely insane.
Brigitta’s classrooms all seemed the same: vast stadium seating, mahogany railings with desks attached, and raised stages for the instructors. The exception was Professor Duvall’s alchemy, botany, and chemistry workshops, nicknamed ABC. Alex considered the room to be a mix between a marine biologist’s dream and a mad scientist’s lab. A sheet of glass comprised the entire right side of the wall, revealing
a tank filled with a variety of sea creatures from pea-sized fish to human-sized squids. To the left, jars wallpapered the room, floor to ceiling, displaying grotesquely unidentifiable contents. The one closest to Alex looked like it was filled with human fingers. Other jars were solid. She could only imagine what was hiding in those.
The only available seat waited for her in the back corner. Calla Bond slouched over the wobbly table, rocking with the precariously uneven legs. Her mousy hair fell over her freckled face, shielding her from the world. She was accompanied by two others: a boy who shared her features right down to the placement of freckles, and a portly boy scratching his scruffy blonde hair. Their feeble island isolated them from the rest of the class as though they were infectious.
Alex slid into the empty chair, and the pudgy boy jumped, gawked at her, and began to scoot his seat away.
A woman sidled into view, exiting from a misshapen door in the front corner of the classroom. She commanded them to turn to page six hundred sixty-six, and snickering filled the room.
Alex rummaged in her bag, but her stomach flip-flopped when she realized she had forgotten her book. What a fantastic first impression she’d make on this teacher. The freckled boy noticed her plight, and he scooted his chair closer to position his book directly in front of Alex.
“Thanks,” she said. “Can you see the page?”
He waved his hand, shooing the thought. “I already read the whole book.”
He had to be kidding. The textbook was the size of a small suitcase, and it was full of formulas and foreign languages. Not the sort of book one could memorize even with an accelerated brain. The pudgy boy met her gaze and winced like he was in pain.
“Ah, right,” said the teacher, “I sense new blood in the room. Where is she?” Like an anorexic runway model with her wiry hair and hollowed eyes, she high-stepped down the aisle and moved like a breeze to the snapping of the loose jewelry around her bone-thin neck and wrists. The thick, colorful beads reminded Alex of stage accessories in a dress-up trunk. Objects fell to the floor in her wake: a piece of paper in one row, an empty cup in another. She didn’t seem to notice. When she came close to Alex, she stiffened, aghast.
Alex greeted her with reserve.
Professor Duvall didn’t respond at first; she just hovered with her mouth frozen in an O . Alex should have been used to this since most of the teachers had behaved the same way. But, unlike the others, this woman’s mouth curved into a Cheshire Cat’s smile and her emerald eyes lit up. “I’ll be damned,” she murmured under her breath. “How did you do it?”
“I’m sorry?” Alex asked, confused.
Duvall waved off the question. “You are the one who took care of that dreadful gargoyle of a bench?”
Alex nodded. News really traveled fast around here.
“Good riddance. I have despised that bench for a century. I’m Professor Lucia Duvall. It’s lovely to meet you.” She regarded the other occupants of Alex’s table with derision, sucking in her already skeletal cheeks. “It would be favorable for you to occupy a seat closer to the front, would it not?”
Alex double checked the seats in the room but saw no vacancies.
“You have much to catch up on.”
“Oh.” She placed a hand on the book sitting between her and the boy. “He’s loaning me his textbook today.”
“I see.” Professor Duvall sneered at Alex’s remote table of rejects before gliding to the front of the room.
Alex let out a breath and curled her arms around her chest. She wondered why she had chills up her spine. Then she realized the freckled boy next to her was grinding his oversized teeth. “What’s the matter?”
“Nothing,” he muttered, glaring at the teacher. “Just the witch.”
Alex didn’t think she’d heard him correctly. “The what?”
He pointed to the front of the room.
“Jade stones!” Professor Duvall’s voice rang through the vaulted rafters. “Mr. Seyferr, if you could be helpful enough to tell us how this substance affects the bodied.”
The round-faced boy on Alex’s other side began to flip through the pages of his book furiously.
“Hello!” Duvall barked. “Reuben Seyferr!”
“I …” Reuben Seyferr squeaked in a voice much smaller than he was. He itched at one of his arms. “I don’t remember.”
“You didn’t read the chapter?”
“I did. I just … ”
“See me after class.” Duvall’s voice was angrily high-pitched, but she seemed pleased that she’d embarrassed him. “Jackery Bond?”
The freckled boy lifted his chin. “Yes?”
“Jade stones?”
Jackery Bond sighed. “For humans, excuse me, the bodied , jade is often a symbol for perfection and immortality. Mesoamerican Indian masks often had the stone embedded within the representations of their gods,” he recited. “The Chinese also greatly value the stone.”
Alex was impressed. Perhaps he had memorized the entire book.
“Humph.” Duvall gave a sniff nod. “And Skye.” She refocused her attention, and her tone softened considerably. “For what do we use the stone?”
“Our doctors use it,” Skye responded in a sing-song voice. “It helps to sustain spiritual injuries in the core area.” She pointed to her hips.
Alex wasn’t sure what to think about Skye Gossamer. That morning, she had walked up to Alex in the vestibule and stared into Alex’s eyes, scrutinizing her own reflection. “You have long eyelashes,” she’d said. “That means you don’t always allow yourself to the see the things right in front of you.” And then she’d turned her heel, and her long auburn hair billowed behind her like a curtain.
“Very good.” Duvall gave a small nod of approval. She openly favored Skye over Jackery or Reuben. She waved her arm above her head in a fist and the image of a primrose yellow stone appeared, hovering in midair.
“Jackery,” Alex whispered, “is that a projection?”
“I guess you could say that. And call me Jack.”
“Where’s the screen?”
“Not necessary. There’s no technology. She’s projecting it herself. When you do see the technology here, you’ll know it.” He grinned. “Give your mind some time.”
“And the Voix,” Duvall continued, tapping her chin and eying the class. “What did you read about this mineral?”
Madison Constance raised her hand. “The Voix is found in parts of France mostly in, hold on,” she said, frowning down at her notes. “Lorraine, France, where they believe the stone helps to enlighten the user.”
“Very good,” Duvall said. “The bodied assume the stone will reveal to them some knowledge they were meant to hear, when in reality, what the Voix really does is endow the user the ability to hear spirits. What was not included in your reading is that the bodied who claim to be clairvoyant will simply keep these stones in their possession.” She gave the class a haughty look. “This was actually why the term ‘medium’ was coined by spirits, because medium means something in the middle or average. Many who call themselves mediums are nothing but average humans with no special gifts at all. Just a large stash of Voix. Legitimately gifted mediums also use the stones but only to help boost the senses of their clients.”
Professor Duvall waved her hand and the image changed to a small red-brown bracelet. “There is much magic to be found in minerals. Some more powerful than others.” She whipped her hand open, spreading her bony fingers wide. Alex watched the tiny bracelet grow to the size of a garden hose.
“This representation is a piece of copper jewelry sold by a vendor here in the states. Unbeknownst to the seller, this bracelet contains magic. It arrived here with us nearly two hundred and fifty years ago, and its powers have never diminished.”
Jack and Reuben shared a knowing look when Duvall mentioned magic. Calla raised her hand, but she was ignored.
“Do the powers of the stone diminish the more it is used?” Madison Constance asked.
“It depends on the type of stone,” Joey Rellingsworth interrupted. “Right, Professor?”
She nodded. “Most minerals are quite temperamental. Some fade with age, some fade with use.” Duvall scanned the room, still disregarding Calla. “Yes, Madison?”
“Is it true that you can divide a stone without killing the properties?”
Duvall rearranged her tangled jewelry. “Again, it depends on the stone. Often, if a stone is divided, the power will divide with it.”
The soft scratching of scribbling pencils filled the room, and Alex realized that she should probably be taking notes. She didn’t want to be on Duvall’s bad side.
“Case in point.” The projection of the bracelet grew even larger. “This piece has been tampered with, because typically with copper, you can split the stone, but it will weaken the power. Not true with this one. Other questions? No? Good.”
Calla sighed and lowered her hand.
Another image flashed in front of the class. The setting was some sort of hospital. People in blue scrubs flanked an operating table with a bench of medical tools to the side. The doctors swarmed around the patient’s head, but nothing appeared to be wrong with him.
“Is that a photo?”
Jack shook his head. “You can’t take a picture of a ghost. She’s projecting it from her memory.”
“This soldier,” Duvall said, “was attacked while accompanying an ambassador to a sister city in Russia.”
“It just looks like he’s asleep,” a boy with a pointy nose remarked.
“Very true, Mr. Darwin, but some substances are toxic to us in our spiritual shells because they are typically toxic to the brain. Copper, for instance. This solider died.”
Darwin. The boy’s black eyes matched his spiked hair just like Tess.
Duvall looked up at her own memory. “During the procedure documented here, doctors were able to successfully imprint jade within the mind of the soldier. But the effects of the copper turned out to be too strong.”
Alex began to raise her hand, but Madison Constance beat her to it. “If jade heals the core area, why would it need to be put into his mind?”
“Because when the solider was attacked, the copper was shot into the projection of his abdomen. His mind creates the projection of his core area, and therefore it needed to be his mind where the healing took place.
“Amazing, yet often unfortunate what a simple rock can do.”
The image of the bracelet began to spin.
“Almost as amazing as what the mind can do.”
“So what do you think of the witch?” Jack asked when the class was dismissed.
“She didn’t seem like a witch to me.”
“Ha! She’s not going to jump on her broomstick and ride around the classroom, is she? Everyone knows what she is, and even if they didn’t, we have our very own tenth generation witch hunter to confirm it.”
Jack beamed at Reuben, whose eyes never left the ground to acknowledge Alex.
The Darwin boy with the pointy nose rushed past them. He chased after a taller boy with identical features, with Tess-the-Pest at his heels, shoving Reuben into the wall and knocking Jack’s books from his arms. Reuben tucked his chin down even lower in embarrassment.
“But the weirdest part”—Jack scooped up his belongings without missing a beat—“is that she came here when she died. Spirits and witches are not friendly.”
The statement seemed ridiculous to Alex. “What? They couldn’t figure out who got custody of the werewolves?”
Calla crossed her arms at Alex in disapproval. She walked unusually fast, and Alex wondered if she was trying to ditch her. Jack, on the other hand, let out a little laugh. At least he had a sense of humor. “Seriously though,” he said, “why would she take refuge in Eidolon? Why wouldn’t she just return to her old life? She must have done something wrong.”
After a minute, Jack began to whistle merrily while Calla scanned the hallway. The way she acted, Alex wondered if they might be under enemy fire at any moment. Reuben tripped over his feet to keep up with them, resembling a meatball rolling down the hallway. This trio of misfits was so very bizarre.
Judging by the expression Jonas gave her when he saw her company, he agreed. “New friends?” he asked once he had stolen her away.
“I guess. They’re an interesting bunch.”
“Interesting? That’s a very political way to describe them. You always were a bleeding heart.”
He pretended to cradle his bag in his arms. “You adopt weirdoes like some people adopt stray kittens.”
“Shut up! Wait. How do you figure?”
“Oh my god. Liv Frank!”
“Liv was not a weirdo!”
“Oh please!” Jonas sniffed. “She had invisible friends up until middle school. She’d even introduce them to people.”
Alex couldn’t deny that Liv marched to the beat of her own drum. Actually, she was her own one-man band. “I always thought maybe you had a crush on Liv.”
Jonas crinkled his nose in revulsion. “How could you have possibly come across that theory?”
“You were so mean to her.”
Alex swallowed her words. Jonas had never been one to control his emotions. If he felt strongly about someone or something, any emotion would do.
She only realized when Jonas pushed her away how close they’d been huddled together laughing. A storm cloud appeared on his face, solemn and pouty, and thus Alex was not surprised to look up and see Gabe and Kaleb standing ten yards away. The way Kaleb eyed his brother, Jonas could have been an insect buzzing in circles around Alex’s head, and Kaleb seemed prepared to swat him away if necessary.
The first time a boy told Alex he loved her, she was four years old. It was February thirteenth. She and Chase sat together in a flour-clouded kitchen helping Danya make cupcakes for Jonas’s class party. They’d already mixed together the ingredients, swiped the batter with their tiny fingers, and licked the bowl clean, but they whined to help more. Danya gave each of them an icing bag with a metal tip and laid out parchment paper so they could practice making hearts with the icing before drawing them on the cupcakes.
Alex concentrated so hard her face scrunched in feverish determination. But no matter how hard she tried, hearts were just too difficult.
Jonas was slamming his hands into the stray flour, sending wisps of white into the air like powdery smoke, so his mother suggested he select candy sweethearts to put on the family cupcakes.
“What does this one say, Mom?”
She glanced over. “U R a 10.”
Jonas scrutinized the cupcakes before placing the heart on the one with a big G for Gabe.
“This one?” he asked.
“Lover boy,” she said absently.
Jonas smirked and put it on Kaleb’s cupcake. “And this one?”
“Hug me.”
He placed it on Danya’s, and she smiled.
“I hate hearts!” Alex burst out in frustration, throwing down the tube of icing. Her blobs looked more like amoebas. “I can’t do them.”
“Just practice your letters, then,” Danya suggested calmly.
Alex stuck out her lip, determined to pout. But it wasn’t every day they were allowed to use icing to color. Moments later, she picked up the tube and began to draw her initials, since those were her best letters. Pretty soon, silver ARA’s were covering the page like stars in the sky.
“This one?” Jonas held up a green candy heart.
“May I have something to eat?” Alex asked.
Danya checked her watch. “Didn’t you eat breakfast?”
Alex hung her head and muttered something under her breath.
“I said I couldn’t find any food at home.”
Danya bit her lip. “I’ll make you something, honey. Wash your hands.” She looked like she might cry as she pulled a chair to the sink. She turned back to her son who watched her cautiously. “Jonas, did you give that I LUV U heart to Daddy?”
“No,” Jonas said, shuffling through the rest of the candy.
“To Chase?”
“Who’d you give it to?”
“Oh really?” There was humor in her tone. “Why? Because it’s green? Alex loves green.”
“No. Because I love her,” he said casually.
Danya bit her bottom lip. “Oh, you do?” she asked. Chase put down his icing and frowned.
“Yep,” Jonas said, holding up another sweetheart. “This one?”
“Alex, I’ll make you a sandwich, but your cupcake is there,” Danya said, pointing to the one with the green I LUV U.
“Thanks.” Alex returned to her stool, oblivious to the message she couldn’t read. “Hey!” She noticed the parchment paper. “How’d you do that?” Where there used to be a sea of ARA’s, there were now upside down R ’s and hearts.
“I just added a sideways 3 to the bottom of the A and flipped it over.” Chase beamed at her. “It wasn’t too hard.”
“Show me how!” Alex didn’t even glance at the cupcake when she peeled off the paper.
Of course Chase would be the one to figure out how to complete her heart. Jonas sat quietly, flicking candy hearts across the kitchen.
Alex had not remembered until this memory came back to her five times stronger during death, but when she attempted to eat the cupcake, it was bitter. Each bite tasted like a violation, like someone was reaching down her throat and trying to steal something that wasn’t his to take.
“Have you thought more about our discussion last time? About purpose?”
Alex groaned. “No, not really, Ellington. And by the way, you sound like a real shrink when you bring up stuff like that.”
He folded his hand in his lap. “A real shrink? What do you think I am?”
“You’re not exactly typical, and I mean that in the nicest possible way.”
“What did those typical shrinks say to make you so apprehensive about therapy?”
“They didn’t really listen. They never accepted my relationship with Chase, the reality of it. They labeled it to be another intense teenage Romeo and Juliet romance gone wrong. They believed I clung to Chase because of my”—Alex rolled her eyes—“daddy issues.”
“In all honesty, I have to say if you were still alive, I might be steering you down the exact same path. But thankfully, on that topic, here everyone is on a level playing field when they arrive. Everyone suffers a bit from the self-esteem and abandonment issues that might result from a negligent parent. We each arrive here alone, usually as young adults who still need the comfort of parental love and guidance. Without people who are obligated to care for us and support us.”
“Why is that? Why are most newburies my age?”
Ellington propped his feet on the nearest chair. “I think young children are braver than young adults. They aren’t afraid of what is behind shiny door number two. They are willing to leave themselves behind. Adults, on the other hand, usually are not even presented with the option. Their spirits have become blemished by the stress and complications of life.”
“Stress and complications? Like going to school and finding a job? How is that different from what we have to do here?”
“Don’t confuse work with purpose.”
Ellington gnawed at his pen. “Have you put any thought into it? You need to find more than one thing in this world to live for. Potential drifts around you like a perfume, and yet you ignore it.”
“I can’t explain what pulls me towards Chase, but I’ve come to realize it isn’t something I can c
ontrol.”
“I will negotiate with you. I’ll accept that Chase is half of you. You’ve been running after this love all your life and death. What do you do once you have it?”
“Live happily ever after.”
Ellington mimicked puking. “The modern spins on fairy tales continue to warp the impressionable minds of children. What will you do during your happily ever after? Sit there and stare at each other for all eternity? No matter how much you deny it, eventually you will resent him.”
“You’ll wake up one day with the air around you stale, in a rotting world, because your thoughts have done nothing except fester.” He glanced at the walls. “To believe that simply attaining companionship and nothing else would truly make you happy would be expected of someone with—as you termed it—daddy issues.”
“You said everyone has those here.”
“In the sense that everyone is looking for approval. Spirits arrive here alone and have to find their place. The aspects of our human nature do not fade away when we pass on, by our choice. One of those aspects being the need for acceptance.”
“Is that why the families stick together here?”
“I believe so, yes.”
“I don’t have family,” Alex said firmly, holding Ellington’s gaze. “Why doesn’t anyone care to discuss why?”
“Even if we had the time to address it today, is it worth discussing someone or something that is gone?”
The irony of that statement was enough to make Alex laugh aloud. Technically, that was the essence of Ellington’s profession. “What would be the purpose of history class, or even sitting here in this room, if we weren’t interested in the past?”
“So what is this meeting about?” Jonas griped. “Besides hard labor.”
Thick brown paper and pumpkin innards blanketed the tables in Grandiuse Hall. The entire student body was put to work carving jack-o-lanterns to decorate the streets of the town. Eidolon always seemed to have a marvelous charge in the air, but the Halloween season made the excitement electrifying, and consequently the Hall stunk of burnt pumpkin seeds.
“Yeah, because carving pumpkins is such hard work,” Gabe joked.
Jonas sniffed. “Involuntary work.”
Alex couldn’t complain. This was better than another Grandiuse lecture on study habits, losing books, loitering in the courtyard, or new consequences for bullying Reuben and the Bond twins.
Reuben sat alone at a nearby table of chokers, a nickname for the newburies who still had difficulty coming to terms with their recent deaths. Jonas called them the “suicides.” They were the only spirits indifferent enough to allow Reuben at their table. He sat clutching a butcher knife in his pudgy hands, and his tongue stuck out from the corner of his mouth as he eyed his jack-o-lantern critically. Someone had dumped a mound of pumpkin guts on top of his backpack on the floor behind him. He hadn’t noticed it yet.
“Do you think there will be a lecture today?”
“I’m sure they’ll talk about appropriate behavior at the haunted house,” Kaleb replied. “You know, that we shouldn’t really be acting like ghosts.”
Alex analyzed the best angle to chip away at her pumpkin’s dangly tooth. In a way, it kind of resembled Jack Bond. “Isn’t the point of a haunted house to scare people?”
“In theory,” Kaleb said. “But the real purpose of the Mansion of Morgues is kind of reverse psychology. If the haunting is considered a joke in this town, our presence is safe.”
“A joke?”
“I guess the more suitable word is scapegoat . Some towns are infamous for supernatural activity, usually because there’s some lingerer hanging out and scaring people. Like our very own Parrish. Moribund has never been one of those towns. And ironically, the largest population of spirits in the United States is only a few miles away. The area is only known for superficial Halloween haunting. Pretty good diversion, if you ask me.”
“Ghosts pretending to be people pretending to be ghosts.” Gabe pushed aside his pumpkin and opened a book. “I wonder if we’ll get Chase back before then. They’ve kept him for a long time.”
Alex remained quiet on the subject. She’d been speaking with Chase regularly in her dreams, and he was still less than optimistic that his release would be soon. When she felt his presence in her mind, a distance remained. The previous night, for instance, her dreams had placed her in a rowboat, stretched out on her back, staring up at the clouds. When Chase entered the dream, his voice couldn’t have been more than a few feet away. She imagined he was in a similar boat, arms crossed behind his head, smiling at a sky as blue as his eyes. She asked him then, as she always did, when she would get to see him. He said when they were done using him , and she’d been too afraid to ask what he meant by that.
Kaleb picked out a sharper knife. “Romey told me this morning that he’s been cooperative. But that’s all. I think she’s missed him more than we have.”
“Weird,” Gabe said, “He’s been nothing but a pain since he got here.”
“What would a mother hen do without anyone to mother?”
The air around Jonas began to crackle softly. “Are you okay?” Alex whispered, but Jonas didn’t look at her.
“So, have they fixed the numbering on the classrooms yet?” he asked the group.
Kaleb groaned. “You know, that’s what they get for making every single door in every single hallway of the learning center look exactly the same. I’ve gotten so used to walking into the classroom for sociology that I should just take the aptitude assessment and get the credit for it.”
Gabe grinned. “I’ll do your homework for a week if you pass it.”
Kaleb twirled his knife through his fingers, considering the trade.
“At least the numbering prank was funny,” Gabe said. “The fountain and the lure birds? Not so much.”
“Don’t forget the furniture on the roof,” Kaleb added. “That one was pretty good. Oh, and the Bonds tied up in the broom closet.”
“I guarantee the broom closet was no prank. That was just a typical afternoon for the Bonds.” Gabe looked at his brothers meaningfully. “By the way, I heard another newbury blaming us the other day at the ball fields.”
Kaleb shook his head. “Whatever. They can’t prove anything.”
Alex picked the pumpkin guts from her fingers. “Blaming you for the pranks? Why?”
“Because for one, the pranks started right after we arrived here,” Kaleb answered. “For two, Chase was running around campus acting a fool and being as inconspicuous as the Hamburglar. For three, we haven’t been the targets of any of the pranks. That just looks incriminating.” He lowered his voice. “I heard why everyone was freaking out about the fountain on the day Alex arrived. It was contaminated with copper. If it had filtered into the air while we were all sleeping, everyone would have woken up completely stoned.”
“Doesn’t sound so bad.” Jonas stabbed his knife into the pumpkin repeatedly. He twisted and turned the blade until finally, grinning, he spun around the pumpkin to show Alex the carving of his name.
“That’s like sniffing household products, moron. It could have killed our minds, depending on how much was used.”
That quieted Jonas.
“Where would someone get copper? The only person in the school who might have a stash of it would be Professor Duvall.”
“Somehow I doubt her guilt,” Gabe said. “Although, Jack, Calla, and Reuben do live in Brigitta.”
Professor Duvall continued to openly ridicule the trio for any shortcomings they exhibited in class. She had a difficult time with Jack, however. He never missed an answer and never let her treatment faze him.
Kaleb held the tip of his knife to his mouth in thought. “What about the Darwins? Do you think they might have had access to the minerals? They spend an awful lot of time with Duvall.”
Alex peeked over her pumpkin. Skye Gossamer was sitting with the Darwins, attracting stares from the adjoining table of boys. She was like a rose among their sharp, thorny exteriors. Tess’s arms were crossed in defiance; apparently she shared Jonas’s views on involuntary labor. Linton Darwin, on the other hand, had crawled off the bench to kneel on the table in order to carve his jack-o-lantern at the right angle. Xavier Darwin, the oldest, pretended to stab himself in the stomach with his knife until he noticed Alex and the Lasalles staring in his direction, and then he sent his pumpkin flying across the room to land with a sickening splat against the wall behind Alex’s head.
Gabe flicked a seed from his shoulder. “Maybe Duvall knows something we don’t.”
The groan of heavy doors interrupted the happy chatter in the Hall. The Bonds entered the room, shuffling quickly down the aisles, Calla with her chin down and Jack with his held high.
“Speak of the devils,” Kaleb coughed.
The Bonds held their hands behind their backs like inmates entering a prison. Linton began flicking seeds in their direction. Xavier looked sour. He was probably upset he’d already wasted his pumpkin on the Lasalles.
“They should have just walked through the doors without opening them. That would have drawn less attention.”
Everyone in the hall, even the chokers, seemed to be sliding down the benches, suddenly needing more space than before. Alex could swear she even saw the arched lamps leaning closer to the tables, shrinking away from the duo. She made a point to wave them over, despite Jonas’s objections through gritted teeth.
The Bonds took a seat next to Alex, and Kaleb shook his head in astonishment. For a moment, she worried he would jump on the ridicule bandwagon, but Kaleb seldom allowed others to steer his course. He set down his knife and rested his elbows on the table. “How did you two get away with showing up an hour late for Grandiuse?”
“It wasn’t by choice,” Calla replied in a soft tone of embarrassment. She moved over to make room for Reuben, who had barreled over to the table, leaving behind a trail of pumpkin innards and desperation.
“I wonder which closet they were locked inside this time,” Jonas said quietly to Alex.
Jack, ignoring his usual withering effect on the world, rubbed his freckled hands together. “I love carving pumpkins!”
Kaleb handed him a knife. “Here. You sure do know how to catch a crowd’s attention.” His tone was almost admiring. “Where were you guys?”
Alex cringed, hesitant to hear their response.
“We had to clean up a bit of graffiti.”
Jonas bent forward to see them better. “You vandalized something?”
Jack didn’t look up at them. “No. We just volunteered to clean it up.”
“Because the words were mean,” Calla replied. “And they were about us.”
Alex felt the pang of pity. Written words were so much harsher than spoken. Ink had the power to marker one's esteem. In the ninth grade, someone had tagged her locker with the word slut . Just because she was friends with the boys. She could still picture the thick, red lettering, and how the tail of the S swiveled across the adjoining lockers. She’d never seen Chase so angry. He was there to save her then, but who did the Bonds have to save them? “We would have helped you wash it off.”
Jack shrugged carelessly. “Probably another prank.”
“We were just talking about the pranks. But what’s the big deal? Why is the city so concerned about a bunch of jokes?”
“Rules here aren’t broken,” Jack explained.
“Hence Chase’s removal,” Gabe said to Alex. “If rules are broken inside the city, rules can be broken outside the city. And that’s dangerous. It really isn’t tolerated at all. This world is successful due to order. They say carve pumpkins, we ask how many. They say yell boo, and we ask how loud.”
“The pranks are being viewed as a form of protest,” Jack added. “That’s why they are being taken so seriously. They want to know who might be objecting to how things are run around here.”
An irritable voice interrupted their conversation. “Silence, please!” Professor Van Hanlin stepped forward and lifted his hands. A gust of arctic air blew through the room. “Time is up!”
Jack stuck out his lower lip in disappointment.
“I’ve got this,” Madame Paleo said, practically shoving Van Hanlin off the stage. When she smiled, her nose took up her entire face. “Movers! Please remove the pumpkins from the tables. You’ll find space for them up front.”
Jack and Calla stood up with a half dozen other newburies, and the Hall became silent except for the whishing of jack-o-lanterns racing to the front of the Grandiuse. They hovered outside a door adjacent to the stage where Madame Paleo stood, directing their paths like an air traffic controller.
Alex couldn’t contain her astonishment. “How do they do that?”
Jonas smirked. “Says the girl who demolished cement. It isn’t magic, just brainpower. You transferred energy, probably from fear, but who cares? Telekinetics is just pushing your own energy into some other object.”
Gabe picked up his pencil and dropped it, frowning. “Yeah, I’m definitely not talented enough yet to move anything. I can close my eyes and see it in my head, but I don’t think I believe it enough to make it happen.”
“Those of you standing,” Paleo continued, “please head outside to practice telekinetics. If a guest at the haunted house doesn’t seem terrified enough, I’ve found that objects flying across the room seemingly of their own accord will usually do the trick.”
“Sweet.” Jonas sat up straighter. “They’re giving us the haunted house assignments.”
Gabe held out his pencil again, staring at it intently. When he let go, it fell to the table. “Jack, I didn’t realize you knew telekinetics.”
Jack nodded, took Calla’s hand, and walked off with a faint glint of smugness in his eyes, while the Darwins booed loudly from the legacy table. Alex glared at them and caught Linton flicking more pumpkin seeds, which bounced off of Jack’s head like misguided raindrops. Her adrenaline tweaked in anger and began to cartwheel in violent circles within her mind. She squeezed her eyes shut to escape her dizziness, but it only made it worse. She shook her head and pictured herself pulling away from the friction, and thankfully it released.
The room filled with gasps, and Alex opened her eyes to find Linton’s bench flipped over and his feet up above his head. Every spirit with the misfortune of sitting near him had also tumbled backwards. Alex’s head pounded.
Had she done that? She could barely hear Jonas over the sound of gongs crashing in her head.
“I wonder why they didn’t pick you to go with the movers.”
“Huh?” she asked, massaging her temples distractedly.
Jonas pointed to the front of the room where Jack was exiting.
“How come Jack and Calla aren’t a part of that little clique, then?”
Jonas snickered. “Have you met the Bonds? Jack isn’t exactly the class president.” He paused, watching Alex. “Are you okay?”
“I’m fine.” The pressure in her head became a dull ache. She glanced at Linton guiltily.
Van Hanlin narrowed his eyes and the lights brightened around him. “Enough foolishness. Please listen carefully for your name and direct yourself to the appropriate mentor.”
Madame Paleo stepped in front of him again. She had a pencil behind one ear and a director’s clapboard in her hand. She beamed importantly. “For those students on my list, please remain here in the Hall and migrate to the back of the room. We will be using the stage to reenact murder scenes from history, which will be performed throughout various rooms in the house while the guests venture through.”
Kaleb was the only familiar name to be called.
Alex waited while the professors announced several more groups. Gabe left with the newburies who would train to be “stalkers.” It was difficult to imagine sweet Gabe pursuing guests and pretending to be an axe murderer. By the time Van Hanlin took the stage again, only a handful of students remained, Alex and Jonas included. He led them outside, where he sliced the air with this arm, dividing the group in half. He was quiet for a moment, assessing his students. His eyes came to a rest on Alex and lingered there.
“Each year we have to shake things up a bit,” he began. “Perhaps the scariest aspect of the house this season is actually outside of the mansion, because the guests are going to think they’re lost. They will be chased through the woods, where we will be guiding them through a predetermined course.”
Skye raised her hand. “What will we be hunting them with?”
“Weapons.”
“That’s nothing new, is it?”
“The chase? No. The difference this year is that invisible spirits will track them as well, filling their heads with whispers. You will use voice boxes,” said Van Hanlin, holding up a small device. “They operate with the use of Voix stones. I want the whispers to come from all around them: left, right, above, below. That should scare them all the more. If a guest strays, use the voice box to get them back on track.”
“How do we know they’ll listen to us?” Jonas asked.
Alex pictured herself floating after some kid running in the wrong direction with his arms flailing above his head. That would be just her luck.
“When a human is scared, it is in their nature to scream, tense up, blink, and even skip a heartbeat. You will use that split second to redirect them.”
“Are you sure they’ll listen?” Reuben asked, eying the trees.
“Yeah,” Joey Rellingsworth agreed. “Because they could end up so lost.”
“They will pause,” Van Hanlin replied with certainty. “The human brain can only withstand a certain number of commands at once. When frightened, the mind tries to refresh itself when it overloads. You are going to command it instead, and your memorization of the routes will make the operation foolproof.”
There were a few nervous murmurs throughout the group.
“I’ll be supervising,” Van Hanlin said pompously. “Nothing will go wrong.”
Chase worried how long they were going to detain him. If it was a month ago, even a year ago, he wouldn’t have cared whether he was detained at the Dual Towers, or stuck in some workshop at Brigitta, or truly dead. It didn’t matter where he was. He wouldn’t feel whole if he was separated from Alex.
It was so strange. She was there in his head. He could sense her. He could feel her now. He felt her anxiety when she first arrived in Eidolon. He felt fear several minutes later. And he felt a burst of happiness soon after, and he wondered which of his brothers had warranted such a reaction.
He knew his newfound talent had resulted in his confinement. When he looked at someone, he could see their desires, their grief, and their passions. Whatever happened to be flowing through them at the time, he could see the color of it.
He should have kept his mouth shut, but when Ellington arrived, and Chase asked him why he was surrounded by flashes of pale yellow light, the cat was out of the bag. And the spirits keeping him here were trying to tame his gift.
They treated him well, pampering him if anything, but they studied him, used him, and forced him to accompany them during interviews. At least, they called them interviews. Chase figured they were more like interr
ogations.
It interested him how one question could cause a spark of new light. He couldn’t hear the questions. He could only see the reactions. From muddy blue to metallic gold, Chase would transcribe what he saw. He wasn’t quite sure what every variation meant, but he was beginning to learn. Ellington, who continued to visit Chase for his regularly scheduled therapy sessions, claimed this was a good thing. According to him, it took some spirits years to figure out how they might fit into this world.
Chase already knew his purpose, however. The only light he was interested in seeing was Alex’s. He had an advantage now. The moment he was close enough, he’d been able to see her true colors. He’d finally know how she felt about him. Her heart would no longer be closed off.
That was the only place he truly wanted to fit.
Van Hanlin had mapped out the routes in the haunted house woods so well that by the time they finally visited the mansion, Alex and her group needed less than an hour to memorize the miles of trails. Van Hanlin strutted around the campus, boasting pretentiously about his leadership and efficiency until finally Paleo intervened. She irritably suggested he put himself to use and disperse his newburies to assist the other professors.
Alex was sent to the kitchen, where Professor Duvall stood stirring a thick, red substance in a black pot. It smelled wretched, and Duvall gave Alex the creeps, so she turned on her heel to escape. Before she could scamper away, Jack’s voice came from the corner of the room. “Alex, hey! Where are you going?”
Alex cringed. Hadn’t he realized she was ducking out? Why would he yell her name?
Professor Duvall whipped around. The cooking spoon in her hand splattered red goo across the cabinet. “Whoops,” she sang, zeroing in on Jack with a grimace. “Bond, why are you loitering in the doorway?”
He shrugged. “The movers wandered off somewhere.”
Alex doubted it was a coincidence that he’d been left behind.
“Well,” huffed Duvall, “go help set up the Porta-Potties on the front lawn. They were delivered last week, but they’re arranged too close to the road.”
“Porta-Potties?” Alex interrupted. “What do we need those for?”
“They aren’t for us. Patrons are encouraged to relieve themselves before entering the house. In the past, many have lost their ability to function because of their fright.”
“Ew.” Alex wrinkled her nose.
“Bond, Porta-Potties! Go!”
“Fine,” Jack grumbled and exited the room.
Professor Duvall muttered something about where he belonged, and then her attention traveled to Alex, and she seemed to shudder a little, though a smile spread across her face. “My dear Alex, follow me.”
She led Alex down a hallway and through a set of sliding doors, where she paused and held out a small paint roller, brush, and tray covered with what looked like yellowy mucus. “I cannot decipher what it is about you to make your presence so electrifying. Maybe it’s your appearance.”
“My appearance?” Alex asked, coming through the sliding doors and entering a ballroom that might once have been stunning. Windows stretched from the floor to a ceiling littered with chandeliers, like a field of butterfly cocoons. Spiderweb cracks speckled the glass, casting jagged shadows along the chipped paint of the walls. A crippled grand piano with a protective coat of dust cowered alone in a corner. Alex sidestepped around the blotches and rusty brown stains on the floor, hoping it wasn’t blood.
“You do look so much like them,” Duvall murmured.
She had Alex’s full attention now. “Them ?”
“I meant to say her . Your mother, of course.”
“You said them . Is more of my family here?”
“Of course not,” Alex said more to herself than to Duvall. “Why is everyone related to me gone?”
“Some people just have magic in their souls. It is unfortunate that they are the ones who don’t get to stick around long enough to reach their full potential. The brightest lights burn out the fastest, or maybe they are just more difficult to conceal.” She shook her head at Alex’s bewildered expression. “Don’t be fooled by the utopian pretense of Eidolon. There is a reason why our city is surrounded by walls and gates, among other invisible barricades.” Duvall’s voice lowered. “Even though our little Garden of Eden itself has been known to contain its fair share of snakes.”
“Never you mind.”
Alex couldn’t drop the subject. She clutched on to it, grasping for any tidbit of information about her family. “Can you tell me what happened to my mother?”
Duvall leaned over a bucket that reeked of old gym socks and rotten honey. “Unfortunately, I don’t know. Nobody knows. She disappeared.”
“Disappeared?”
“Presumably gone, I’m afraid.”
“Why is that presumed?”
Duvall poured some of the goop into Alex’s paint tray. “Fear. People are afraid of the unknown. And no one could predict the extent of what your mom could do.”
“But Ellington Reynes told me that my mother didn’t have any special talents.”
Duvall adjusted her shawls, and her jewelry clinked softly. She reached into the bucket and extracted another paint roller. “Sometimes a mind will take its time before opening itself to its gifts. Some buds wait longer to blossom.”
“And why would anyone assume she had something worth waiting for?”
“There was enough evidence.” Duvall allowed Alex to ponder the meaning of this. After a few minutes, she clunked one of her heels against the bucket. “The Rhodo gel has a little kick to it, doesn’t it?”
“It stinks.” Alex lifted her paint roller from the tray. The mixture clung to it like a gigantic wad of yellow bubblegum. It pulsated, gripping the side of the container like the tentacle of a squid.
Duvall hummed a tune, harmonizing with the squeak of her paint roller spreading the gel over the wall. With her free hand, she held out a stone and extended it in Alex’s direction. “Tell me. Were you immensely strong-minded in life?”
“What do you mean?” Alex asked, gingerly dipping the tip of her brush into the goo.
“Oh you’ll need much more than that,” Duvall barked. She placed her hands on her hips, and the paint roller continued to spread Rhodo gel along the wall all by itself. “I mean, were you intelligent?”
Alex attempted to let go of her roller as Duvall had done, but it slammed to the floor with a clatter and a splat. “Average, I guess.”
Duvall seemed disappointed. “What about your strength?”
“Physically?” Alex laughed and picked up her roller. “I could barely lift my pencil without breaking a bone in my finger.”
“Any special gifts?”
“If you had them you would understand.” She twirled the stone with her fingers. “You weren’t one of the gifted, were you?”
“Magical?”
“Not that I know of.” Alex slopped a glob of gel against the wall, where it stuck like superglue. She kneaded the slime with the brush in her other hand to try to smooth it out.
Duvall placed her free hand back on her paint roller, which squeaked like a rusty old swing. Finally she said, “Undoubtedly your bloodline runs deep here. There are few explanations to explain why you are so skilled. Heredity might be the answer.”
Oh my gosh , thought Alex, not her too.
“Spirits evolve like anything else. Members of certain spiritually inclined families are more talented. Where did you say you were from?”
Alex swiped her hair from her eyes with her forearm. “Parrish, Maryland.”
The creaking from Duvall’s roller ceased abruptly. “Come again?”
“Parrish? It’s a tiny town outside of Annapolis.”
Duvall turned and began painting feverishly. “That’s a busy town.”
“Not really. It’s actually pretty small.”
“I wasn’t referring to the physical world, my dear.”
Alex dipped her roller into the tray. “I suppose there were a lot of ghost stories. Is Parrish like Eidolon?”
Duvall shook her head. “Not the same at all.”
“Then why is Parrish is so”—she used the word Duvall had provided—“busy ?”
“Some towns just are, my dear.”
Alex didn’t appreciate the vague answer. She absently rolled the goo onto the wall, lost in thought.
“Pick up the pace over there. We need to coat the entire perimeter, but just about six feet or so. It doesn’t have to be higher than the height of the average human. No one is going to back into the wall twenty feet up.” Duvall’s bony arm swept the length of the ballroom. “Newburies will be ballroom dancing in here. Once the guests are chased into the room, they have to make their way through the horde of masked dancers, who have various weapons to flash in their faces. There’s also a stunt guest who runs through and gets stabbed, a scene that propels the other guests to the walls, where they have to fight their way out of the Rhodo gel.”
“Sounds traumatizing,” Alex said.
For several minutes, the only sound in the room was the clinking of Duvall’s bracelets and the shlop of the slime bucket. It was quite uncomfortable, especially since Duvall kept staring at her and inching closer with the stone. By the time Calla arrived to save Alex, Duvall’s outstretched hand hovered close enough that if Alex had turned her head, her nose would graze the rock.
“Paleo ordered me to come and get you.” Calla shriveled under Duvall’s piercing glare. “We, um, we’re supposed to begin walkthroughs as mock visitors.”
“Oh,” Alex said, absolutely relieved. “Professor, would you like me to finish before I go?” They had barely finished one wall. The room was so massive Alex doubted it would be coated in time.
Duvall was mumbling words under her breath, words that made no sense. “No, dear. I’ve got it under control.”
“Okay,” Alex said, backing away slowly. She followed Calla toward the front foyer of the mansion, but halfway there, she realized she had left the paint roller but accidently taken the brush. She darted back down the narrow hallway.
Alex reached the ballroom and gripped the side of the door, preparing to deposit the brush quickly and avoid another weird conversation. When she rounded the corner, she stopped dead in her tracks. Duvall had vanished, and in her place, covering every inch of the enormous room, was a thick, dripping layer of gel. How had she finished so quickly?
If the task was so easily accomplished, why had Duvall asked for help? And why had she wasted her time in awkward silence with Alex?
“Can I show you something cool?”
When Jonas asked, Alex had hesitated, and he didn’t blame her. Her mind probably conjured the image of a childhood Jonas asking her that very same question right before beheading her favorite doll and holding up the head like a trophy. No wonder she seemed wary of what “something cool” might be.
He held out his hand and she eyed it like it was a bear trap. Would he ever release her if she gave him that much? She smiled, of course. Alex was always too polite to reject him completely. She reached out and cupped her hand around his bicep, barely grazing his arm, accepting the invite but not the gesture. That was good enough for Jonas. He took what he could get.
He debated whether or not to share this place with her. At first, he’d adamantly thought no , but Alex made things difficult. He’d never known how to handle himself around her. Alex was like a sunset on the horizon, beautifully unreal like the fingertips of the world grazing the edges of heaven, and yet painfully unattainable. Something he knew he could never reach, although that didn’t stop him from wanting it.
Since he could remember, he’d searched for hiding places. His brothers took up so much space that he couldn’t always breathe around them. This place he’d found by accident while attempting a detour during one of Van Hanlin’s scripted chasing routes. Among the trees that stretched so high they could, quite possibly, be gateways to eternity, one tree was different from all the others. It had thick leaves like a giant’s teardrops and branches that swayed without wind. Short and stout, it was blatantly out of place, overshadowed by its surroundings, kind of like Jonas.
Alex followed him beneath the protection of the tree and sat down. “What did you want to show me?”
“You’ll hear it before you see it.”
She cocked her head, listening for something. “Hear what?”
“Wait a few minutes.”
Alex folded her tiny hands in her lap.
He shifted his eyes as far as he could to look at her without turning his head. He wanted so badly to reach out and grab her hand.
“Where do you go when your brothers are around?” she asked out of the blue.
“You aren’t you .”
Perhaps she sniffed out his vulnerability here. Jonas knew very well that the sullen person he became in the presence of his brothers was the type of person Alex became without them. “Where do you go when they’re not around?”
“Point taken,” she said.
He held her gaze longer than he was allowed. Her oversized eyes matched the dusk, whatever shade of blue was left to survive alone without the light from the sun. It was a bittersweet color. Like the ending of something good.
“In all seriousness,” Alex pressed him. “You sneak off a lot. I think maybe I’m the only one who notices.”
She noticed when he wasn’t around? Something inside of him fluttered. He’d missed that feeling. Optimism. “You aren’t the only one, believe me. My brothers have never really trusted me. Without Chase to babysit, they’ve been watching me like a hawk.”
Who would they ridicule without him? They couldn’t possibly turn on each other. “Who knows? Boredom?”
“Do they have a reason to be concerned?”
Jonas wondered if he should tell her about his little secret. He always seemed to get himself into messy situations. It wasn’t a reason for concern but rather something he was proud of, an opportunity, but it was also something he was supposed to keep to himself. Alex made him weak. He would tell her everything if it meant he could keep her.
Kaleb was the leader; Gabe was the genius; Chase was the heartthrob. He’d never voice it aloud, but he was dreading Chase’s return. Charm filled the air when just Kaleb and Gabe were around, but when Chase returned, it would spill over, and he’d be forced to wade through the weight at his ankles. It was tiring to keep up with them. And who was he if he didn’t maintain his own role?
“No,” he finally replied. “They don’t have a reason for concern. But if they didn’t assume I was up to no good, something would be wrong.”
“What do they think you’re up to?”
He grinned mischievously. “You.”
“Ah,” Alex sighed. “You’re using me to get under their skin.”
Of course she wouldn’t take it seriously. He began to respond, but stopped when the air around them began to ripple. “Here they come.”
He lifted a finger to his lips, and within seconds, there came a palpitation so intense the world seemed to tremble. “This is what I’ve been waiting to show you.”
Hundreds of butterflies swarmed the tree. “Why are they here?”
“Maybe they just like the tree, but I’ve been here three times now when it’s happened.” Jonas liked to think they flocked to this tree in particular because it was different. It was proof that bigger wasn’t always better.
“It’s like magic.”
He was pleased to find her so in awe. He’d known she’d appreciate this. The butterflies were all different sizes, all different colors, a Monet painting blotching the world. With a whispering whoosh, the tree shifted its branches in a ticklish shudder. He watched Alex reach out her arm. The first butterfly to land on her was black and blue, proving a bruise could be beautiful, as though it knew how her life had been.
“Ever heard of the butterfly effect?” he asked. “If the wings of one butterfly can alter the path of a storm … ” He waved at the scene around them. “Imagine what this could do.”
He liked the idea that something so trivial, so small, could have such a big effect. It gave him hope that with even the slightest imbalance, the weight of the world, and maybe even the fate of the world, could be shifted.
Then maybe he’d stand a chance.
On October first, the last-minute preparations for the Moribund Mansion of Morgues had turned into such frenzy that the manor itself had actually begun to hum like the steady buzz of a beehive. That evening, Duvall partnered Alex with Skye and gave them a bucket the size of a baby pool filled with giant spools of what seemed like thick white yarn. She ordered them to decorate every nook and cranny of the house with fake “spider webs,” a task that proved to be extremely tricky because Duvall had invented the substance, and when the threads broke, they regenerated.
Skye ended up in the doorway of the billiard room, swaddled by the adhesive. Duvall drifted past and paused to commend Skye for being so creative. “Next year,” she cackled, “we should assign spirits to be stuck in the webs, screaming for help!”
There seemed to be a competition among the teachers to outdo one another with fresh ideas for the mansion. Strobe lights, mirrors, and fake murders would only get you so far, Van Hanlin had said.
“Alex Ash!” Duvall snapped her fingers. “Remove your friend before the webs go down her throat. That would be extremely uncomfortable for her.”
“Technically, her throat doesn’t exist anymore, right?” Madison asked from across the room.
“No, it doesn’t exist, but she hasn’t been dead long enough to believe that. She’d feel the pain of it.”
It took Alex nearly an hour to extract Skye from the heart of the web without breaking any of the threads. “Thanks,” Skye chirped once her face was freed. “I bet this is the stuff we diagrammed in Duvall’s ABC class the other day.”
The diagram had been excruciatingly difficult even with accelerated brainpower. Alex was grateful that Jack had been her partner. The compound was a mixture of dozens of elements, many of which the physical world had yet to discover. Duvall’s periodic chart was nearly two times the size of the one Alex had used for chemistry when she was alive.
Alex struggled to disentangle the rest of Skye and finally freed her arms. “I wonder if it’s the same goop Duvall used in the ballroom. Rhodo gel, or whatever it’s called, was even stickier.”
“Rhodo gel?” Skye asked in surprise. “That’s what she wanted it for? The ballroom?”
Alex examined what was left to unravel. “Yeah.”
“I was there when Duvall started to prep the ingredients in her test tubes. It seemed like a pain to make, so I thought she had a more significant purpose for it. Amid a million other ingredients it has peppermint, ginkgo, basil, rosemary, and of course rhodiola.” She spun her hands in circles around her head. “All that cleansing stuff.”
“What would she need to cleanse?”
“Good question. Rhodo gel is supposed to make someone understand things that aren’t clear to them. Why would she use something so complicated to gloop a bunch of walls when she could have just used this?” Skye kicked the baby pool of webs.
“Maybe t
o help the guests get out of the ballroom?”
“Maybe.” Skye lifted a finger to her chin thoughtfully. A thick thread of web broke off from around her elbow and twisted its way around her torso like a vine. “Damn,” she murmured.
Alex began to unwind it, twirling Skye around like they were partners on a dance floor. The released threads clung to Alex like static. “This is probably the sort of thing they do at couples counseling retreats.”
“I doubt they have witches there to spin webs.”
“So Duvall really is a witch?”
“Of course. You have to understand that the word witch merely means someone who is gifted ,” Skye picked at her fingers. “What? Why are you looking at me that way?”
“You say it so nonchalantly.”
Alex glanced around nervously as the taboo reached her tongue. “Witches,” she said in a low voice.
“How else would I say it?” Skye let out a tiny laugh. “And you don’t have to whisper. Why do you think—Oh.” She paused, her smile fading. “You sit with the Bonds during Duvall’s class, don’t you?”
“So?” Alex was defensive. She didn’t understand why everyone felt the need to pick on them.
Skye snorted. “The typical Bond thing to do. They’ve infected your pretty little head already. I thought under all that hair you had more sense.”
Alex self-consciously spun her hair around her finger. “Why would that be typical?”
“Multigenerational spirits stick to their stereotypes. Everyone knows that Gossamers”—she pointed her thumb to her chest and winked—“are always captivating. Darwins are always aggressive. And Bonds are always cursed.” Skye plopped down on the floor with her long legs blocking the hallway. “They really haven’t told you anything?”
Alex shook her head.
“I guess that’s the smart thing to do. Before they were known for being cursed, they were known for being manipulative. I’m not sure which is worse. They wouldn’t want to scare you away, but you have a right to know who the Bonds really are.”
Alex crouched down next to her. “What do you mean by cursed?”
“Once, the Bond family was well regarded around here, but they pissed off the wrong gifted coven and now they’re doomed to remain at the bottom of the food chain.”
“What did they do?”
“Who knows? It must have been something pretty bad, though.”
“How do you know all this?”
“I’m a Gossamer. My family has been around for a while.” She grinned. “And we’re pretty good at getting what we want. Information included.”
“Right.” Alex murmured. “So people are afraid to be around them because the curse might spread? Are you afraid to be around them?”
“Yes and no. I understand why they do the things they do. I don’t think they’re bad people.”
“But you hang out with the Darwins,” Alex argued.
“I can’t change the fact that I’m a legacy. Not to mention the Darwins also have justification for their behaviors. Half of their family died in the Witch Wars compliments of the Bond family.” Skye shifted her legs when several spirits trumped by, sliding their hands along the wall and leaving trails of blood. More spirits followed, ripping dry wall, chipping paint, and depositing tattered objects along the hallway floor. Even though Skye was blatantly in the way, they smiled at her. One even thanked her for no reason, and she chuckled. “Anyway, I’d be careful if I were you. The Bonds will do anything to get ahead. They’ve been that way for a long time now. They’re like quicksand, and they’ll pull you down fast.”
A whistle sounded, indicating that they should report to their stations. Alex hadn’t even noticed that the air outside had dimmed in the approaching dusk. The first guests would be arriving soon.
“This is exciting!” Skye exclaimed. Evidently the previous conversation was over. Any trace of seriousness vanished from her face as she pointed to the sky. “The clouds are moving in circles tonight, and that means everything will go routinely.”
Alex didn’t know what it was about Skye that made her believe she was right. She picked up her bucket and followed the strange girl into the utility shed. Alex shoved the leftover webs under a counter, disturbing a thick layer of dust, which puffed into the air like flour in a bakery. “This place is filthy.”
“The dust is there on purpose. It helps the bodied to see us.”
“Oh.” Alex lifted her hand to examine the dust that stuck to it. “They wouldn’t be able to see us without it?”
“They could because we want them to, and technically they are searching for us without knowing it. The dust is there just in case. It’s another one of Duvall’s concoctions. Make sure you don’t have any of that dust on you now, though, since you’re supposed to be invisible. Here, wipe it on me, since I have to chase them.” Skye lifted a chainsaw from the workbench.
“If I were bodied, I probably would have run away from this place, screaming.”
“Oh, that’s the point though.”
“I know. I just mean—”
“But each guest does have to sign a waiver. Don’t worry,” Skye said, smiling at Alex’s alarm. She held up her chainsaw. “The blade is gone. It’s the people with certain medical conditions who are advised not to enter.”
This precaution seemed a little extreme to Alex, but once she saw the reactions of the guests, she understood. When the guests stepped out from the back door of the manor, their faces were completely drained of color, even before the chainsaws or daggers were raised. Some even came out sobbing.
At a quarter to one, Alex stretched wearily. The hordes of terrified visitors had slowed. Skye said this was good because the clouds were no longer moving, whatever that was supposed to mean. Alex yearned to go home and sleep so she could see and hear Chase again.
“The next wave is coming out,” Skye warned, gesturing with a machete and yawning. She looked like Rambo Barbie. Reuben had direly wanted the chainsaw, so she’d swapped with him hours ago.
The door creaked open, and four more guests exited. “Oh, thank God,” a boy said.
A girl heaved before bending down to comfort a whimpering friend. “It’s over!”
Alex heard Skye cluck her tongue in sympathy before she concealed her beautiful face with a morbid mask and stepped out of the shadows, lifting the knife to her own throat and pretending to slash her neck. The group of guests backed up slowly and collided with Reuben, who revved the engine of his chainsaw. For the hundredth time that night, the grounds were filtered with ear-splitting screams. But this group didn’t follow the unscripted plan. Three of the kids bolted straight ahead, exactly where they were supposed to go, but the whimpering girl veered to the left and disappeared into the trees.
No, no, no, Alex thought. There was no one else left to go after the girl. She hesitated, willing Jonas, someone , to appear so she wouldn’t have to go alone. But she had no choice.
The girl was fast. Alex kept pace easily, perhaps because she no longer needed to breathe. She just needed to concentrate on following the girl. When they scampered past the butterfly tree, Alex realized how far they’d gone. Fabulous, now they were both going to get lost.
It wasn’t until they reached a clearing and the moon provided some light that the girl finally stopped and keeled over with her hands on her knees, gasping violently. Alex was so irritated she considered smacking the girl. She strained to listen for any sounds to indicate how they might find their way back to the mansion. The droning of the chainsaw erupted far off in the distance, and despite the girl’s heavy breathing, Alex heard a series of raspy whispers, each overlapping the last. She shook the voice box in her hand, wondering if it was somehow having an effect on her. The Voix stone rattled inside the cube, but the whispers neither shook nor ceased. She thought about what Van Hanlin had taught her in Intro about searching to find the visibility of sound, and then the trajectory would lead to the source. She studied the night air, and from the center of the field sparks of calligraphic letters escaped into the night, dissolving and quieting once the world broke them apart. She slowly crept close enough to find a black chest the size of a shoebox nestled in the overgrown grass.
This had to be a joke.
She waited, thinking someone might jump out and claim the babbling box, but her senses could only catch the chattering teeth of the runaway girl. In the distance she heard a faint buzz of energy, like the humming of electricity. Across the field, the runaway raked trembling fingers through her disheveled hair.
What’s the matter? The voice was comforting, like the familiar beats of her favorite song.
“Chase?” she called out before remembering he wasn’t there. This was not a dream. Chase , she thought in her head.
Alex. Are you okay?
She wasn’t dreaming—at least she didn’t think she was, so how could she hear him?
The buzzing returned. This time, it was no more than a few yards away. Whatever it was, it was fast. Her intuition slapped her with fear.
Jonas appeared so quickly that Alex was in his arms before she even realized he was there. He cradled her tightly like someone, or something , was about to rip her from his grasp.
He breathed panic into her ear. “Don’t make a sound.”
Someone emerged from the dark protection of the woods and floated noiselessly into the clearing. When the moonlight illuminated his features, Alex swallowed the terror that clawed its way up her throat.
“Don’t scream,” Jonas commanded, tightening his grip.
In the glow of the moon, the carcass of the man seemed faded like an old photo. His pasty hair hung lifelessly, stringy and wet, draped over his face. He came to a stop directly behind the lost girl. She shivered, sensing the danger she couldn’t see.
He slowly moved around the girl, watching her with sunken eyes. Then, he turned abruptly to focus on Alex and Jonas. Both pupil and iris were coal-black, and framed by webs of crimson mazes spiraling demonically. For the first time since she’d died, Alex wished for her human eyes, which could not have seen this man. Could she even call him a spirit?
Jonas clutched his fingers around Alex’s chin, pulling her face to his. His eyes locked into hers. “Don’t look at him. Look at me. Are you listening?”
She nodded. She wouldn’t dare open her mouth to allow the scream to escape.
“When I say the word, you run. As fast as you can,” he ordered. “Don’t stop.”
The “you” stung Alex, setting her voice free. “What are you going to do?”
“I’m going to distract him.”
There came a loud zap. Alex snapped her attention back to the man. His body shook violently, traveling towards them, convulsing in its electrocution, his stringy hair whiplashing his face.
Jonas flung Alex behind him and began to run forward.
“No!” Alex thrust out her arms and shoved the air in opposite directions, separating Jonas from that monster. The force of it pushed into the ground and rose, curling into two waves, knocking Jonas to one edge of the clearing and the demon to the other.
She swatted away the dirt kicking up in her face, in time to see the heap of a man straighten. He rushed forward, writhing, opening his lips, baring his gray teeth. From his mouth spewed a bloodcurdling screech.
The shrillness of the wail sent shocks through Alex’s head. She fell to her knees and couldn’t stop herself from screaming out in agony.
Alex! Chase resounded in her mind.
The word dulled the screech only slightly before the pain sliced her head again. The scream was alive, tearing into her scalp, scooping out pieces of her mind, and stabbing her soul. She was going to die here, she realized. Without Chase. But the pain was so intense, she didn’t care. She just wanted it to end.
Alex? Chase’s words were strained now. Where did you go? Alex!
She gasped. With each word, the scream became more hollow and distant. She needed to form a word in her thoughts, but it seemed impossible. How could she think? How could she talk? She couldn’t remember how.
Alex , don’t listen to it. Talk to me. How was his voice so strong? He was always so much stronger than she was. SPEAK ! he commanded, but she couldn’t think through the mind-numbing pain. Then she thought of the one word she could say even if she did lose her mind. The most beautiful word in the world.
Chase .
He was urgent now. Talk to me.
She tried, but she had no words, no thoughts.
Come on, Alex.
Chase. It was all she could say, and it wasn’t enough. She could feel the whipping threads of the demon’s hair, and smell the stench of his breath as he wrapped his body around her.
Her mind snapped shut.
It was like a blackout, except everything turned gray. Alex blinked her eyes several times, but a sheet of ice blocked her vision. It surrounded her, constricting her movements, forcing her to keep her palms pressed against the glacial coffin. The numbness began in her fingers and toes and spread throughout the rest of her.
The unbearable ache gave her the sudden urge to scream, and writhe, and fight, until a figure appeared on the other side of the ice. It was impossible to see who it was, but they placed their hands over hers, and Alex began to feel the tingles of warmth—of life—in her fingers. She heard a crunch as the ice cracked.
BOOM ! An explosion resonated from the depths of the ground. The grayness disappeared, and she found herself back in the field.
A dozen figures appeared and positioned themselves equally around the perimeter of the clearing. A small girl with the definition of an Olympic gymnast broke ranks and twirled through the air, sending strikes of energy to lash the screaming demon. She spun gracefully but viciously, kicking one foot in the direction of the spirit’s deranged face. There was no impact, but the force generated a loud smack . The other foot followed, knocking the screaming man to his knees. She swung her arms, chopping the wail with an invisible sword. The pieces of it turned to jagged sparks, charring the night. The man collapsed further, breathing heavily, and glaring up at the girl who stood defiantly with her hands extended.
A uniformed man stepped forward. Like the rest of the spirits who had appeared, he was dressed in combat attire. Everything about him was pristine, except for his hair, which stuck out at awkward angles. “Let’s hurry up and get rid of it.” He turned to Alex, still on the ground, gasping for air she didn’t need. She wrapped her arms protectively around herself to block the chill, but her teeth chattered uncontrollably.
The army flinched when Alex tried to stand. They were poised for fight, although why they would choose Alex as the target, she didn’t know. The man that seemed to be in charge remained hunched in anticipation.
Professor Van Hanlin suddenly emerged from the trees with his hands in the air. “Stop!” he shouted. “She’s one of ours!”
Some of the guards turned to salute.
“Officer!” one of them greeted him.
“Don’t break ranks,” the messy-haired guard commanded.
“You don’t need to fear her,” Van Hanlin said.
“She was exposed to the scream for nearly an entire minute!”
A minute! It had only been a minute ?
“Did you not hear the banshee scream?”
Banshee.
“And yet they both stand here unscathed, civilized still.”
“Both?”
Van Hanlin threw out an arm in the direction of Jonas, who was still crumbled at the outskirts of the clearing.
“Impossible,” the same guard spat. “She was right in front of it!”
The guard in charge gave Van Hanlin a stiff nod. “Who is she?”
“They are children .”
“It’s impossible for an untrained child to withstand the direct shriek of a banshee for so long.”
Van Hanlin raised his palms in bewilderment. “I cannot explain what I didn’t see. You were the ones to swoop in on the scene.”
The guards continued to drift forward, slowly melting into the space between themselves and Alex, confining her.
“You don’t know who she is,” Van Hanlin said. He didn’t try to disguise the awe in his voice. “You saved her, Federive.”
Alex’s mind shifted through its contents featuring a bronze plate on the wall of the Brigitta hallway. Kender Federive, Service General.
Kender Federive’s long ponytail rippled behind her like a superhero’s cape. “What do you mean, who she is ?”
A booming voice suddenly erupted from the shadows. “I’m afraid this is my fault.”
A thick man clamored into the clearing. It was the brute whom Alex had seen on her first day driving out the lure birds, the one pictured in the tableau of the city. Why were all these people here? And where was everyone two minutes ago when she needed them?
“Westfall!” Van Hanlin exclaimed. “What are you doing here?”
The members of the guard buzzed with interest.
Westfall gazed at Van Hanlin in contempt and leaned toward the girl who had crippled the banshee. “Lieutenant Federive warned me about the sightings of banshees close to town. The Patrol was stationed here.”
“Why weren’t we warned?” Van Hanlin demanded.
“Certain staff members were warned. Why do you think I’m here?”
Van Hanlin threw his hands in the air. “How about warning the professors who had newburies in the woods?”
“You don’t have the best track record.”
He pointed at the guards. “I used to be one of you, for goodness’ sake! I led your patrol!”
The messy-haired leader took a step closer. “A newbury angered the banshee?”
“Knocked it clear on its head.” Jonas ambled over to Alex. With him next to her, Alex finally felt comfortable enough to stand up straight.
Some members of the Patrol crept closer to her cautiously, still trying to get a better look. The closest guard elbowed the guy next to him and pointed at Alex. “Do you see what I see?” he murmured.
“You should educate your newburies on the dangers of the world before you lead them to open pastures,” the leader said.
“She strayed,” Van Hanlin explained.
“You know all about that, don’t you?” Westfall said.
“Don’t start with me about—”
Westfall cut him off. “Straying is the nature of a child, which is why you are supposed to keep such a tight grasp on the newly buried.”
“No, that was the point of our job,” Jonas called, rising to his feet. “To follow the strays .”
Professor Van Hanlin surveyed the group with worry etched on his face. “Where is the human she followed?”
“She ran off that way,” Alex said, pointing beyond the trees.
“Both of you followed her?”
“I followed Alex,” Jonas answered quickly. “She didn’t know.”
Another member of the guard began to march directly across the clearing. “There’s a spirit lurking in the trees across the way. There, a few yards in.”
How would he know that?
“Who?” Westfall asked.
“I aim to find out,” the guard called over his shoulder.
Westfall took another step tow
ards Alex, but unlike the others, he wasn’t trying to get a closer look at her. He stood at an angle to block her from the patrollers.
The guard reappeared, carrying a portly boy by the cuff of his shirt. Alex squinted to make out the form. “Reuben?”
Reuben Seyferr covered his face with his sausage-like fingers and peeked through at his horror movie of an afterlife. “I heard the banshee scream. I was curious.”
“What are you teaching these kids?” one of the patrolman exclaimed. He looked charily at Van Hanlin, who sputtered, “That’s not my department!”
Some of the guards swayed from side to side like pendulums, trying to catch a better glimpse of Alex. More of them pointed, and others began to whisper.
“The children should come with us,” another member of the Patrol said. “We need to make sure they are okay.”
“Don’t worry about it,” Westfall said. “Take care of the banshee. I can escort the children to the medical center if need be.”
“They should be questioned,” the patrolman argued, trying to smile, but the messy-haired guard held up his hand.
“There was no crime. The banshee should not even have been here. They didn’t know. Besides,” the messy-haired guard added with a glance at Westfall, “the Patrol can’t override an order given by an Ardor Service member.”
Westfall gave Van Hanlin a shove. “Come on. Let’s get these children out of here.”
The patrol turned to leave, stealing glances back at the field, some ogling Westfall, some still trying to peek at Alex.
Westfall ushered all three newburies back in the direction of the mansion with a push that had much more force than necessary. “That was not supposed to happen,” he growled under his breath.
Alex could only wonder what he was referring to. What she wondered more was how this whole scene could play out right in front of that little black box, and no one noticed it sitting there, blatantly out of place, spitting its thoughts at them.
No one had even looked at it.
The Patrol recommended that the teachers eliminate the woods from the festivities, but the commotion around town was too intense to ignore. Natives and tourists alike were raving about the “closing act” and how the voices were the greatest illusions they had ever experienced. Skye told Alex that in September and October alone, the insignificant town of Moribund typically brought in more tourism than Redwood National Park did year round, and now the number of guests had risen higher than ever.
Thus, Van Hanlin promised to oversee the woods at all times. Not that Alex could have escaped again if she had wanted to, because her peers were so interested in the banshee encounter. Her reputation had quickly morphed from “bench girl” to “banshee girl.” At least that sounded slightly cooler.
But when spirits asked her about what happened, the topic always seemed to shift to Reuben:
“How could he be so stupid?”
“He’s not too bright, that kid!”
“Why didn’t he try to help you?”
“Who actually hears a banshee and then goes to find it?”
And Reuben hid in the corner of the yard, his mouth downturned and his eyes despondently turned away from his hecklers. Alex attempted to comfort him once, but he stood up without a word and walked away.
At the mere sound of the word banshee, Alex could still hear shrill shrieking, and it felt like shards of glass being plucked from her brain.
Van Hanlin ordered her to stay at the manor and “direct” the chasings outside, which was completely pointless and utterly boring. How much direction was needed to follow sporadic groups exiting one door? The Patrol captured the banshee, and it wasn’t like the monster targeted her specifically. She’d been in the wrong place at the wrong time, so she didn’t understand her punishment.
“I don’t think it’s a punishment,” Skye assured her. She’d sought out Alex in order to give her a bouquet of chamomile flowers. Alex didn’t ask why, because she figured she probably wouldn’t understand the explanation anyway. “But people do seem to be a little freaked out by you.”
“Nah.” Skye flashed a dazzling smile. It nearly glowed in the moonlight. “I don’t scare easily. I do feel badly for you, though, sitting here and twiddling your thumbs. It can’t be stimulating.”
“That’s an understatement.”
“Duvall asked me to fetch a dozen buckets and shovels, but I don’t really feel like going all the way to the shed. Are you allowed to do it?”
Alex jumped to her feet. “Probably not, but I’ll do it anyway.”
Skye tilted her head to listen for something. Alex wondered if she could hear the pounding of Alex’s nonexistent heart. She desperately wanted to get back to that clearing.
Thankfully, Joey Rellingsworth poked his head out from the doorway and warned the girls that another group of guests was about to exit the mansion. Skye sighed and tugged her mask from her pocket.
“Take this wave,” Alex suggested, “and I’ll go run and grab the stuff.”
Alex nodded. She couldn’t believe she was doing this alone, but the whispers called to her the moment she stepped away from the mansion. They urged her along through the darkness.
When she reached the field where the chatty box waited, she marched forward and kicked it for causing her so much grief. It slid across the grass like a hockey puck and collided with a tree, spewing its contents onto the ground.
Alex picked up a dilapidated black and white photo of two young boys grinning widely. One was dressed in shabby play clothes. Suspenders held up his loose slacks, overlapping a dirty white smock. The other boy was adorned in wealth. His slicked hair shone brighter than his shoes, and he had removed his suit coat and slung it over the shoulder of his perfectly cuffed dress shirt.
The box brimmed with aged brown envelopes tied together with string. Alex carried it back to the center of the clearing where the glow of the moon could provide a reading light. She extracted a random envelope and slid her fingers underneath the flap, breaking the wax seal etched with a capital E. The brittle paper was decorated in the most artistic handwriting Alex had ever seen.
Dear Sephi,
Professor Melbourne is late for the morning session as usual, and I am once again avoiding Paul Bond and his embarrassingly zealous offers to proofread last week’s work. Knowing his family’s defiled history, I’d be likely to fail the assignment if I allow him to touch it. Thus I’m writing you this note to make it seem like I’m immersed enough to disregard him.
I sit here among the mindless prattling, and it’s apparent that plenty of rumors still swirl about your death, even though you’ve been here for several months. The newburies continue to gossip about Ulysses S. Grant, especially the dead soldiers to my left, who claim they knew about your involvement in the war.
The cockroach of a girl who sits in front of me was far too eager to hiss loudly about what had happened to your family. Let me express my condolences. Now I know why you encourage me to conceal my own talents. To think that a person is hunted for having extraordinary gifts! It dishonors your family the way people talk.
Admittedly, I was most annoyed with the uproar of excited hysteria during your arrival. I was insanely jealous that you were stealing all the attention, but that was before I saw you. The moment I caught your gaze, I never wanted to let it go. I felt like I’d known you forever, and you filled a piece of me that I never knew I was missing.
Will you meet me again tonight?
Alex let the paper rest in her lap and it retracted, curling itself back into a protective bud. The recipient of the letter was dead. These were written by a spirit.
Alex snatched the next letter from the stack.
It must be difficult to be so well known. Especially as a child. It’s a bit tragic that you can’t simply be left alone. You handle the burden with such humility and patience. It only makes my affection for you stronger.
I’ve put some thought into what you’ve said to me. That you are not encouraged to develop friendships with anyone here. They just want to isolate you; they want your talents for their own. You’ve never been given the chance to make your own decisions. To follow the paths you see before you.
I’ve seen how they try to detach you from the rest of us. Duvall especially. But you also said that despite your efforts to avoid me, you already knew what was going to happen between us. So why do we need to be given the chance to let it develop when it’s already full grown? Let’s skip the beginning.
Here’s to backwards thinking.
Eviar
I caught her staring again, sneering at me in revulsion like vermin infesting her classroom. I sat oblivious in class, without the faintest notion of why there were shivers creeping down my spine, and then I realized the witch held me in her gaze. Perhaps she sacrificed a goat and drained the blood of a virgin to coax the devil into revealing her foes. Thus I have more respect for the slugs she adds to her potions. The school can label it “alchemy,” but “witchcraft” is more like it. I hate that you allow her to have so much influence over you.
Alex was more than intrigued. Duvall! The Bond family! All from over a century ago. Alex lowered her gaze to another sheet of yellowed paper.
I hate to admit weakness, but you have completely taken over my mind. I swear on my soul that every inch of my desire belongs to you. Even if I tried to change it, to deny it, I cannot envision a future without you in it.
I understand that you are apprehensive, and with good reason. You have never been allowed happiness. You are feared in death more than you were feared in life. But I promise that I will always be the one to protect you. We just need to find where we belong. A large city may not be the most favorable. Perhaps a smaller one like Vorbild or Paradise.
Paradise. Where had Alex heard that before? Her brain began to shuffle through its filed memories, and finally an image remained. Her psychology classroom, but she hadn’t a clue why.
There was something about these letters that was completely consuming. They called to her like a siren song. Alex reasoned that it shouldn’t matter if she took them with her. Beyond doubt, the box wanted her to find it, and if everything she’d heard about visibility was true, some part of her must have been looking for the box if she could see it when no one else could.
She felt it no crime when she stood up and tucked the box securely under her arm and made her way back to the lights of the manor. Oddly enough, during the journey back through the trees, she felt an iambic pulse, as though the box had a heartbeat.
I will admit to only you how much I miss home. I vividly remember my father’s intense eyes and the warmth I felt when I was around him because I adored him so. His words had such eloquence that everything and everyone around him fell silent the moment he parted his lips to speak. I have memories of curiously peeking into our study, which was filled with the clinking of ice in liquor glasses. This was where my father typically presided over a meeting of the most esteemed gentlemen in a town he himself founded. He would smile at me over the misty swirl of cigar smoke.
I pray that I may always recall the pride with which my parents gazed upon me. I wish you could have known them. I can only hope the death of their only son did not destroy them.
Gideon brings me comfort. I know you are wary of his sense of humor, but he has been my companion since I can remember. His mother worked in our kitchen, and every opportunity I could muster was spent with him, scrounging some sort of a childhood among incessant lessons to become high society royalty. One day, I will go back to retrieve the only picture I had of us. We have shared so much, including the unfortunate illness that led us here together. I am thankful to have something about my past to hold on to. I think I need to be reminded of myself. Unfortunately he has befriended one of those obnoxious DeLyre brothers. Ben DeLyre is not quite so much of a nob as the others, but he seems to share Gideon’s immaturity and inclination to trickery and cabbaging. Regretfully, their alliance will make the Darwins less prone to assisting me in finding my ancestry because the Darwins and DeLyres continue to clash.
They must know something. I wouldn’t be able to do the things I can do if my family history was not extensive.
“Alex?”
She snapped back to reality.
“Are you all right?” Gabe asked.
“Oh. Yeah.”
“You’re really into that homework, aren’t you?”
She gave him a sheepish grin, stuffing the letter she’d been reading under her ABC textbook. It had become routine for Alex to spend her evenings outside at the ballparks. She would have been perfectly content to lounge all evening in the warm Brigitta vestibule, but the Lasalles preferred the fields, and she preferred to be wherever they were. She clutched to whatever pieces of Chase she could.
That night, something felt different. A good sort of different. Though she’d grown accustomed to her newly sharpened senses, Alex couldn’t quite trust the scent of hope gripping the coattails of the night.
“I’m sorry. What were you saying?” she asked, folding the letters.
He tilted his head towards the field in front of them. “I asked if you saw that play.”
“Oh,” Alex muttered. “No.”
There came a commotion at the foot of the stands, and Gabe ducked behind his book, cursing under his breath.
Gabe peered around the side of his book. “Romey’s coming. I missed front desk detention this morning because I was helping Jonas.”
“With what?”
Gabe shushed her and tried to crouch further behind his text. Like anyone would actually mistake his blonde curls for someone else’s.
Romey came to a stop beside them. “Hello, you two.”
Alex smiled. She liked Romey and the visible softness surrounding her, smoothing the roughness of the world wherever she went. “Is everything okay?”
“It would probably be better if I hadn’t been pulled from a directors’ meeting this morning to babysit an unattended desk that I’d already staffed weeks ago.”
“Sorry, Romey,” Gabe mumbled from behind his book-cover shield.
Romey didn’t seem to accept his apology. “You have double duty at front desk tomorrow night. Be there at 6:00 p.m. sharp.”
Gabe groaned.
“Like I said, double duty. And the next time you decide to blow off an obligation, give me a heads up or your punishment will be much more severe.” Romey ambled away, excusing herself because she was due to supervise the fields.
Right at that moment, Alex felt a marvelous jolt of anticipation. It was the kind of feeling one experiences on only a handful of occasions in a lifetime. Like a first kiss or a last dance. The kind that one wants to relive over and over, even if the memory is less satisfying than the real experience.
She knew Chase had arrived before she even saw him.
Each of the Lasalles was mesmerizing in his own way. People were always drawn to them, hypnotized by the melody of their movements. Chase happened to be the worst of them. All he had to do was turn his eyes on someone and they were smitten. And watching him walk out onto the field, Alex knew she had been wrong about the beauty of this world, the colors, the buildings— to rank them the way she had—because Chase himself was without a doubt the most beautiful thing her eyes had ever seen.
He must have felt her too, because he stopped midstep to scan the valley until he found her face. He stood dumbstruck, with one hand over his mouth in disbelief and the other hand clutching a bag that dangled closely to the ground.
He was even more stunning in death. Alex would never have imagined this could be possible. His blue eyes filled the air between them, the vibrancy of their color somehow more brilliant than any of the palettes she’d seen yet as a spirit. They flooded Alex’s sight, tinting her world a stunning hue until he blinked and lowered his hand. His lips parted and soundlessly mouthed her name.
Alex couldn’t catch her breath, not that she needed it anymore. She only noticed the discomfort because her chest began to heave and air ripped through her lungs in sharp gasps. As she said his name, it wasn’t accompanied with a taste of loss and suffering for the first time in so long. Instead, it contained the simplicity of recognition, of happiness. It tasted wonderful.
The moment was not lost on Gabe, who glanced from Alex to Chase and back to Alex, sighing loudly. Down on the field, Jonas crossed his arms and stared at his brother, who didn’t divert his eyes from Alex even when a ball clocked him right on the crown of his head.
Gabe wrung his hands as Chase greeted Romey, who hugged him tightly, like a son. It appeared she was trying to be firm with him, but her warm, maternal mannerisms interfered. Although she shook a reprimanding finger with one hand, she reached up with the other to smooth out a stray piece of his hair.
Every few moments, Chase found Alex in the stands and when his eyes met hers, the world seemed to stop, and his face would break into an iridescent smile.
“I’m really not used to that,” Gabe said quietly.
“I’d forgotten that Chase could smile.” The spectators around them erupted in response to a play Alex didn’t care to see. “Will you do me a favor? You of all people know how Jonas can be. Don’t go off riding into the sunset kicking dirt in his face just yet.”
“You know exactly what I mean,” Gabe said, intercepting another of Chase’s smiles to Alex.
“Chase is my best friend,” she replied softly, feeling heat in her cheeks. But the flame was obvious, and no amount of watering down her words would extinguish it.
“In the grander scheme of things, this isn’t about you. Jonas resents us. Me. Kaleb. Chase.” He hugged his book against his chest. “I don’t want him to think that Chase has stolen something from him. I don’t want it to get any worse.”
“Why would he think that?” She recognized the foolishness of her question. Jonas was territorial and spiteful, and she knew she’d allowed him to get a little too close.
“I guess I didn’t really know the extent of it until about two minutes ago when Chase looked at you the way he did. And then the way Jonas looked at Chase.” He turned away to watch the field again. “But I’ll speak to him. Do you think you can just keep things under wraps for a little while? Jonas is pretty mercurial. With any luck, he’ll be preoccupied with something else soon enough.”
“Under wrap
s? What do you think is going to happen?”
She could not stop herself from smiling merely considering the possibilities.
In the final few months of Alex’s life, it had been nearly impossible to distinguish reality from the illusions her mind created. This was the reason she started “cheeking” her pills at the Eskers. Yes, she longed to hear the whispers of Chase’s voice in her head, but how could she know that they were real? The pills they forced down her throat distorted her world into a gray Salvador Dali painting, and she didn’t want to forget the last time she’d seen Chase alive. That night, for certain, she knew had been real.
It was all because of a dance. She’d been to many before. The dresses, the drama, the partying—this one changed everything. Chase had jumped out from the limo and walked toward Alex like Prince Charming himself. Too bad he wasn’t her date.
“Jonas better stand next to you all night,” he advised.
“Where is Jonas?” Alex asked, but when she slid into the car, she smelled the reek of alcohol right away.
“There’s my pity date,” Jonas laughed. Alex was unsure of who the pity party was in this case. He’d asked her to go with him because he wanted to win back his ex-girlfriend, and he said Alex wouldn’t make her jealous. He opened his suit coat to reveal a flask. “Want some?”
“I do!” Posey Freebelanger shimmied her way onto Chase’s lap. She’d bombarded him in the hallway after the word spread that Jonas was taking Alex to homecoming. Posey had pined for Chase for years, and when she jumped at the opportunity, Chase was far too polite to let her fall from cloud nine.
“Hey, Posey,” Alex said through her teeth.
“Our boys look nice, don’t they?” she said, taking a sip from the flask and scrunching her face. Her eyes filled with tears as though the alcohol was leaking right out of her.
Our boys? Alex didn’t like to share them, and if Posey truly knew them, she would realize that their fancy get-ups wouldn’t last for long. As soon as Jonas and Chase sauntered through the front door past the teachers, jackets came off, ties were loosened, and sleeves were rolled up. The boys in the room stared enviously, and the girls reapplied their makeup, inadvertently inching closer to the Lasalles like water to the pull of the moon. They would wiggle their hips on the dance floor to push their way to the closest brother. Liv Frank was the only one candid enough to comment, giving each of the other girls a snotty onceover.
“These girls look like they charge by the hour,” she said, loud enough for them to hear.
The girl closest to Alex angrily pursed her crimson lips, which were as red as her dress, but before she could retaliate, Liv beat her to the punch. “Wait, that’s mean.” Liv gestured to the girl’s attire. “A prostitute wouldn’t even wear that.” The girl stalked off, and Liv grinned deviously. “You’re welcome, Al.”
“For what? You didn’t get the girl away from my date.”
“Of course not,” she said with a knowing glance. “I got her away from Chase. I was hoping she’d make a comment about my plus size dress so I could belly bop her off the dance floor.”
The music slowed, and Chase extended his arm, pointing to Alex from across the circle. He grinned and made his way to her.
She allowed herself to fall into him, and allowed herself to inhale the fresh scent of his crisp, white shirt. She closed her eyes and pretended for a moment that he was truly hers.
“What are you thinking?” he asked.
“You look handsome.”
“Nothing compared to you. Every guy in this room is trying to sneak a peek at you.”
“Okay, don’t believe me. I feel like I should be blocking you right here.” He flattened his hands against her back, and Alex felt her body soften underneath him. “Or actually maybe here.” He lowered his hands. “Since that’s where everyone is looking anyway.”
She smacked his arm. “Shut up. I look like a ten-year-old.”
“You’ll never believe me, will you?”
Alex decided to change the subject. “Where is Jonas?”
“Taking shots in the bathroom with my date. He’d never get away with acting like this if Kaleb and Gabe were here.”
Alex wondered whether to blame Chase’s chagrin on his date leaving him, of Jonas being responsible, or of Alex questioning Jonas’s whereabouts. Maybe all of the above. They swayed to the sappy music for a few moments before Alex pulled back to examine him, wondering if studying his face might reveal his true thoughts.
He stared right back at her, and just when she thought he couldn’t be any more gorgeous, his attempt to be serious failed, and his smile illuminated the room like a burst of sunlight. “What did I ever do to be lucky enough to have you look at me like that?”
Funny. She’d been thinking the same thing about him.
“I can’t describe it.” He twirled her hair around his fingers. “Words wouldn’t do it justice. There usually aren’t words to describe you, Lex.”
She marveled at the irony of this beautiful boy saying these things to her. “Why are you saying this now?”
He spun her around effortlessly and then gently lifted her arms to place them back around his neck. “Because the feeling I get when I see you is kind of like riding on a rollercoaster. It’s just a small dip in my stomach, but the adrenaline is enough to make me wonder.”
“Wonder?”
“If I never really knew how to interpret you at all.”
Then why don’t you love me? she wanted to scream.
She didn’t get the chance, because their dates returned, stumbling into the crowd together, and Alex spent the rest of her evening trying to hide Jonas from the chaperones. Babysitting him was exhausting, and she was relieved when the dance finally ended.
The limo took them home to meet up with Kaleb and Gabe, who had returned from college to watch their brothers play in the homecoming game. They planned to drive to the after-party across town. Alex had packed a change of clothes so she wouldn’t need to go into her house and tiptoe past her father. Good thing because Jonas decided to vomit all over her driveway.
“At least he held it until you got home,” Gabe said. “The limo driver would have charged extra if he got it in the car, and Mom would have really loved that.”
Chase eyed the clothes in Alex’s hand. “Go use my room.”
“Don’t you need to change too?”
“Yeah, but I’ll wait.”
“You’ve seen me change before, Chase.”
He swept his arm up and down. “Not when you were wearing that.”
Alex crept into the house and up the stairs, hoping she wouldn’t wake up Danya and David. She figured if their son’s violent puking wasn’t enough to disturb them, she should be safe, but just in case, she didn’t shut the door all the way, knowing it sometimes jammed.
Unlike his brothers’ rooms, which were shrines to their accomplishments, bedecked with trophies, titles, and crowns, Chase’s room was a shrine to everything he loved. His awards puddled in the corner, while his walls displayed team photos, family pictures, banners from pro sports games, and tickets from concerts. Alex allowed her eyes to linger on a photo of them on his desk. His arm was slung around her, and they smiled so widely that their noses scrunched and their eyes squinted shut. Neither of them had front teeth.
She focused on the picture so intently, she didn’t notice Chase standing in the doorway until his soft voice startled her.
“I wondered what was taking you so long,” he said, glancing over his shoulder to be sure his parents weren’t approaching.
Liar , she thought while Chase stepped into the room. She’d barely been there for two minutes.
Alex flicked her chin toward the window. “What’s going on out there?”
“More like what’s going out.” He stuck out his tongue in disgust.
“Serves him right. Do you want me to go change in the bathroom?”
“Nah.” He shook his head, grabbing a pair of shorts from a basket of clean laundry. He reached down and began to unbutton his shirt.
“Chase … ” she warned him.
He laughed and finished changing. Alex waited for him to leave the room, but instead, he took a seat on his desk.
“Here.” He motioned for her to spin around.
Her stomach fluttered, but she did as she was told. She backed up against him, placing her hands gently on his knees, which were on either side of her. His breath tickled her neck and sent chills throughout her body. He touched her right shoulder and gently removed a strap, allowing his fingers to touch her skin longer than was necessary. He held up the right side of her dress and used the other hand to remove the remaining strap.
“Now what?” Alex breathed.
“Well, you’re holding up my dress, but my clothes are over there on your bed.”
“You’re going to kill me,” he said in a hushed voice.
Alex inadvertently lifted her arms at the same time he did, and her dress fell to the ground in a pretty blue heap. She heard Chase draw in his breath before she spun around. When she did, she was surprised to find that with all he could be staring at, his blue eyes were focused on her lips. Her head was spinning like a roulette wheel, and she wondered if they would finally take this gamble.
He lifted one hand and brushed his fingers over her cheek. Then he lifted the other one and held her face in his hands gently. He bit his lower lip and leaned in towards her, only to press his forehead against hers and sigh in exasperation.
She didn’t have the courage to look at him. She ran her palms up his shirt until they reached his neck. Wrapping her arms around him and holding the base of his head, she raked her fingers through the threads of his hair.
When he first moved his hands down her back, his touch was so light that his fingertips barely grazed her shoulder blades, but when they ventured back up, he seemed to give in to it all. He pulled her even closer, touching the skin that electrified against him. He must have opened his eyes then, because she felt his eyelashes tickle her brow.
She didn’t know what would have happened if a loud cough hadn’t erupted from outside the window. It was followed by a stomach-churning splat, so she determined the culprit was Jonas.
“We’re going to be in trouble.” Chase hopped off his desk, walked over to his bed, and grabbed her shirt. “Put this on before you really do kill me,” he said, tossing it across the room.
Alex nodded, still in a daze.
As they walked outside, Alex dusted herself off, worried she still had Chase’s handprints all over her. Kaleb sat in his jeep, comically holding up his wrist to tap his watch. Posey was sitting shotgun, barely conscious, while Kaleb’s girlfriend Mackenzie tended to Jonas in the back seat.
“Jonas is actually coming?” Chase marveled, opening the door to Gabe’s car.
Gabe’s date reapplied her lipstick while Chase and Alex climbed into the back. Alex turned her head to the window, almost embarrassed. She felt Chase buckle her seatbelt for her, perhaps in a feeble effort to keep her on her side of the car. But in the end it was he who ventured toward her. Only a minute had passed before Chase undid his own seatbelt and slid next to her. She started to unbuckle hers, but he rested his hand over it. “No,” he whispered, “you stay safe.”
He brushed his lips over the nape of her neck, her collarbone, and her jaw but never kissed her lips. The streetlamps whizzed by every few seconds, threatening to expose them, but Gabe was babbling on, either trying to make small talk or trying to ignore what was going on in the back of the car.
When they arrived at the party, Alex guiltily ventured toward the jeep to find Jonas snoring, one arm draped over his eyes.
Mackenzie had a look of disgust on her face. “He said he was done throwing up, but I’m not so sure. Technically, you’re his date, so you should be taking care of him.”
Jonas groaned loudly, and Alex was reminded of all the horror stories on the news about kids who had passed out and choked on their vomit. “Maybe I should stay out here with him.”
Chase turned to Gabe. “Give me the keys. I’ll take him home.”
Gabe hesitated, eying his brother in silent reprimand.
“Oh, come on,” Chase said. “You’re not going to make Alex sit out here and babysit him all night, are you?”
Kaleb snickered. “You better hope Mom doesn’t wake up and look outside to see you driving.”
“She won’t.”
Gabe reached in his pocket and extracted the keys reluctantly. But when they attempted to move Jonas to the station wagon, he awoke. “I’m driving.”
“Sure bro,” Chase said with a smirk. “Except in this car the steering wheel is on the right.” He shoved Jonas into the passenger seat and rolled down the windows to give him some air.
When they turned onto the main road, Alex’s teeth began to chatter, so she curled up in the back seat.
“Are you cold?” Chase asked, reaching to turn on the heat. “You need some color back in those cheeks. You look like a corpse.”
His wording hit a little too close to home. Even he knew it. He winced like he’d stung himself.
With each passing street light, Alex took the opportunity to stare at his reflection in the rearview mirror. If only that would help to reveal his thoughts. Shivering, she covered herself in Gabe’s jacket. “I read an article the other day. This woman in New York, she died at twenty-eight. Arterial rupture.”
His eyes flashed angrily. “I told you to stop reading that crap. You could live to be older than me.”
Unlikely. They both knew that.
“About tonight … ”
He shook his head. “Don’t do that.”
“Don’t plan to move backwards. I’ve thought about this for a long time.” He glanced over at Jonas when he said it.
“You know it isn’t a good idea.” She would die, and then where would he be?
“I tried to say something to you once a long time ago,” he said. “The beginning of ninth grade. I wrote you a note in your Shakespeare book. I even wrote it in iambic pentameter. It was so lame now in hindsight. And embarrassing. I’m glad you didn’t read it.”
“What did it say?”
“What do you think it said?”
“I don’t know. I never got the note.”
“Of course not. You lent your book to Becca Blackman, and then I had to fight her off because she thought I wrote it for her.”
“Then why did you date her?”
“Because the day Becca walked up and asked me out, you stood there and said nothing. You smiled like you didn’t care.”
“What was I supposed to do? Pull her hair?”
Chase shook his head. “It wasn’t the right time anyway. I should have known better.”
“Why do you always think you need to be so perfect?”
Chase twisted the knob to the volume of the radio. “What, buddy?” he asked.
Jonas stirred in the front seat. He turned to look at her, smiling. “Al-ex.”
“Hey, Jo.”
Jonas poked his brother’s cheek. “Isn’t she the prettiest girl you’ve ever seen in your life?”
Chase’s hands were suddenly tight on the wheel. He gave one stiff nod of his head.
Jonas flopped back against his seat. “Alex, will you marry me?” he said sappily and began to laugh hysterically. Then he was asleep again.
The silence was brutal. “I’m sorry,” she heard Chase whisper, but she didn’t know if he was talking to her or to Jonas.
That was the last time she saw any of them alive.
Chase was to be escorted directly to Brigitta. Kaleb and Jonas bolted from the field without hesitation, and Gabe followed suit, shoving his books into his bag with the vigor of a shoplifter. The group remained uncommonly quiet while they rushed to the tower. Questions bubbled frantically in Alex’s mind, and she feared if she opened her mouth to unclog her voice those questions would boil over. They’d surely sear someone, probably Jonas.
There was little relief back at Brigitta. Chase was nowhere to be found, and after an hour of keeping a nervous vigil in the vestibule, Alex had had enough of the thumb-twiddling and nail-biting. She said goodnight to the boys and grudgingly began the dizzying ascent to the seventh floor. Strangely enough, the higher she climbed, the more at ease she felt.
There was a big difference between walking toward something and walking away from something, and her intuition suggested the former.
The door to her room was already open, waiting. The top of the frame dipped low as though the doorway itself was smiling. She immediately felt Chase and hurried inside, her heart racing. He stood on the balcony, leaning against the railing, and the boyishly handsome guilt that plagued his angelic face sent a throbbing ache through her damaged heart. She had witnessed the expression so many times before. It served as a reminder of every act of mischief in which they’d been caught, of every time she’d noticed him staring at her when he thought she wasn’t looking. It was a mere taste of the smorgasbord of things she’d missed, things she assumed she’d never have the privilege of seeing again.
The intensity of it all was too much. Alex seemed to be moving in slow motion as she collapsed. Chase rushed forward, and whatever caught her—his presence, his energy, his projection—was strong enough to send volts of electricity through every part of her. It was equally jarring and riveting. Alex heard a loud pop followed by tiny clangs, and shards of glass rained down from the sconce above them. The light bulb had burst.
Holding her close, Chase nuzzled into the nape of her neck which erupted in pleasant chills. Everything around them seemed to blur. It was only them, and death had never beleaguered them at all. She burned in bittersweet happiness, and for a second she waited for impossible tears, knowing they could never suffice the feelings she felt at this point anyway. She looked upward, mouthing a “thank you” for each time she had wished for this moment. He was here. She could see him. She could feel him.
This one moment alone was worth her seat in Heaven.
Chase finally let go with one arm and stared at her. She’d so often wondered lately what it would be like to touch him here in death, and for him to touch her. She worried it wouldn’t be the same. But it was better. Here she could feel the force of the emotion. A faint ribbon of smoke curled around them, the heat of their energy contrasting with the temperature of the room.
“How,” he whispered, “do I begin a conversation I never thought I’d get the chance to have, but one I’ve thought about every day?” His eyes never stilled, tracing and retracing her face. “In my mind, I never went over the beginning. For the longest time, I just keep asking myself how this could happen to us.”
“Chase,” Alex murmured, loving the taste of it. “We always knew the ending of our story wouldn’t be happy.”
“But how did it end up with me in a coffin and you in an institution?” He picked her up and set her on the edge of the armchair, grabbing her hands. “How did we become a tragedy?”
“A tragedy is something that wasn’t supposed to happen. I was supposed to die.”
“You weren’t supposed to die alone.” The creases in his forehead deepened. “Eidolon was like a curse for me. I had the ability to see you, and yet I was stuck here with these overbearing rules.”
Alex released one hand from his and stood to push her finger
tips softly to his furrowed brow, trying to smooth out the frown.
“But if they’d kicked me out, chances are I’d have ended up confined in something much worse than this city.” His eyes searched her face so intensely she could actually feel it pressing against her. “I’m so sorry it turned to hell for you back home.”
“Colors. There’s a gorgeous pink light surrounding you.”
She laughed lightly. “You’re losing it.”
“My God, I missed that laugh. It’s the same color pink. I can see it in your head. I’ve been seeing these colors in my mind since I got here.”
“My laugh is pink?” She didn’t know why, but she completely believed him. “Speaking of minds, how have you been getting into my mine?”
The corner of his mouth lifted. “I don’t think you’ve noticed, but you’re in my head too.”
He nodded. “Sometimes, during a thought or two, I feel you there.”
“I really don’t know.”
“And how were you able to get into my dreams?”
He let go of her palm and weaved his fingers through hers. She was never more aware of her senses. Desire traveled from his hand to hers, tingling up her arm and then down through the rest of her.
“I’ve heard the mind is much more open to possibility when it is sleeping. Are you angry about me being there?”
“No. But why my dreams? Why can’t I get into yours?”
“I’m sure you can. The mind is not always a one-way street. Although”—he grinned—“I don’t think I want you to know the things I dream about you.”
Alex felt her face grow warm, and she wondered if her mind could program her cheeks to flush.
There were so many mornings after Chase had died when Alex would awaken to find pillows propped up next to her bed, slouched in the position of someone beside her. Other times, she’d find things out of place. Pictures of them. Mementos. She’d always convinced herself that it wasn’t him, that she was just going crazy like everyone said. But now she realized the cool scent of him had been there in the room on those mornings, and her heart had felt as light as it did now.
“Why didn’t you tell me you visited when I was still alive? Why didn’t you say something to me?”
“You couldn’t have heard me, and if for some odd reason you had, I worried it would have broken you. It practically drove me crazy to be there, knowing I couldn’t really do anything to help you. Knowing your sadness was because of me.”
Voices outside caused him to flinch. “I should go.”
Alex felt a sharp panic. She stood quickly. “Stay.”
“I can’t do anything to jeopardize my space here anymore. I’m sure they’ll send someone to check on me tonight. I’d better get back to my cell —I mean my room.” He smiled, wrapping himself around her again, cradling her tightly. His voice flitted into her mind. I just needed to see you. He brushed his fingers through her hair, and before she could beg him again to stay, he was gone. But somehow she knew he was happy. She felt like she was holding a piece of his smile.
Alex was never more eager to wake up than she was the following morning. Gray light peeked through the thin crack between her curtains, casting an ashen spotlight on a note next to her pillow.
Just wanted to be the first one to tell you good morning. I’ll see you after sessions today.
Love, Chase
She couldn’t take her eyes off the word love . She carried the note during the entire agonizingly long day, feeling its warmth in her pocket. It felt like an eternity before she reached her final workshop. Madame Paleo favored the lecture style of teaching where she could bark at her newburies. Usually Alex took ten pages of notes within five minutes, but for obvious reasons, she found it difficult to concentrate.
The distraction only multiplied when the live version of her daydream came waltzing in the door, and Madame Paleo came to a halt midsentence. Chase had to skip over backpacks and squeeze past students to make his way down the aisle. He handed a note to Paleo.
What are you doing here? Alex asked. Her entire being itched, wanting him to be closer, wanting to feel the sparks of energy again.
Chase’s eyes pieced through the crowd until he found her and winked. I need to attend extra workshops. I wasn’t exactly the model student last year. With respect to my actions, they don’t think I’ve learned much about the past especially.
Many of the girls in the room seemed to be sitting up a little straighter. Some hurried to fix their hair, and some even projected their clothes to be more flattering. But Chase’s eyes stayed on Alex until Madame Paleo suggested he take a seat “in the front this time.”
Chase agreed solemnly. I need to be on my best behavior , he told Alex, choosing a front row chair. He acted oblivious to his effect on the female population. She could only see his profile from where she was sitting off to the right, but she thought the way he nibbled on his pencil in concentration was adorable. He must have felt her eyes on him, because every few moments, he’d give her a quiet Hey and smile while he took notes.
At the conclusion of the session, Paleo did not dismiss the class, but instead ordered them to report directly to the Grandiuse. Several students asked what was going on, but Paleo held up her arms and ushered them out the back of the room without explanation.
Alex remained in place, allowing her peers to stomp past her. And she wasn’t alone. She noticed a few groups of girls merging into their respective huddles and tracking Chase’s movements. Even from several tiers above them, Alex could smell wafts of perfume, hairspray, and intrigue.
Chase hurdled the railing in front of Alex and grabbed her hands to help her out of her seat. The jolt of his touch was addicting. She didn’t dare look at those other girls now. He swung an arm around her shoulders while following the flow of newburies through the dark hallway leading to the Grandiuse.
Chase’s brothers were already waiting at their usual table in the middle of the Hall, on display per usual.
“What is this about?” Chase asked. He slid onto the bench next to Alex. “I’m guessing it’s not a welcome home party for me.”
“It better be short,” Jonas grumbled. “I want to head to the fields before it gets too late.”
“It must be exhausting to be so cranky all the time,” Kaleb teased, but Jonas ignored him.
Chase was sitting so close to Alex that she could practically hear the purr of electricity between them. It was like a thunderstorm approaching, and Gabe kept lifting his palms upward, waiting for rain even though they were inside.
Many newburies tried to steal a peek at Eidolon’s favorite delinquent. Alex could see the trajectory of the whispers arcing like the paths of missiles over the heads of the newburies. Chase was the target. Everyone loved a bad boy. He’d stolen the title from Jonas.
Alex hoped the meeting would begin soon to divert attention. “Hey! What’s that guy doing at the podium?”
“Who?” Chase asked.
Alex pointed to the bulky man with the long hair who looked very out of place standing next to the prim and proper Van Hanlin. “That Westfall guy. He was the one who got rid of the lure birds, and he was there that night with the banshee. Jonas, look!”
Jonas glanced at the podium passively.
“Commander Westfall?” Kaleb asked in awe.
“Yeah, do you know him?”
“I just know of him.”
“He’s a fighter, right? Is he one of the Patrol? Like Van Hanlin?”
Kaleb shook his head vigorously. “No way. Patrollers are like cops. Westfall was a part of the Ardor Service, which is more like military, but far more exclusive. Think Navy Seals.” He swayed from side to side to get a better look. “I wonder what he’s doing here.”
Gabe raised his eyebrows, openly intrigued. Kaleb rarely spoke with such admiration about anyone. “I think the more appropriate question is why he’s been here without announcing himself. You say he was there the night with the banshee?”
“I wonder if you blew his cover.”
“He wasn’t exactly hiding when he took care of the lure birds.”
“No, but newburies wouldn’t recognize him. The Patrol certainly would. He’s the most famous member of the Ardor Service.” Gabe reached for a nearby book and began flipping through the pages.
Jonas was trying to appear unaffected, though he kept glancing up at the podium. “So what’s he doing at Brigitta with us babies, then?”
The question was answered moments later when Madame Paleo took center stage. “You are probably wondering why this meeting was called so abruptly and so early in the evening. Brigitta’s learning center has been given the honor of hosting a spirit from whom we can all learn a thing or two. He’s been generous enough to donate his time.” She beamed at the brute of a man standing next to her. “Ardor Westfall’s objective will be security, his specialty.”
“Look at Van Hanlin!” Kaleb cackled. “He’s pissed!”
It was true. Van Hanlin looked like he was ready to spit nails. The former Patrol officer prided himself on guarding the campus and maintaining order. The professors must have doubted his adequacy, to bring in someone else to ease the rash of misbehavior.
“Furthermore, Ardor Westfall has also volunteered to assist in your studies.”
Westfall stepped down from the platform and began crookedly to circulate the room.
“Assist?” Joey Rellingsworth asked.
“Teach. If we’re going to have a seasoned ardor on campus, we should put him to good use. Consider this your first physical education session of the term.”
“This is going to be fun.” Kaleb grinned widely, sitting up straighter.
Westfall still stood among them and began to speak. He didn’t need to be front and center. A podium wouldn’t provide any more attention than he already had. “As a spirit, your world is up here,” he rumbled, pointing to his head. “And physical feats are no different. It’s all a matter of mental manipulation. I assume the campus still honors the time-honored tradition to haze newburies during arrival. Although you can exercise your brain, your initial response to whatever object is thrown at you is a pretty relevant indication as to what you have to work with.”
All four Lasalle brothers glanced at Alex, but they quickly resumed attention because Westfall ambled past their table. He swept his brown hair into a ponytail, revealing smooth, ageless skin, with the exception of his brow. Even when he wasn’t frowning, the lines on his forehead were ever-present. Alex was surprised to find that this man who had supposedly served Eidolon for centuries looked only slightly older than Kaleb.
“Half of the battle is reflexes!” He launched a glass orb to the other side of the room.
Reuben instinctively covered his head with his hands. The orb slammed into his forearms and ricocheted to the wall, where it smashed behind his head.
Ardor Westfall grunted in disapproval. “Quick reflex but wrong reaction. You allowed the force of it to hit you.”
The Hall was filled with nervous titters of laughter. Reuben slouched deep in his seat and tugged at his shirt collar.
“Don’t be embarrassed. That was a typical reaction for a newbury.”
A hand shot up in the air. “The object can’t hurt us, can it?”
“The object itself cannot, but the force of it can, especially with certain materials.” Westfall walked to the front of the hall. “Reflexes can be conditioned, but only to an extent. In their absence, we must tighten the mind and concentrate on exercising it. Please look for my notes,” he ordered, pointing upward.
A projection hovered above him like a thought bubble. The words appeared letter by letter, dictated by his mind. He displayed several tactics under the title: Defense . The words didn’t make sense to Alex.
Sword swipe
“Many talents are too difficult to learn consistently and effectively. You might never have the mind power to execute seventy percent of the abilities we will be discussing in the next few weeks, but it’s beneficial to learn about them anyway. You don’t learn history to fight a war, do you? But today! Today, you get a taste of it all. It’s time to strengthen your minds using action. Those spirits to whom I spoke before the lesson, please come up front!”
Four kids lifted themselves from their seats, including Jack and Calla Bond.
“Movers,” Gabe said curiously. “Why does he want the movers?”
Dex Justice, a Darwin ally, sauntered arrogantly to the front of the room, shoving Jack with his shoulder before positioning himself in a horizontal line with the others. Scrawny Jack scanned the room nervously with his green eyes until they rested on Alex who smiled, trying to make him feel more comfortable. He offered a little wave and half the room recoiled, thinking it was directed at one of them.
Westfall leaned in to whisper something to the group, who listened to his command with avid interest. He handed each of them a glass orb the size of a softball.
“What are you doing, Ardor?” Van Hanlin asked with a frown.
Westfall didn’t even look at him. “Conducting a little experiment.” He lifted his hand high in the air and brought it down swiftly like he was giving the okay to begin a race. At his signal, all four spirits elevated the orbs in the air before pelting them forward at a speed to rival professional baseball pitchers. Alex would have found this interesting to watch if all four orbs weren’t aimed directly at her.
It began so quickly, yet somehow her mind slowed the seconds leading to the impact. In her peripheral vision, Alex saw the kids around her curling away, but she focused so intently on the orbs that her vision began to blur. The contents inside the orbs, silvery flakes, rose and spun like a sandstorm, and in her thoughts, she ignored the glass and snatched the sand with her hands.
Chase gasped and leaped from his chair to block her, but it was unnecessary. Alex didn’t need to look at the shock on the faces of the Lasalles because she could see the reflections of their wide open mouths in the four glass bulbs that remained suspended in midair, twirling before her like harmless bubbles.
They remained trapped by the stagnant sand until Alex relaxed, and the hands in her thoughts spread their fingers, allowing the grains to trickle down. Without the pull of her concentration, the orbs clanked to the ground and rolled away.
Westfall shrugged without remorse. “I was curious.”
The room filled with laughter.
“Don’t look so offended. I wondered if you might dodge them before they were even thrown.”
“How would I have known to do that?”
“Sometimes we don’t know what our minds are capable of until they’re put to the test. Hence your banshee encounter and survival.” In a blink, he appeared beside Alex, shaking sand from his shoes even though none of the orbs had shattered. “You have natural ability, just not the one I was expecting. What’s your name?”
“Your last name?”
“Ash.”
She noticed that his gray eyes seemed weathered like his frown lines. They were older. Deeper, troubled, and tainted after seeing too much. He turned to face the rest of the newburies. “Don’t expect yourselves to execute a block of that caliber without some practice.” His voice was low when he added, “I was merely proving a point.” And he shared a look with Professor Duvall. “Alex, you’ll work with the Bonds. Maybe they have finally met their match.”
For Westfall to speak so candidly about the Bonds, he mustn’t be intimidated by curses, but Alex doubted he was intimidated by anything.
“The rest of you will also form groups of two or three and use the provided guide to attempt the different ways to shield. Do not focus on just one method. You need to know them all!”
“We get to throw things at each other?” Kaleb asked in excitement. “Sweet! Come here, Jonas!”
Alex rubbed her shoulders, allowing the weight of Westfall’s judgment to lift.
Jack approached, mumbling an apology. Calla was quiet at his side.
“I’ve been nothing but nice to you and you throw a glass ball at my head to thank me.” When Jack smiled, his freckles seemed to blend together. “I should have just let that bench crush me. It would have saved me all this grief,” Alex said, turning her attention to the other groups in the room, who were hurling orbs and books and pencils at one another.
Chase mouthed, “Are you okay?”
“Well, we already know that you’ve mastered the barrier method,” Jack said, glancing at the booklet in front of them.
“What is slingshot ?” Alex asked.
He continued running his thin finger along the text while murmuring, “Oh, it’s almost the same as barrier.”
“ Except you reverse the direction of the object,” Calla added softly.
“I thought most spirits weren’t very good at telekinetics.”
“This is different,” Jack said. ”You’re using the force the object has already generated to divert it. That’s much easier—”
“Than moving the object all by yourself,” Calla finished.
“Do you two always finish each other’s sentences?”
“Typically.” Jack tried to lean against the table smoothly but he accidentally slipped. Alex tried to hide her smile.
“Twin complex,” Calla muttered. “When he falls, I bleed, and vice versa.”
She didn’t seem pleased about this.
“Even when we died, it was the same way,” Jack shook his head of matted gray-brown hair. “I had a brain tumor, and when I died, Calla died with me, even though she had no symptoms.”
Calla lifted a finger to her forehead. “He has too much up here.”
Alex was confused until Jack snickered. “A brain tumor has nothing to do with an excess of brain power.”
“So were you a genius in life, too?” Alex asked.
“I was probably headed to an Ivy League school.”
“Lots of people do that.”
“At sixteen,” he added.
Jack’s grin accentuated the puffy half-moons under his eyes.
“You look tired. Must be from staying up late and memorizing books.”
Jack vigorously shook his head back and forth, trying to wake up. “I know we need an adequate amount of sleep, but my mind just feels like it’s moving so quickly. I can’t sleep.”
“And therefore, I’m tired,” Calla growled.
“It can’t be fun being in each other’s heads,” Alex said, glancing over at the Lasalles. Kaleb was firing orbs at a disgruntled-looking Jonas. She could hear Chase’s pity for his brother.
“Quit staring at your boyfriend,” Jack joked.
Alex wasn’t quite sure who he meant.
“You’re always saying the wrong thing,” Calla accused him.
“Am not.”
“Are so.”
Alex held up her hands. “No. I’m just not sure who you’re talking about.”
“Jonas. You’re with him all the time, aren’t you? I notice things.”
“Jonas isn’t my boyfriend.”
An orb flew across the room and slammed into Jack’s back. He ignored it and kept his eyes on the text. Calla lifted an arm to rub between her shoulders “Ouch.”
“Why do you let people treat you that way?”
Jack shrugged carelessly. “I guess we’re just used to it.”
“That doesn’t make it better!”
“Heavy lies the head,” Jack murmured. Calla nodded, fiddling with her sweater. “
We have more important things to worry about than people teasing us. They’ll learn their lesson one day. Calla’s and my luck will change. We’re good people. And good things happen to good people. Even if we don’t stay here in this city.”
“You’d leave?”
“It isn’t written in stone that we have to live here.” Jack paused with his mouth ajar, revealing his horsey teeth. “Let’s try flickering .”
“Flickering,” he read, “is when a spirit momentarily flickers out of visibility. Why do you look confused?”
Alex studied the text. “I know the bodied can’t see us, but how can spirits hide from one another?”
“If we aren’t looking for each other, it’s possible to fool the mind, if only for a few seconds. You just have to move yourself to a different place. Give it a try.”
Embarrassed, Alex glanced around the room at the other students.
“What’s the matter?” Jack asked. Realization spread across his face. “Oh, I’m sorry.” He smacked himself. “You don’t know how, do you? No sweat, it’s one of the simplest things to learn. Just imagine yourself shrinking in all directions.”
Calla jumped in. “Like a genie being sucked into a lamp.”
“Except you’re condensing yourself into a ball in midair. Then quickly move to a space you don’t think I’ll look for you.”
Alex closed her eyes and imagined that the walls around her were closing in, the air constricting her. Nothing happened.
“You forgot to move. And keep your eyes open so you know where you’re going.”
She focused on the corner of the Grandiuse right next to Westfall. Jack wouldn’t expect her to venture anywhere near a man who had just ordered an attack on her.
She heard a tiny gazump like sealing Tupperware. She blinked, and she was completely across the room.
“Wow,” Jack yelled. “That didn’t take you very long at all.”
Alex practically danced back to their table. “Could you see anything?”
“Right before you moved, I noticed your light.”
He considered his answer for several moments. “It’s never still. Like the reflection of the moon over the ocean.”
Calla nodded. “It’s pretty.”
“Could the bodied see it?”
“Rarely. But it has happened.” Jack flipped through the text. “I think that’s why sometimes the bodied think we aren’t in a whole form, why they think that we’re hazy or we flicker.”
Chase appeared beside her. He turned his head and kissed her cheek before disappearing again. Jack and Calla both stared at Alex, openmouthed.
Alex hoped she wasn’t blushing. “This is pretty cool. Thank you so much, you two.”
Calla looked away. She’d probably never been complimented in her life. Jack grinned, exposing his large teeth.
“I can’t believe something like this is possible,” Alex breathed.
“Why wouldn’t it be?” a voice barked.
“Hello, Ardor Westfall,” Jack said, saluting.
“After all, all you are is a projection. A memory,” Westfall said, crossing his arms. “And memories never stay in one place.”
Kaleb was always suspicious of Jonas. He loved his brother, of course. He loved all of them, but the others made it easier than Jonas did. Jonas was sneaky. Kaleb was certain he would stab any of them in the back in order to make himself look good.
He drummed his pencil on the table and glanced at the door, but the rest of his clan had yet to arrive. Despite its old-fashioned exterior, the Ex House on Lazuli Street was relatively modern. Its thick wooden tables and armchairs deep enough to sink into resembled a coffee house. They served flavors of the misty froth passed around during festival street parties. The newburies around here called it the Ex drink. Every cup displayed a blurb explaining the history of the mist and its creator, Xander Aris, but Kaleb didn’t care enough to read it. He liked to have it, though, because it provided a brief buzz like a shot of some super energy drink.
Usually Kaleb hung out in the Back Room of the Ex House, an area much louder and rowdier, with pool tables, foosball and ping pong. But today he had work to do. Instrumental music drifted through the more studious front half of the bar. The little black notes rose to the ceiling and arranged themselves into a life-sized sheet of music. He didn’t know how, but his mind told him it was called Vivaldi. He’d never admit it to anyone, but he actually liked it. Kind of.
It was easy to distinguish the various newbury cliques. The legacies typically loitered in the Back Room, competing to see who could hold their nose the highest. Tonight, they’d arrived without Skye Gossamer, so Kaleb didn’t give them a second glance. She was the only one worth staring at. Then there were the movers, whose belongings hovered around them like flies. The chokers sulked in the corners reading Poe or Emily Dickinson. You’re dead , he always wanted to shout, get over it ! The crew of “earthly” newburies showed avid interest in stones, plants, and herbs. Naturally, they faithfully followed Professor Duvall. Kaleb hated teacher’s pets.
Tonight there were a few random spirits, like Hecker Smithson, who took up more room than a pro lineman and never spoke to anyone, or Reuben Seyferr, who was always itching like he had fleas. Kaleb had waved to both when he arrived. The Lasalles—as they had done in life—discriminated against none, but befriended few. Kaleb had learned a long time ago that trust was not something to hand out like candy, but friendliness went a long way.
Jonas was the first to show his ugly mug. He stood at the serving station with one foot propped leisurely behind the other, leaning against the counter of the bar like a wannabe cowboy watching the door. Probably waiting for Alex. Pitiful. Jonas didn’t seem to realize that his fifteen minutes with her were over. Chase was back, and things were normal again.
Jonas always went after things he couldn’t have. And then he got pissed when he didn’t come out on top. Impossible odds.
When Alex predictably arrived with Chase, Jonas turned around and pretended he hadn’t been waiting. Kaleb shook his head in amusement. Jonas was wasting his time. Alex and Chase had been attached at the hip since they were born. In life, Kaleb would sometimes enter a room and wonder how in the middle of winter it could possibly smell like spring. Then he’d hear giggling and look down to find the two of them playing together. That strange feeling in the air, it had to be love. It followed them now like a trail. He thought of those two as one entity. Before Alex died, Kaleb would look into Chase’s eyes and his brother would not be there. Some part of him was missing. She was that part of him. How the hell could Jonas not see that?
Kaleb wasn’t sure he believed in love. But he believed in whatever hovered between Chase and Alex.
Jonas turned and acknowledged Alex, a dowdy straw dangling from his mouth. None of them noticed Kaleb sitting behind a computer.
The barista appeared. “What will it be?”
“Want anything?” Jonas asked Alex, but she shook her head. “What about you, delinquent?”
Chase stepped up to the counter and surveyed his options. Jonas waited, resting an elbow on Alex’s shoulder and flicking the straw in her hair.
“Cut it out,” she said, swatting him away.
“Did you have fun trying to beat the crap out of Jack Bond? I know I would.”
“I thought you didn’t mind Jack.”
Jonas shrugged indifferently. He was trying to act cool, but he just looked dumb. Kaleb snorted loudly, and they all turned to see him.
Alex drew back her head slightly. “Kaleb! I’ve never seen you look so serious!”
He winked at her, and she walked around the table to sit next to him. “You’re going to scare all my admirers away,” he joked.
“I don’t think any of your admirers have ever been intimidated by me.”
It was true. Alex was a good wingman, actually. He wouldn’t have put up with her for so many years if she wasn’t.
“What are you wearing that for?” she exclaimed in surprise.
She picked at his shirt. His mind projected a jersey each day by default. He typically didn’t question it because it didn’t bother him. Now, however, he looked down and realized why Alex was wrinkling her nose.
“You hate that team,” she said as if he didn’t know.
“I have no clue why I have it on. Maybe because I hate doing homework.”
“History research for Paleo. It sounds very high school, but it isn’t so bad.” He twisted his head left to right and then leaned in close. “Don’t tell anyone, but research doesn’t make me want to slit my throat anymore.”
“Now that you finally have a brain.”
Alex stared at his paper. “Josephine Anovark,” she read. “Eighteen forty-nine to eighteen sixty-five to nineteen-oh-one.”
“It’s odd to have two death dates, huh?”
“She didn’t last very long. Who was she?”
Kaleb held up his notebook. “We were supposed to focus on the advancements within a particular time period, not the people, but I couldn't help myself. This chick was everywhere. She was the first advisor for the DeLyres and some sort of celebrity.”
“DeLyres?” Alex perked up. “I’ve heard of them. Who are they?”
She was joking, right? He studied her face. Nope, not joking. “You know … like our Chancellor?”
“The Chancellor basically runs the city, Alex. He’s in charge around here. You’ve been here a few months. You should know these things by now.”
Her Intro teacher must be slacking. She probably got stuck with Van Hanlin.
“You haven’t heard of someone named Eviar, have you?”
“Eviar?” Sounded like a brand of bottled water. “No.”
Disappointment clouded her face. “So the DeLyres are in charge, but this girl helped them?”
He nodded. “Actually, she even ran away with one of them. Except their little union didn’t last long because some lunatic named Syrus Raive hunted her down and killed her.”
“I think he was pretty irritated that she destroyed his side of the war.”
“And he killed her?”
He nodded. “Totally slaughtered. I’ll have to thank Paleo for assigning me a time period with such heartwarming stories.”
He was actually pleased that this project hadn't been a snore. The spirited world treated this girl like some sort of second coming.
Jonas and Chase arrived with steaming mugs. Jonas wore his typical peeved expression, and Chase seemed bemused. All was right with the world.
Alex lifted her bag and took out a text the size of a phone book. Because spirits could read so efficiently, the teachers assigned hundreds of pages to read for homework. He didn’t envy her right now.
“I still need to do that, too.” Chase sighed. “I usually like Van Hanlin’s law class, but amendments to transportation laws are just boring.” He opened his own law book. “Maybe I’ll just get that out of the way now. Let me know if you need help with it.”
“Or you could just do it and I’ll copy.” Alex suggested.
“Oh, may I please?” Chase turned to Jonas and reached for his notebook. “Can I borrow some paper?”
“No.” Jonas snatched the notebook and stuffed it in his bag.
Kaleb narrowed his eyes at his brother. “What’s your—”
“Here,” Alex said quickly, handing Chase several sheets. “Gabe gave me some earlier.”
“Where is he?” Kaleb asked. Gabe would be so proud of him for being interested in history, and he wasn’t even here to witness it. What a waste.
“He isn’t coming,” Alex replied. “Romey came to see him at the fields last night. He has to play watchdog for the front desk.”
Jonas began to gather his things feverishly. What was he up to?
“I forgot I need to go to the Grandiuse and check out some books.” Jonas scooped up his pile of belongings.
The only person less likely than Kaleb to check out books would be Jonas. Kaleb didn’t believe him for a second.
“Don’t you want your drink?” Alex asked.
“You can have it,” he said quickly. His sports gear spilled over the armload of books.
And now he was giving things out? Something was definitely up.
“That was strange,” Chase murmured after Jonas disappeared.
Kaleb nodded. “What’s in that drink of his? Hand me that,” he said to Alex.
She adjusted her seat to reach for the abandoned drink, and the leg of the chair caught on a backpack Jonas had forgotten in all his hurry. When Kaleb reached down to dislodge it from the chair, flower petals fluttered to the ground.
He made eye contact with Alex. Flower petals? Alex shrugged in response and held up the bag. There, condensed together snug as pickles in a jar, were dozens of yellow flowers.
Were these for Alex? She certainly wouldn’t admit it if they were. That girl could be so damn naive. Jonas could march into the Ex House wearing an I Heart Alex sandwich board and she would still deny his feelings.
The thing was, though, even if Chase saw the flowers, he wouldn’t do anything about it either. Hell, he would probably watch Jonas get down on his knees and give them to Alex and still keep his mouth shut. Kaleb didn’t understand it at all. Either Chase felt guilty, or he knew that never in a million years would Alex pick Jonas over him. This was exactly why Kaleb didn’t keep one girl around too long.
He watched Alex quickly close the bag, but not before the stench of moldy, wet dog reached his nostrils. He stifled a gag and swatted in front of his nose.
“Back so soon?” Chase called over the ruckus.
Jonas was pushing through the crowd again. Alex kicked the bag further away. It fell to the side, exposing a warped, brown water ring. She was a better person than Kaleb was. He wanted to call Jonas out on the flowers. Embarrass him. Knock him down a few pegs.
Jonas dashed through the maze of tables, his eyes bugged wide until he saw that his bag was lying on the floor, seemingly untouched. He breathlessly pointed to his property. “Oh good. I did leave it here. Can you hand my bag to me?”
When Chase passed it to him over the computer, Kaleb couldn’t help himself.
“You’re looking a bit yellow , brother.”
Jonas clutched his bag snugly against himself. “Huh?”
Alex smacked Kaleb across the chest, and he turned to smile mischievously at her. “Where are you going again?”
“The Grandiuse.”
“Back-petaling , are you?”
Jonas turned his heel. He didn’t get the joke. Moron.
Kaleb returned to his assignment and worked quietly for several minutes until something caught his eye. Parrish Park. The words were there on the page like old friends, waving and smiling. He kept reading. Civil War. Soldiers. Cove.
He shot back in his chair. “Holy—”
“Kaleb!” Alex cut him off. He fought the urge to say the word just to spite her. They weren’t sitting in church or anything.
“Things just got weird. This girl.” Kaleb pointed to the computer. “Guess where she died?”
Alex shrugged.
“Take a wild guess.”
Chase stretched his body around Alex to get a look at the monitor.
“I’ll give you a hint. There once was a girl who fell off a cliff because there were confederate soldiers chasing her. Well, actually, this says they pushed her. I never heard that before. She died when she smashed into the rocks below. She paces the beach and haunts the woods around it, digging up the ground. Ring a bell?”
“What does the Parrish Cove Ghost have to do with anything?” Chase asked.
“The Parrish Cove Ghost is all over the time period I’m supposed to research.”
“You’re kidding.”
“It gets better.” Kaleb’s voice shook in anticipation. “She died there twice . In life, soldiers chased her to the edge, and then in death, Syrus Raive found her there once the Restructuring War ended. That was where he killed her again.”
Chase laughed. “So we were afraid of those woods for nothing? She only haunted them from … ” He glanced at her death dates. “Eighteen sixty-five to nineteen-oh-one?”
“Guess so! Hey, don’t tell Jonas. If we ever go back there we can make fun of him for being afraid.”
“You’re sure this was our ghost?” Alex asked.
“Unless there were two of them.”
“Because that doesn’t explain why footprints still show up on the Parrish beach.”
“Oh, don’t ruin the moment, Alex. Half the time the people who attempt to see the ghost pass out in a drunken stupor. Any idiot could walk by and leave footprints.”
He’d never heard the name Josephine Anovark in Parrish, but then again, he’d never tried to uncover the true identity of the cove ghost. According to his research thus far, before Josephine was recruited to help the DeLyres, she assisted the Ardor Service. She’d spent years helping them track down spirits who became unstable or who broke the law in significant ways. One of the spirits she’d helped to imprison was Syrus Raive, the man who later killed her.
The creepiest part was that according to the statements following her second death, the two had been friends.
I worry so often about a world the mind engineers. Your gifts cause you to question your sanity, and I admit I have similar concerns.
Sanity. Insanity. The line between the two blurs in dreams. You can get away with so much in the dream world. What makes this world any different? What is real, and what is not? I’ve been inside your head. Are things really the way you see them or the way I see them?
I’m pleased you were invited to speak to the Ardor Service at the Dual Tower. If you are amongst the strongest in the city, the risks are diminished.
If all goes well, perhaps you can introduce me to the infamous Ardor Westfall.
The man was up so high Alex could barely see his shiny shoes. Due to the gaggle of girls huddled at the foot of the ladder, she wondered if the invisible man was the notorious professor, Dr. Darby.
“Some of the animals get distressed in bad weather,” she heard a cheery voice call down. “Best to calm them before they get too worked up.”
Oh, it was Darby, all right. Gabe called him the zoologist to the dead.
Darkness lurked behind the glass of Duvall’s aquarium. Storm clouds blocked what little sun could break through the massive cover of trees. Alex took her seat, pulling out several of Eviar’s letters. She carried them with her now, justifying her obsession with the idea that it was comparable to carrying around a novel. And even if she wanted to leave them behind, the box found ways to sidle across the room and wait patiently by the door like a faithful dog.
Eviar’s talents kept growing, the most interesting being his ability to persuade. He began by willing other newburies to give him their belongings or homework, but he grew bored and began to use his skill for amusement. Alex had laughed out loud when she read about the day Eviar persuaded Paul Bond to dive into the fountain and flail like he was drowning. He insisted to Sephi that
he was just very influential. Sephi believed the ability would more aptly be termed mind control.
And that was just the tip of the iceberg. Eviar was a mover, but even that grew into something extraordinary. Typically, advanced newburies learned to elevate pencils and books. Natural movers were usually able to channel their energy into more substantial objects like furniture. Eviar, on the other hand, had taught himself to move clouds and treetops. With such gifts, there was no possible way that his life wouldn’t be documented somewhere besides his letters to Sephi. But no matter how much she searched, Alex failed to unearth any spirits with powers like his. She couldn’t find Sephi’s name in history either, which was even more frustrating because Eviar had said she was well known.
The more Alex read, the more she felt attached to the two of them. She would frequently find herself entranced by Eviar’s words, unable to move, losing track of time and responsibilities.
She was forced out of her reverie when a man slid down Duvall’s ladder, calling to order the giggling girls and irritated boys. Thin and lanky, yet polished and proper, he was the type of dazzling man one could call pretty and get away with it.
Alex searched for Duvall and found her hovering in the back of the room where she could freely cast the weight of her glare onto Reuben and the Bonds. She didn’t approach the podium.
Darby flicked his head and a light appeared at the front of the room. It circled around him like a spotlight. “Slight change of plans,” he said. “I will be your guest lector this morning. We have much to cover and an inadequate amount of time to learn it because you weren’t supposed to delve into banshees until next term.”
The class began to buzz with excitement.
“And that,” he sighed, “is precisely why Ardor Westfall suggested we jump the curriculum. For some reason, newburies find these dismally dangerous demons to be fascinating, but I can tell you there should be not such enthusiasm. There have been various sightings of banshees in our territory, and many think it sport to battle them.” The light around him grayed. “That would be as foolish as a human jumping into a tank to battle a great white shark. Something tells me that you wouldn’t be lining up for that one.”
Without warning, a life-size image of a banshee flashed in front of the classroom, resulting in a handful of screams. Alex shivered violently when the maniacal eyes bored into her through the gangly threads of its greasy white hair.
“Banshee,” Darby began, “in the physical world is derived from Irish myth as an omen of death. The Irish weren’t far off. They just had it backwards. A banshee does not warn someone of their imminent death; it can often be the cause.”
Alex’s stomach tightened. She attempted to take notes, but her hand trembled too much.
“A banshee’s shriek can cause heart attacks in the bodied, but only to those who have an uncharacteristically vast sense of hearing. Most humans cannot hear the scream at all, even if the beast is hovering right next to them.”
Alex shivered again.
“Celtic Christians had an even more accurate description for banshees. They called them ‘fallen angels,’ which in a sense is correct. The scariest aspect about a banshee is that you or I could all too easily become one of these decrepitly hollow creatures. A banshee is simply a spirit like us whose mind has been shattered. It still exists but in pieces. Now I’m not saying we’re angels, per se, but we could be mistaken for them.”
It was hard for Alex to believe that this vile being had been born from a normal spirit. The image zoomed in on the banshee’s face. She couldn’t bear to look at it. Her whole being zinged with discomfort.
“Folklore mistakes banshees to be only female, probably due to their frail frames and, sorry to say it, ladies, but female spirits have a higher tendency to lose control of their minds. Don’t shoot the messenger,” Darby said defensively. “I’m just citing statistics. A banshee remains in this world because he or she still has somewhat of a mind, though it doesn’t function. If you notice the features of its face—” Dr. Darby gestured with such vigor that the momentum caused the image to ripple.
The image billowed like an enemy flag, floating towards her. Alex felt heavy, clammy, distressed. She hunched forward and cradled her throbbing head in her hands, and appropriately on cue, a rumble of thunder resonated outside.
“The purple rings under its eyes are something to be thankful for. Banshees have no reason, no thought processes besides the will to survive. They’ve gone back to their primal instincts, like wild animals. They barely function enough to realize that they need sleep, so eventually they just fall to the ground in a heap. The more tired they appear the less strength they have, and thus the better chance of your survival.”
Alex raised a trembling hand.
Darby didn’t seem surprised. “Do you need some air?”
Alex shook her head. If she left class now, there would be nothing else to fill her mind besides the low wail echoing in her ears. “Why are they so strong if they have little brainpower?”
His face brightened in surprise. “Very good question. Just because a banshee can’t control its mind doesn’t mean the power is gone. A banshee has nothing else besides force. It isn’t thinking about what it is doing, nor does it care, since the mind is broken.”
“And by broken, you mean … what?”
“Without repair. A completely maniacal being without a thread of sanity. Unfortunately, we all have demons stitched into the patchwork of our souls. We cannot allow them to become strong enough to rip us apart.”
“Does it happen in life? Or just in the afterlife?”
“Both. Strength of soul has nothing to do with the condition of the mind. A body without mental sanity can still transition into the afterlife.”
“There’s no treatment?”
“There are theories. Research. No cure thus far, however.”
Alex thought of the way the creature thrashed and convulsed in a rain of sparks. “Why the frenzy of electricity?”
Lightning flashed outside and the projection of the banshee flickered.
Darby shoved his hands into the pockets of his tight dress pants. “Fury. They can’t control anything, let alone their feelings.” He took a step closer to Alex. “Do you mind if I ask you a question about the one you encountered? What did you do to anger it?”
Jack guffawed beside her. “I heard she sent it flying across town.”
Reuben scooted his chair even further away from Alex.
“What does it sound like?” Joey Rellingsworth asked.
Alex glanced at Dr. Darby, who gave her the go-ahead by waving his hand.
“It’s hard to describe.” Her peers leaned toward her, listening with morbid fascination. Even Tess widened her bored, hooded eyelids. “The worst part wasn’t so much the sound of the scream, but the pain like arrows being shot into my brain.” Alex cupped her skull with her hands. “I can still feel it if I think about it.”
Darby flinched. “Unfortunately, that never goes away.”
“You’ve heard it too?”
“Only once.” He pulled his sleeves back to reveal a maze of scars. A girl next to him gasped. In some places, circular gray contusions marked his thin arms like rocks had skipped across a lazy lake and left permanent imprints. In others, it looked like a whip had cracked against his skin, indenting his arms without altering the pigmentation, like the skin had simply been scooped out.
“It attacked me even though I didn’t provoke it. It was so close I had to use my bare hands. This is from the electricity.”
Newburies stood up to get a better look at his battle wounds. “How did you survive?” Linton asked.
“I ran at it. I threw my entire body at the creature. I’d been fighting it so long I figured doing so would either kill me much faster or it would save me. Thank goodness it was the latter. It wounded both of us enough to end the fight. When I awoke, all I had left were the scars.” He gently replaced his sleeves. “Such a lengthy exposure should have been detrimental to your mind, Alex. The fact that you sit here with us now is nothing short of a miracle. You must be pretty durable.”
Of half-crazy herself.
“What could’ve happened?” Linton asked.
“If she had been exposed to the scream long enough, it would have driven her to the point of insanity. Within minutes she would have lost everything that makes her who she is, and she would have become one of them.”
Alex could have heard a pin drop in the classroom. No wonder the Patrol had behaved so oddly after they’d found her. They thought her mind had surrendered to the scream.
Joey gasped. “It can’t kill us?”
“Not by wailing.” Dr. Darby shook his head. “Remember, you exist because your mind exists. A banshee’s scream causes the mind to crack into pieces. Those pieces are still alive, but broken apart, they cannot function. It’s a fate worse than death. Your mind no longer belongs to you.” He flicked his hand and the image changed to a drawing of a banshee hovering over a lifeless human form.
“How come Alex still has her mind, then?”
Darby shook his head. “Your guess is as good as mine. She was lucky, I suppose. Alex, don’t scream though, just in case.”
She regarded him with trepidation. “Are you saying that a scream can shatter someone’s thoughts? Ruin their mind?”
“A voice is a powerful thing.”
“How are they hunted?” Reuben called out louder than Alex had ever heard him speak.
Finally, a topic he enjoyed.
“The Patrol contain them if they are able to. Most banshees are destroyed in their attempts to fight back, however.”
“How do they fight them?”
“Training. They know their habits, their weaknesses, and how to keep them from screaming. Plus, they rarely battle alone.”
Darby waved his hand again and the next image appeared on the screen. It resembled a Louisiana bayou with its drooping dull green branches and muddy gray water. “Banshees do not wander into our area, which is why the sightings have raised questions. Banshees are prone to warmer climates because they are attracted to energy. They flock to the swamps for the seclusion. Now whether their attraction to swamp plants is a result of this habitat or if it is simply a part of their survival strategy, we don’t know, but they have been known to appear in areas that grow bladderwort and sundew.”
“What the heck are those?” Linton yelled.
“Here is where we get into your science lesson. Be sure to take notes,” Darby recommended. Another image appeared. “Drosera!” Darby’s voice rang from the rafters. “Typically referred to as sundew!” It looked like an alien slug. Dozens of purplish-red antennae sprouted from its green peapod body. “If you notice the ends of the tentacles, there are bulbs composed of an oozing substance called mucilage, which lures insects to their deaths. The insects are attracted to the syrupy scent, and once they venture near enough to touch it, they adhere to the liquid and the sundew envelops them.”
Ironically, Alex thought the vicious plant was rather pretty. It was more like something that would live at the bottom of the Caribbean, not in a disgusting bog somewhere.
“The second plant, Utricularia, or bladderwort, is also carnivorous. A teardrop-shaped pouch opens at the sharp point to swallow its prey, much like a beak. These traps protrude from the stem-like tree branches.”
“Is there a picture of the bladderwort?” Madison asked curiously.
“You were supposed to see them up close and personal. I thought there were plenty in stock here to show you, but it seems the number has depreciated.” He squinted into Duvall’s tank. “We’ll have to live without a visual for the time being.”
At the end of class, everyone visited Duvall’s aquarium, hoping to catch a glimpse of what Darby described to be “banshee catchers.”
Duvall scoffed. “Bladderworts in November? Any idiot knows that they won’t bloom again until May!”
Chase walked toward Alex, who stood with her back to him in the Brigitta vestibule, watching the rain pelt the pavement. He didn’t need for her to turn around to know it was her. He could probably wander the world with his eyes closed and somehow eventually find her. That was how he’d felt the past year without her. Blind. Did it make him a horrible person that he wanted her to die just so he could have her back again? He’d always been drawn to her. It seemed the strings of his life were attached to hers. If she tugged in one direction, they both had to move. In two separate worlds, the pain of the pull was too much to live with but also too much to live without. Marionettes don’t do well without their strings.
Most of the spirits venturing across the square had given up on the idea of umbrellas. Vicious raindrops fell like stones, and they stung like paintballs. The other day, he'd overhead a newbury asking Westfall how pain could exist when spirits existed only as energy. Westfall had replied by saying the reflection of the sun on the ocean stings the eyes nearly equally to the pain of staring at the sun itself. Like most of the veteran spirits, Westfall liked to speak in rhymes and metaphors.
Chase came up behind Alex, and her body relaxed as the pull of the strings slackened.
“Hey,” she murmured without turning around. The colors flickering around her changed from lavender to bright pink. He’d grown accustomed to seeing the rainbows of emotions around people. Usually he saw lavender during workshops when someone was staring into space or out the window, daydreaming. He usually saw pinks and reds around Alex.
Chase wrapped his arms around her waist. He would never tire of the way her touch sent shockwaves throughout him.
“This isn’t going to be fun,” Alex said, gesturing out the window. “Thank goodness I don’t bruise so easily anymore.”
Chase sighed. There was something about Alex that was still very fragile, but he couldn’t say that to her now. It wasn’t a bad thing. The most beautiful things in the world were also the most breakable.
Alex turned to look over her shoulder, and he couldn’t help himself. He grazed his nose against her cheek. The feeling was better than skin-on-skin contact in life. Here touch had a current, a life of its own. Although, his mind clung to its old sensations, too, like when his stomach dipped because his lips hovered so close to hers.
It took all his strength to take a step back. He still didn’t know how much was allowed. In life, the only thing he ever cared about was keeping her safe, and that included her heart. He had watched her body slowly deteriorate, and it tortured him to witness it. How could he be selfish enough to fall for her if that would only make her death more painful? He’d never imagined they’d get an opportunity like this one. They couldn’t have dreamed of a better place. His feelings were so strong now, but what would happen to him—what would happen to her —if he gave in for just one moment and decided to kiss her? Half of him worried the force of it might devour the slice of life they still had. The other half of him feared it wouldn’t be perfect, that it might not live up to the years of desire they’d both endured only dreaming about it.
That was the thing about them. The intensity between them was not born from their death. When they were alive, sometimes he couldn’t breathe because she was just too much. It would always be all or nothing with them. And he’d rather have this uncertainty between them than broken expectations.
He tugged at her hand. “Come on.”
She followed reluctantly when he led her to the door. The force of the rain would feel like stepping through sheets of glass, but Chase would choose to brave this hurricane with Alex tucked beside him rather than choose to walk in the sunlight alone for the rest of his existence.
“What are you doing?” she yelled over the rush of the storm. “Why are you moving so slowly?”
Was he? She squinted at him through the rain, flinching with each drop that struck her. He yanked at her arm, forcing her small body to fall toward him. He hunched over her, sheltering her. If he could help it, nothing would ever hurt her again.
When they entered the Grandiuse and headed to their usual table, Jonas was grumbling in typical fashion. “You’d think Duvall would be happy that her students are so excited about one of her dumb plants for a change.”
“No teachers are happy that students are so enthused to learn about banshees. It seems like they’re afraid we’re trying to fight them for some reason,” Kaleb said, flipping pages in his ABC text. “How gross were those pictures though? Is that what they really look like?”
“They’re worse,” Jonas said. Alex took the seat opposite him, and he allowed his eyes to rest on her for longer than was necessary. She didn’t see it, but Chase did, as did Kaleb who snickered loudly.
“How did you hold on for so long?” Gabe asked. “Darby told our class it was impossible.”
Chase glanced at Alex and the ferocity of it caused the lamp above them to flicker like a strobe. He’d hated that he’d been so helpless that night. He’d seen the image of the banshee in her head like watching the scene through a one-way mirror, pounding his fists uselessly against the barrier.
Alex’s dark eyes flashed in his direction. “He told my class that the banshee was really, really weakened. Dead on its feet. We got lucky.”
“Jonas was lucky you threw him out of the way.” Kaleb chuckled. “What a knight in shining armor.”
Poor Jonas. Chase opened his mouth to defend his brother, but Alex beat him to it. “He ran at it! If Jonas hadn’t been there, I don’t know what would have happened. I didn’t even know what the thing was.”
“I don’t need you to defend me,” Jonas snapped. “You were stupid to provoke it.”
Alex pulled back from the sting of his verbal slap.
Chase watched his brother’s eyes sweep back to Alex to observe the effect of his words. In Jonas’s mind, if Alex allowed his words to harm her, it meant she cared. This pleased Jonas. It was written on his face like a confession.
Chase decided to pay him back. He inched his fingers closer to Alex’s on the table and intertwined his pinky with hers, an action that was as personal to Jonas as Chase kissing Alex square on the mouth. Consequently, the air around Jonas began to pop.
“Calm down, Jo,” Gabe said under his breath.
Skye Gossamer floated gracefully down the aisle and dropped her books next to Alex. She was oblivious to the eyes in the room that followed her like gravity. Her looks excused her peculiarity. “What are you guys talking about?”
“Banshees,” Alex replied.
Kaleb scooted closer to Skye. “What could possibly be bringing these suckers to California? There aren’t any swamps around here.”
Skye scrutinized the small space Kaleb had left between them. “Do you need more room?” She asked innocently.
Bewilderment struck his handsome face. He wasn’t used to such a reaction from the opposite sex. “No. Sorry.”
“Maybe there are secret stashes of bladderwort growing in the river,” Jonas joked.
Skye shook her head vigilantly. “Nope. It can be grown many places, but this climate doesn’t produce sufficient amounts.”
“Duh, the plant is a carnivore . It needs those swamp bug
s to survive.”
Jonas snorted. “There are bugs everywhere! And who asked you to sit at our table?”
“Who asked you ?” Kaleb said, glaring at his brother.
Skye lifted her chin. “The average temperature here is about sixty degrees. There are not that many bugs,” she replied, flipping her silky, red blanket of hair over her shoulder. “And do you think the bog plants could survive the snow we get here sometimes? Probably not.”
“Okay, think about it. The banshees barely have brains!” Jonas insisted. “They can’t tell the difference between bog plants and pine trees!”
“Sounds like someone we know.” Kaleb elbowed Chase and directed a smirk at Jonas.
Chase didn’t reciprocate the thought. He was too busy watching the array of colors swarming his brother. Jonas had been so wound up recently that the air ticked around him, a bomb ready to detonate.
“What are we doing in this climate if it’s so hard to function?” Jonas spread his arms wide in emphasis.
“We sleep,” Alex reminded him.
“And we need the protection,” Gabe added. “We can’t exactly hang out in the south with the banshees, but we needed some sort of consistent warmth and seclusion, hence the massive trees.”
Kaleb was suddenly serious. “Reverting back to the subject of bog plants, I don’t buy that ‘out of stock’ ploy. I bet they just don’t want someone to pocket the plant and lure out a banshee.”
Gabe shut his book with a bang. “No one would be that dumb.”
Skye raised her eyebrows. “The school had plenty a month ago.”
“What?” Jonas’ eyes were huge. “How do you know that?”
“I’m in Duvall’s ABC Circle.”
“Like a club?” Alex asked. “Ellington keeps urging me to join an organization. I wonder if that would work.”
“Why do you think I know so much about plants and stones?”
Jonas keeled over, clutching his stomach.
Jonas’ body was shaking, but Chase knew his brother too well. He was laughing hysterically.
“A club for alchemy?” He snorted. “And botany and chemistry? I’d rather cut off my arm.”
“Oh leave her alone, Jonas,” Kaleb said.
“You said yourself that teacher’s pets are eff—”
Kaleb cut him off. “We don’t know him, Skye, I swear.”
But he didn’t stop. “So, you’re one of the earthly, huh?”
Skye gathered her hair to one side and braided it into a pretty, red coil. “The earthly? Please. Aren’t we past all these group stereotypes?”
They would never grow past them. Stereotypes existed for a reason. Besides, Skye called herself a legacy, so she had little room to judge. Chase’s mind conjured images of glass houses and stones.
Jonas grinned snidely, resting his chin on his fist. “Tell me, did you pre-order your Wicca for Dummies book?”
Chase bit his lip to keep from smiling. Jonas could be obnoxious, sure, but Chase had always thought him to be the most entertaining of his brothers. He had admitted this to Jonas once, just once, because immediately following the compliment Jonas had snapped at Chase and insisted he was being ridiculed. Too many seeds of scorn had been planted within Jonas to make him ignore the bitterness that rooted him to his unhappiness.
“When did they disappear?” Kaleb asked, trying to get back on track, or perhaps trying to turn Skye’s attention back to him. “The bladderwort flowers?”
Skye shrugged. “All I know is that the shelves were stocked when Duvall did her intake in October. She did everything early to get ready for the haunted house.”
Van Hanlin entered, pushing his arms to send an invisible jolt throughout the room. It was his way of telling them to end all conversation during study hall hours.
Kaleb lowered his voice to a whisper. “So someone stole it,” he mused. “Who would want bait for banshees?”
Who indeed. Chase only hoped that whoever it might be was finished with their experimentation.
Though I do not regret what I did, I am severely sorry for disappointing you. I was able to convince the Patrol that the incident this morning was a misunderstanding that spiraled absurdly out of hand, but you and I both know differently. I’ve warned Paul Bond on numerous occasions to stay the hell away from you, and yet he refuses to obey. With hunters in the area, I can only imagine the Bonds are the family with which they’ve been communicating.
It sounds like an excuse, but I do not remember anything after I lost control. It’s like a hole in my mind.
A message reached me that Paul Bond will be released from the medical center today. Bully for him.
I am afraid I’ll be held here in solitary for some time because I refuse to show off what I can really do. I won’t do what they ask. I won’t help them, not unless it will get me into the Ardor Service. I’ve had difficulty controlling myself. My thoughts explode only to burn more holes in my head. Where there are flames, however, there is power. I need to remind myself of this. I promise I will learn to channel the energy into use.
Don’t you dare let them get to you while I’m gone.
P.S. Since I’ve been here, I’ve heard several mentions of Paradise.
Nothing much to do here in solitary except read. The selection is more extensive than I imagined. I have access to every book in the Grandiuse archives. I need only request it. I stumbled upon a book written anonymously by a gentleman who does covert work for the Service. I think perhaps it might secretly be the notorious Crete Reynes. The entire book is rather intriguing. I’ll have to get it to you somehow, but there’s a passage I would like to quote.
“Few have seen it, but my eyes have borne witness to the quote etched in bloodstone on the wall: “
Within the strongest spirit, one finds Paradise.”
Those who reside in the underground city have the most powerful of minds. The location of the exclusive Paradise remains a mystery to most.”
Paradise, Sephi. If we can live in a city so exclusive, maybe you can finally be safe. No one can hunt you in a hidden city.
Skye Gossamer was not used to waiting. Even prior to her death, before she learned about her ancestry and its perks, doors opened for her willingly. In life, she’d been just as captivating as she was now. It wasn’t always a good thing. She’d captivated the wrong person, and it had led to her premature death.
She’d had a very odd upbringing with her free-spirited parents and their communal life. The colony in which she’d lived housed several families with few rules. Perhaps if they’d realized this was the twenty-first century, if they’d accepted the fact that the world was not a safe place, and they needed locks on their doors, Skye would not have been attacked. She would not have been murdered.
She tapped her foot now waiting outside of Alex’s door. They were going to be late for Duvall’s ABC gathering. “Are you ready?” she called.
“Almost!” She heard from behind the door.
Seriously, how long did it take to imagine oneself in an acceptable outfit? Finally, the door swung open to reveal a small black box in the entryway. Had the box itself opened the door? She shook her head to discard such a weird thought.
She reached out to pet it, and it shut its lid with a bang. She didn’t like its vibe at all, so she avoided touching it when she entered the room.
Alex’s clothes were slightly wrinkled. She must have overslept. Skye made a mental note to bring her friend some valerian root from Duvall’s storage room. That would calm her nerves. Alex seemed pretty high-strung.
Alex twisted her hair into a bird’s nest of a bun even though her mind could have done it for her. “How do you manage that hair?”
Skye dramatically ran her fingers through it. She knew her hair was stunning. “I never cut it, so my mind doesn’t know the difference, I guess. I did always want waves like yours though.”
However, the way Alex's flyaway hair stuck out this morning, she wasn't so sure anymore.
“Wait, you never cut your hair?”
Skye shook her head. “My parents were hippies. Haircuts didn’t make the priority list.”
“Hippies, huh?”
“Technically, it’s communal living.” She held up two fingers. “Peace, love, and harmony.” She remembered her last day there and stifled a shudder. It was the furthest thing from peaceful. She hoped someone had cleaned her body well so she looked beautiful in her casket.
She led the way across campus and into the school. They floated up the large center staircase and into Duvall’s ABC classroom, where several newburies chattered happily. She chuckled at Alex’s double-take while seeing the dozens of rows of glass test tubes and flasks sending wisps of perfumed vapor into the air.
“I was expecting a cauldron,” Alex whispered.
“It must be in the back.”
Skye didn’t know why she bothered to formally introduce Alex to the others in the room. They already knew who she was. Between benches, banshees and Westfall’s orbs, Alex was well known. That didn’t mean other spirits weren’t wary of her, however. Being a strong spirit didn’t change the fact that the girl was a mystery. She had to be multigenerational, but no one knew her family history. She could be cursed like the Bonds or greedy like the Rellingsworths. The spiritual world deemed some families as rejects, and Brigitta was more cliquish than high school.
She heard the office door slam behind them. Professor Duvall entered in her usual getup of shawls and beads, and intertwined within them was a thick yellow and white snake that arched its head into the air. A long red tongue rippled out of its scaly jaw, and Skye could have sworn it smiled at her. She smiled back.
Duvall held up a sheet of paper littered with chicken-scratch of swirls and spirals, and flashed a wide grin at Alex. She winked at Skye and nodded her approval before turning to Whit, one of the group leaders. “Go ahead and take your team to the wormhole. I need you to fetch me some Kahuli.”
“Ka-what -i?” Whit asked.
“Sounds like an island,” said Linton, sliding off the desk to join Whit. He stood obediently, watching Duvall with avid interest. It was the only time Linton ever acted polite.
“Actually, it is found on an island. Kahuli are tree snails found on Oahu.”
Skye sensed her opportunity. “Professor, can Alex and I go with them, since she’s sort of observing today?”
Duvall didn’t even look up. “Absolutely not. Alex needs to stay safe and sound in bounds.”
Safe and sound? What did that mean? Duvall had never expressed concern before.
Skye hated to feel dissatisfied. Like hunger, once it hit, it couldn’t be ignored. “But I got to tag along with Whit on my first day.”
“Off to Oahu, my dears,” Duvall ordered, flicking her wrists with finality and ignoring Skye. “Aloha.”
Skye crossed her arms. Too bad her charms had no effect whatsoever on the teachers.
“Team two, Matthew, please take your group to the wormhole and head for the National Zoo. We need the hairs of a baby polar bear, and the zoo just announced the birth of their newest addition. The younger, the better.”
Matthew furrowed his brow. “They get Hawaii and we get the zoo ?”
“Would you rather chase them down in Antarctica?” Duvall remarked curtly. “Because I need the hairs by tomorrow, and it would probably take you two weeks to track down a baby polar bear in the wild, let alone get close enough to extract the hairs without upsetting the mommy.”
Matthew relented. Skye patted him on the back, and his cheeks turned pink.
When team two departed, Skye and Alex were the only students left with Duvall. “Now, my loves, I’m running low on Thymoserum.”
Skye cocked her head. “What is that?”
“It’s a combination of chemicals that function to trick a bodied mind.”
This sounded fun. “To do what?”
“To forget. Sometimes we need things, tangible things, and although the bodied can’t usually see us, we still have to be sure they can’t see the object we take. We can’t make the item invisible, but we can trick their bodied minds to make it seem so. Everything is mental, even sight. So, I need for you to go fetch me some banana slugs.”
“Okay, how many?” Skye asked, extending her hand to pet the snake. It had a good temperament, but clearly Alex did not agree, because she recoiled against a cabinet when the snake stared at her openmouthed. The edges of its glistening fangs caught the light, and Skye directed a look of reprimand at the serpent.
“At least ten,” Duvall replied. “I know it isn’t mentally enticing, but you work so quickly, and this really is the most important job of the day.”
Skye tapped Alex on the shoulder and pointed upward. “Grab some of those.”
“Test tubes.”
“What test tubes?”
Seriously? The girl could fight off a banshee, but she refused to open her eyes. Skye stretched up high to strum her fingers along the bottoms of the thousands of tubes suspended from the ceiling. They clinked together and began a ripple effect throughout the room, like wind over a wheat field. “You really need to start looking for things.”
Skye tugged a few from their strings and trudged out the door. Alex followed so closely behind her that she accidentally stepped on her heel, no doubt eager to get away from the snake.
Banana slugs were easy to find, even though they camouflaged among many of the plants. Skye could walk right up and yank them from the branches. Admittedly, they were pretty cute. One of them really liked her, she could tell, so she decided to keep it for a pet. Lulu, she called it, perched on her shoulder like a parrot.
“Skye?”
“What?” She could barely hear Alex. Her face was buried in the depths of leaves and dirt through which she was furiously sifting.
“Are the Darwins always so well behaved in ABC?” Alex sounded amazed.
“They really aren’t the monsters you think they are.”
“The other day they hung a boy from a gargoyle on the top of the school! How is that not bad?”
“He must have done something to make them angry,” Skye reasoned in her most innocent voice. She plucked a slug from the ground and said hello to it before placing it in a tube and wiping her hands on her pants. “They don’t usually act without reason.”
“How are you finding those slugs so quickly?”
“I always get jobs like this,” Skye complained. “I’ve gotten used to finding needles in haystacks.”
“Yeah, but how do you know the slug is under two feet of dirt?”
Skye stood up and flicked a slug into the container. “They leave a trail.”
“Use your eyes.”
“Oh, my fault,” Alex joked sarcastically. “I’ve been trying to see with my ears.”
Skye gave her a stern look. “I guess the more accurate advice would be to use your mind to see, since that’s what you’ve used all along, spirit or not.”
“You’ve lost me,” Alex groaned. “It’s too early in the morning for a lesson.”
This was Alex acting like she still had a body. “Concentrate on the ground. You can see much farther now than you ever could before, right?”
“It’s the same thing with something right in front of you. Don’t limit yourself to what is just on the surface.”
Alex squinted.
Skye stepped closer, studying Alex’s face. The slugs smudged the ground with a fluorescent yellow slime like highlighter ink, but Alex would never see it using her eyes instead of her mind. Skye was a natural at seeing and believing the unbelievable. Chalk it up to her upbringing in nature, but Skye knew objects had their own energy, their own history. “Refocusing isn’t going to help. Eventually, you’ll learn to use your mind to push through the ground.” Skye flicked one last slug into the container. “That’s it! We have plenty.”
“Why the rush?”
Skye hadn’t even noticed she was practically running. “Oh. If we get back early enough, Duvall will probably let us help her mix the serum.”
“That stuff in the glass bowl on her desk. She’s always making some sort of concoction, whether for students, or the Patrol, or for the doctors at the medical center.”
Once they reached the learning center, Skye hurried down the hallway en route to Duvall’s room, so preoccupied with holding the container steady without dropping Lulu that she completely collided with Alex, who had stopped abruptly. She placed a hand on the wall to steady herself, and she felt a rippling ambience of concern and heard the murmuring of voices. Why would the wall be worried? She tilted her head towards the door to indicate that they should move closer.
She heard Duvall speak first. “You think it’s the real thing?”
“We don’t know,” a gruff voice answered.
“Westfall,” Alex mouthed to Skye.
“Who could possibly be in charge?” Duvall asked.
“A lot of people wanted her dead. The possibilities are limitless.” Westfall sighed loudly. “The Ardor Service questioned a few of the spirits who lived in Paradise at the time of the original members. But nothing out of the ordinary came up. I saw those spirits firsthand. I watched Van Hanlin hand pick those who left Paradise. This seems too juvenile for them.”
Skye heard the clinking of Duvall’s bracelets. “Have you considered that perhaps Van Hanlin is the reason they sent you here? To keep an eye on him?”
“I don’t know. Maybe. He’s made some crucial mistakes. But I think it’s more because of Alex Ash.”
Things were getting interesting. Skye eyed her popular friend, who listened ardently.
“So you agree with me about her?” Duvall asked.
“No,” Westfall replied. “If Alex was who you think she is, she would have moved before I even planned to throw the orbs at her. It doesn’t matter if she stopped them in midair. She isn’t who you think, Lucia. Besides, the incidents began before she died.”
“Are you forgetting that Alex’s arrival was predicted? This is certainly the year!” Duvall exclaimed. “We were told specifically, ‘the year of the siblings.’ Or have you been around for another class of newburies with so many family members? There hasn’t been a group of siblings since the DeLyres! She predicted it, Ardor! And don’t you dare lie to me and tell me you don’t believe this is the year! Why else would you have arrived here, my dear? I’m guessing you heard about the multiple sets of siblings and came running!”
Skye was in awe of Duvall. No one spoke to crotchety old Ardor Westfall in such a way.
Duvall’s voice became quiet. “At least it justifies the mother’s death.”
Mother. Skye had overheard the Darwins whispering something about Alex’s relatives, but they’d never mentioned a mother. There was something special about Alex, but if Westfall was involved, her past had to be tainted. Westfall was famous for three things: fighting, protecting, and sniffing out criminals.
“We couldn’t have known they would go after her,” Westfall said. “Or that they would make assumptions off of mere resemblance. But again, I blame Van Hanlin. He said he could handle the surveillance in Brigitta.”
“Well,” Duvall said softly, “the girls will be back soon.”
Skye put a hand on
Alex’s shoulder and guided her backwards down the hallway. Alex nodded to her, showing she understood. They would make it appear like they were just arriving. No sooner had they reached the edge of the hallway when Westfall stepped from the classroom. He eyed the duo suspiciously, but then again, his face always twisted in such a way.
“Hello, Ardor Westfall,” Skye and Alex both mumbled, sidling past him.
Duvall stood behind a large bowl on her desk. She was staring into space and stirring a liquid that hissed angrily. Smoke rose from the concoction in the form of a gray tongue writhing like a sea serpent. “It isn’t polite to eavesdrop,” she said absently.
How did Duvall know everything? From what Skye deduced, witches were not physic.
“Slugs, please,” Duvall said, holding out her hand.
Skye handed them over and peered into the bowl. The mixture chomped its lips and spat at her. She withdrew quickly, cupping her hand over Lulu protectively.
“See anything new?” Duvall asked.
“You finished even more quickly this time, Skye.”
“The ground was dry. It was easier to see the trail.”
“Wouldn’t it be nice if everything that was buried left a trail?” Duvall gazed at Alex meaningfully, and then she pointed to the far wall. “Go into the cabinet above the sinks and fetch two daggers.”
Skye did as she was told and then handed one of the daggers to Alex.
Duvall handed each of them an Erlenmeyer flask filled with brown kidney-shaped objects. “Spear the little critters and collect the juice in a vial. Take your time. Don’t leave any juice to waste.”
Alex didn’t know what she was in for. This should be entertaining, Skye thought. Alex lifted the dagger and prepared to slice the skin. When the blade grazed the Alybon, the seed propelled from the table like a bullet.
Alex whipped back in her seat, shocked. She lowered her chin to the desk, analyzing the seeds, but they remained still. Skye bit her lip to keep from giggling. Alex lifted the dagger again, ever so slightly cutting the nearest Alybon, which cackled in a raspy voice and bent in half, clutching its belly in hysterics.
Alex shrieked, and Skye burst into laughter.
“You could have warned me,” Alex huffed, pointing to the creature. She certainly had a quick temper.
Skye grinned. ”And miss the look on your face?”
Though the corner of her mouth was upturned, Duvall continued to stir intently.
“Hold it like this.” Skye demonstrated how to grasp the sides. “And after you cut, just squeeze a little bit, so it doesn’t tickle it so much.”
“It’s alive?” Alex asked, sticking out her bottom lip crookedly to blow a curl from her face.
“Well yeah,” Skye said. Wasn’t it obvious? “Seeds become trees, you know.”
“Silly me. Trees aren’t usually ticklish.”
“Sure they are,” Skye said. Wasn’t that common knowledge? She’d heard them laughing so many times, even back when she was living. She finished squeezing the first Alybon and placed it back on the desk, where it pulsed up and down, catching its breath.
“Does it hurt them?”
“Does it sound like it’s in pain?” Skye knew that seeds were resilient, much more durable than the saplings they’d sprout after their burial. “They enjoy it. They fill back up in a few days.”
“Alybon juice, of course.”
“Now,” said Duvall, “come on up and pour it in very slowly. One at a time!” She held up one hand to halt them from moving together.
Alex stepped up and tilted the vial, releasing its contents into the steaming mud-like goo. A cloud of brown smoke puffed into the air, carrying the aroma of cinnamon.
Duvall smiled. “Very good, my dear.”
Skye emptied the contents of her vial into the mixture next. The serum turned an incandescent shade of purple. It was liquid sunset. And right as she smiled in delight, the color faded to a dull hue. Fingertips of disappointment pinched her.
“It’s done,” Duvall announced in satisfaction.
“Do you need us to help you package it?” Skye asked, eyeing the rows of tubes waiting behind Duvall. “I promise not to drop any this time.”
Duvall glanced over her shoulder. “No. Go ahead and get ready for your day.” She shooed them off. “And be sure to go the back way.”
Skye clucked her tongue in disappointment. “Why?”
But Duvall already had her head halfway into the bowl.
Your dreams have been odd, Sephi. I know you don’t like it when I visit them, but being here I think of you constantly. Rocks, sand, and soil? What are you looking for? Are you thinking of Paradise, too? I do think our connection is something neither of us can control. Why else would our minds be so open to one another?
Don’t worry about my confusion. I just need to exercise my mind a bit more. I wish I had an ancestry to guide me.
I tried to get some answers from the Darwins and DeLyres since they both have such substantial history here, but the card game last night was a debacle. I knew it wasn’t a good idea for Ben DeLyre to invite his brother, Leo. The boy is more of a nob than anyone I’ve ever encountered. Technically, it isn’t cheating when I toss my cards under the table. If no one else notices, I believe it is their fault, not mine. Leo caught on towards the end of the night and began a tirade about morality. Gave me quite the headache.
Leo DeLyre asked about you several times. I think you have an admirer.
Ellington couldn’t stop beaming. Ardor Westfall had seemed impressed with his findings. He struggled to steady himself on the bumpy path back through the trees, precariously balancing a stack of thick folders stuffed with his uncle’s precious records.
“Ellington!” He heard her voice and his heart skipped a beat. For a moment, he thought it was her , but he should have known better. Of course it was only Alex. Why was she awake so early?
“Ellington!” she bellowed again.
Without slowing his speed, he peeked over his shoulder. She was right behind him. There was no escaping. He tried to sound jovial. “Alex, hello! How are you?”
“I’m fine! What are you doing? Why were our last few sessions cancelled? Not that I’m complaining. No offense.” She quickly held up a hand. “You know I hate therapy.”
“Oh!” He did his best to hide the folders in his arms. He’d exited through the back door in order to avoid seeing anyone. “I’ve been asked to do a bit of research, I’m afraid. It isn’t usually my responsibility, but the mission falls under my area of expertise.”
“What are you researching?” Alex asked breathlessly.
“Oh,” Ellington said with a start. “Um … ” Not your mother , he almost blurted out. He’d been skirting around Alex’s questions about Erin since the poor girl arrived here. How do you tell a child that her mother was hunted like an outlaw with a price on her head?
“What is it? Paradise?”
This girl was behaving more and more like her mother every day. How did she hear about that?
“Er … why?”
“I read about it.” She shrugged. “And it’s written there on your folders.”
Ellington shifted the folders, but it was no use hiding the labels now. “I have been asked to take a look at it, yes.”
Alex’s eyes lit up. “It’s a city, right?”
She sounded so hopeful, and Ellington wondered why. She should be terrified of Paradise. “Not quite.”
“Oh. What is it, then?”
Drat , thought Ellington. How was he going to get out of this one? For a second he considered running away like a scared child. He adjusted his folders and sighed. He could give her pieces of the truth. He would just have to sieve it a bit. “I suppose people call it a city, but spirits do not make the choice to live there.”
“Paradise is a prison.” He absorbed Alex’s shocked expression. “My uncle Crete Reynes was also a psychologist, and often he traveled to Paradise to help the inmates. The prisoners tend to be rather extraordinary spirits, but they don’t really have it all together up here.” He pointed to his head. “Paradise is a place for them to get help and repent their actions.”
“A prison?” Alex began to fumble with the strings on her sweater. “Did you by chance ever know of anyone named Eviar?”
Ellington noticed relief on Alex’s face when he shook his head. “No, I’ve never heard that name before.”
“Oh,” Alex said slowly. “So, why are people suddenly interested in Paradise?”
He let out a little laugh. “No one is interested. Why would you think that?”
“Because you told me. Just now. You’ve been asked to research it.”
Darn my big mouth , Ellington thought, perplexed. “Yes, I suppose I did.” He balanced the stack of folders in one hand and swiped at his glossy hair with another. If he were human, he’d be sweating bullets. He’d been given explicit instructions not to give Alex any information that would put her in harm’s way. Such things had led to her mother’s demise, so they’d chosen a different tactic for Alex. “The people who end up there are typically very talented. Often, their profiles are researched to see if they can be of some service. At one point, the government sent Van Hanlin and my uncle to evaluate the inmates for release to help with the war. Although they were useful to the city, they also secretly terrorized it with what they thought were harmless jokes. Pranks.”
He used the last word carefully, and she seemed to understand. “You think those inmates never went back to Paradise?” she asked.
“No, they certainly never went back. They were recruited to help fight during the Restructuring, but they were on the losing side of the battle. They were all killed.”
“So then what is there to research?”
“Other inmates. Pranks aren’t unusual in the city of Paradise. The inmates need something to do, and according to the guards, they channel their creativity into practical jokes and such.”
“You think some more were recently released?”
“According to the Patrol, no. But I’m looking into it.”
Alex nodded. “But you’ve never heard of someone named Eviar?”
Ellington wondered why she was so sure this was someone’s name. “No. Never.”
She nodded, seemingly satisfied. “Thank you for talking to me, Ellington.”
“No problem.” Ellington was very happy to end the conversation.
“Is your uncle still alive?”
“No, unfortunately he isn’t. His job was rather dangerous. He had to speak to those spirits, to counsel them. There was risk that he would uncover things that others wanted to keep a secret. He practically walked around with a bull’s-eye on his back.” Ellington turned to leave.
“If all those inmates are gone, why would he have been targeted?” she called after him.
“Why indeed,” he muttered.
I was too cowardly to admit to you earlier that I saw something in your thoughts, but something tells me that you already knew that. Were you aware that I was there in your mind?
I know you worry about my friends. I have to admit that at times I do, too. What they consider to be “harmless fun” is often not harmless at all. If I hadn’t intervened last week, there’s no telling how long that cluricaun would have been hanging from its ankles in the courtyard. No one likes a cluricaun, especially one that has been drinking, but regardless, the last thing this town needs is bad luck.
I don’t know why it has been so difficult to control myself recently. I regrettably admit that a part of me wants to lose control because it is then that I feel the most powerful. When I’m involved with Gideon’s hijinks, the nerves spark something within me. Could the plague of my temper, or my anxiety, my emotions, be what makes me so extraordinary?
“Why do you care so much?” Chase asked. “Just out of curiosity.”
Why did she care so much? It was a good question. The letters had nothing to do with Alex, but she felt addicted to them. And perhaps the letters were drawn to her as well. Sometimes she would go to sleep with the box tucked away in the corner, and she’d awaken in the middle of the night to find it halfway across the room, inching its way towards her.
Whoever Eviar was, his talents were unmatched. He could control things with his mind so well that it made Alex wonder if his magic had leaked out into his writing. In one letter, he explained how he had silently willed half the students in Duvall’s class to fall asleep mid-lecture and how hilarious it was to watch their heads drop like victims of the guillotine. Duvall had been infuriated.
He had not been successful, however, in forcing spirits to go completely against their will. For instance, he could not manage to make Professor Duvall stop glaring at him, or to get his friends to stop cabbaging—stealing—for sport, or to force his classmate and rival Leo DeLyre to make a fool of himself.
So, who was Eviar? She needed to know. Did he ever find his family? Did he and Sephi end up safe together?
“Are you ignoring me?” Chase asked.
Classes had finished for the day, and Alex tried not to gawk at Chase’s perfectly chiseled form sprawled out on her bed. His mind had forgotten to project him into a shirt. “I’m sorry. What did you say again?”
“Does it matter who this guy is? I’m just wondering why you’re so obsessed.”
“Obsessed?” Alex asked defensively.
“It’s just the idea that this kid violates minds, and people don’t even know it. It’s creepy. And he’s kind of an ass.”
“You of all people shouldn’t judge someone for being in another person’s head.”
Chase offered a crooked grin.
“Besides, he’s not making them do anything bad. It’s pretty funny. And you might be interested to know that he mentioned an interrogation at the Dual Tower, but he said they called it an interview.”
Chase perked up. “Really? Anything about colors or someone transcribing?”
“No, he went on and on about Paradise.”
“Like Adam and Eve Paradise?”
“No dummy, like an underground city Paradise. Well, detainment center Paradise. This Eviar guy wanted to find it to keep Sephi safe. He just didn’t know it wasn’t a real city.”
“Why would he need to do that?”
“Because for some reason he thought she was in danger. Her relatives were killed. Maybe she was a witch or something, because in one of the letters, he mentioned that hunters were tracking her.”
Chase adjusted the pillow under his head. “Toss me one.”
“One of the letters. I want to see.”
He nodded. Alex eagerly searched for the box, which had been next to her bed but was now hiding underneath her desk. She crossed the room and ducked down to give the box a scolding look before extracting a letter. “Here.”
Chase sat up and the muscles in his arms rippled and settled like a wave. Stop staring , Alex told herself. Then she froze, wondering if he had heard her. When a playful grin spread across Chase’s face, their eyes met, and Alex knew she was busted.
“Stare away.”
Alex snatched a pillow and threw it at his face with a little too much force.
“Now you’re in trouble,” he said, scooping up the pillow.
Alex was already cornered. Chase had the pillow gripped tightly in his hands, blocking her from any escape. She tried to fake a cut to the right and leap to the left, but Chase shoved at the air around her, and the energy of it threw her flat on her face. Chase burst into laughter. Alex swiped violently at the space nearest to his ankles, satisfied when it pulled his feet from under him, and he fell backwards to the ground.
“Now who’s laughing?” Alex asked, but Chase spun over top of her, pinning her down and swiping the pillow across her face. The seams exploded and feathers flew into the air like birds freed from a cage.
“My pillow!” she cried.
He mimicked her in a squeaky voice. “My pillow!”
Alex pretended to scowl. “You are totally going to give me one of your pillows,” she ordered him.
“Oh, am I? Are you going to make me?” he said, inching toward the bed. He grabbed another pillow.
“Don’t you dare,” she growled.
“You’re much more fun now that you’re not a china doll anymore.”
“Shut up.” She flung her arm toward the pile of books on the nightstand, and the force of it nearly knocked him from his feet. As he caught his balance, she was able to snatch the pillow from his hand.
“How did you get to be so strong?”
She didn’t buy his peaceful tone or his flattery for a minute, and predictably, he pushed against the air between them. She wobbled but reacted quickly, retaliating with her own hands outstretched.
Stuck there in a battle of flirtation and stubbornness, Chase smiled and curled his fingers, clasping the energy between them. An outsider might think they were in the midst of some formal dance, staring each other down in a rainstorm of white feathers.
“Say I win,” Chase whispered, tightening his grip on the charge that zinged between their palms. She could feel the pressure of it.
“Not what I meant.”
Alex tried to push him away. She couldn’t take her eyes off of him. If she had, she would have seen the walls trembling. “Why are you breathing so hard?”
“You take my breath away,” Chase joked.
“That’s fine. You don’t need it.”
“I hear old habits die hard.” One side of his mouth curled flirtatiously, and he stepped closer to her. He grasped her hand, sending shockwaves through her being. They locked eyes and Chase ever so slightly wetted his lips. The intensity of his gaze generated crackles in the space between them.
She stood. And waited. Until the moment passed, and she knew he wasn’t going to act on what they both wanted to do. The relationship was even more agonizing than it had been in life. “Don’t you need to get to the fields? You’re going to be late for your game.”
He scrunched up his face, pretending to be offended. Instantly, a loose lacrosse jersey covered his torso. “You don’t want me here?”
No, because I don’t understand you at all , she wanted to say. “Are you going like that?” She waved her hand up and down. “What’s with the dirty clothes?”
“I’m going to run around in the dirt.” He shrugged. “I don’t blame my mind for projecting it onto my shirt.”
“So if you envisioned a space suit, that’s what you’d wear?”
“Okay then, I dare you to go to the field wearing a space suit,” she said, tossing his bag to him.
“What do I get if I win the dare?”
He blew through his lips. “Puh.”
“What? My respect isn’t worth anything?”
Chase let out a soft laugh and bent down to tie his muddy shoes, which somehow he hadn’t tied in his mind.
Alex made a disgusted face. “Those things are filthy.”
“I’m not exactly rolling around in feathers out there, am I?”
Alex laughed. “You could take some of these,” she said, ges
turing to the feathers that covered the floor “That would be interesting.”
“And very manly.”
“Girls play out there, too.”
“Yeah, yeah. Do you want to walk to the stadium with me?”
Alex shook her head. “I have a lot of work to do, and the stadium is distracting.”
“And that”—he pointed to the box of letters peeking out from under the desk to watch the show—“isn’t distracting at all.” He picked up the letter he’d meant to read before and opened it, turning it over several times. “Is this a joke?”
“There’s nothing written here.”
This was probably a trick, a diversion so he could pin her to the ground again. She inched towards him gingerly.
He held up his hands in surrender. “Truce. I’m not kidding.”
She took the letter from him and started reading aloud. “January eighteen sixty-six. Dear Sephi, I hate to admit weakness, but you have completely taken over my mind … ” She held up the letter. “Clear as day.”
“Alex, I don’t see anything.”
She realized he was serious. She folded the letter, tucked it back into its place, and pulled out a new one, double-checking that the writing was there. “What about now?”
“Nothing.” he said with a shrug.
“You honestly can’t see it?” She thought she heard the box sigh in exasperation, and she whipped her head around to glare at it. Chase kissed her softly on the forehead, like it was completely normal that she could see something that he couldn’t. Then he left her alone with her confusion. And the box.
I wish I had access to what you are seeing in your thoughts, but the window has become clouded. This is your doing, I suppose. You have never been allowed any extent of privacy, so I will console myself by assuming you need some privacy in your own mind. When you initially admitted that maybe the holes in my mind are because of you, I was beside myself. But the instances when I can’t control my emotions are the same instances when my mind doesn’t feel like it’s my own. And I become this way when the situation involves you. So maybe it’s time to put some distance between us. The last thing you need is more attention, since your fame is worldwide, and my antics have not exactly been kept quiet.
Please know that no matter what happens, my feelings for you will never change, but I feel like I need to do this for us. I have hope that Paradise truly is a place to keep those with talents safe. I have hope that maybe those spirits might know more about me. And if that’s the case, then I need to go find Paradise.
Go? He was leaving Eidolon? But, the story wasn’t over. Alex had barely read half the letters.
Against my better judgment, I continue to write to you during my journey. I will be enslaved by my thoughts unless I free them somehow. Thus, as dangerous as the written word may be, I have reached a point of desperation. I write these words faithfully to you and only you. And I thank you for being my deliverance.
Perhaps my most significant accomplishment thus far has been securing the opportunity to practice my talents without the Dual Tower to report to. I need to learn to distinguish the difference between what is real and what I imagine. And if I imagine it, can I make it reality, or is it already so?
At first we encountered only the bodied along the course of our travels, and so I was unable to practice manipulation tactics. There’s no game involved. But I’ve recently found a large group on which to practice. You’d be shocked to discover how beneficial a banshee fight can be when searching for hidden strengths. When stretching the boundaries of mental endurance, perhaps it is best to face something, or someone, with nothing to lose.
Alex couldn’t wrap her mind around the idea that Eviar had actually left. Why would he leave Sephi? She reached into the depths of the box for the very last letter, skipping over mounds of weathered envelopes she had yet to open, tied together tightly like mended pieces of a broken dream.
My Dearest Sephi,
My mind is a blessed asset and a malignant curse. In the past few decades, I have trodden down a fresh path, revolutionizing the extent to which our mind power can bend, no matter the sacrifice. I have opened doors through which no one would have ventured had it not been for my abilities and tolerance. And alas, my memory depletes. I am finding day by day that my memory no longer permits me to revisit much of the journey that brought me here. I don’t understand, but I wonder often since our minds are linked, has the information leaked to you? Doubtful.
Why are there so many wretched holes in my mind? I have asserted that most likely the abilities and deterioration are dependent upon one another. Is this the cost of what I’ve conditioned myself to do?
Is that why you cannot seem to find me? I know you are hunting me. I’ve felt you elbow your way into my mind a time or two. Did it frighten you when I attempted to grab your elbow when it interrupted my thoughts? Is Westfall with you, too? Are you even trying? Surely if you gave it your all, you’d be waltzing through my door at this very moment.
I wish for that.
I am aware of the threat these written words may present. What else could be so binding, so incriminating? I do not want to forget the road that I’ve traveled both dead and alive. Mainly, I cannot forget that you are my purpose. I realize that without you, without these words, I irretrievably forfeit my sanity, but regardless, when the time is right I must dispose of your letters. You are already a target. You believe you are the hunter, when really you are the hunted.
Do you know what I’ve learned? That we make our own way. We make our own fate. I’ve been chasing things that were already mine before the journey. I’ve built what I intended, finally, but I sacrificed my mind. I sacrificed you. And I sacrificed time. That is the most valuable thing.
And time isn’t on my side. I cannot find enough room to accommodate the memories of others in addition to my own. I once reveled in the fact that I was finding gift after gift, strength after strength. But now something is harming my mind. Can you see it? Perhaps if you are willing to open your thoughts to mine again, you would see what is
Alex gasped as the ink on the page rippled and then vanished. What happened? Where did it go? She flipped over the letter. Bare. She snatched up another letter. Bare. And another. And another. What was going on? She frantically thumbed through the box until she was back to the beginning.
Professor Melbourne is late for the morning session as usual …
She snatched up a letter in the middle of the stack. The ink remained. Why were only some of the letters now blank? She glowered at the box, which now had its back to her. Seriously? Was it punishing her for trying to share the letters with Chase?
And then it occurred to her that if the ink didn’t reappear, she would never know the ending. This was all she was going to get to read. She had been hoping for Eviar to have a happy ending, to prove that true love really can conquer all.
But her hope for him had vanished like the words on the yellowed page.
Alex was desperate to read the rest of the letters, but that stubborn black box had zipped its lips tight. She figured there was one person who might be able to help her. The next morning, Alex perched on a desk with Skye, waiting for their ABC assignment. Duvall cursed under her breath, squinting at the bottom of a list.
“What is it?” Skye asked, setting down a large white stone the size of a human skull.
“I forgot to tell Matthew to add bathroom mold to his list.”
“He’ll be just thrilled about that,” Skye remarked, and Alex thought she caught a tinge of amusement flicker across Duvall’s face.
“Skye, could you please chase down his group and inform them of my little addition?”
Skye didn’t look like she wanted to be the bearer of bad news. “Uh, sure.”
Alex focused on the shelved jars, eavesdropping over the room like birds on a wire, and pretended not to see Skye’s signal for her to follow. She waited a few moments and then sidled closer to Duvall. “Professor?”
“Hmm?” Duvall didn’t look up.
“It’s about a kind of ink.” Above her head, the hanging test tubes clinked and clanked. “Have you ever heard of writing that can disappear?”
“My dear, I believe that toy is older than you are. You can find it at any joke store, I’m sure.”
“No, this would have been long before joke stores existed. And it’s weird because, well, not everyone can see it … ” Alex stopped speaking when a look of warning clouded her teacher’s face.
Duvall used a pair of tongs to hold a crucible over a green flame. “Sounds like make believe.”
“If Thymoserum tricks the mind into forgetting something, I just inferred there’d be something counteractive, something that could make things appear to the mind.”
“That sort of magic isn’t something spirits can create. A mind must be trained to open up to such extensive levels of visibility.”
Alex eyed the murky goo inside the bowl. “Can someone who isn’t a spirit create it?”
“Do I have to say it, since you already know the answer?”
Alex shook her head, knowing full well this was witchcraft, yet she supposed a part of her had hoped that Eviar wasn’t involved with that. Was witchcraft the reason why he was so powerful? She longed to ask Duvall but avoided bringing up the name of someone whom Duvall had despised. “How could one person see something that another couldn’t?”
“Because of you. If the writing is meant for you to read, only you can see it.”
“But it wasn’t written for me. It disappeared right in front of me.”
“All of it?”
“It’s a glitch, then.” Duvall placed the crucible on a ring and stared down at the contents. The silvery substance levitated as one large mass and then broke into a dozen globs, each of which landed in a vial.
“A glitch? Can that happen?”
Duvall’s face twisted into a hint of a sneer. “Only if the person who wrote it didn’t know what they were doing.”
That evening, when the door to her room swung open with a resounding bang, Alex wondered whose presence needed to be announced so violently. After spending most of the evening staring daggers at the unyielding black box and cursing the blank paper inside, she didn’t feel like having company.
She stepped out into the hallway and faced the engraved caption of Kender Federive. In place of the mirror, the large frame displayed an image of Kender fighting the banshee in the clearing. It had appeared to Alex after the night of the attack. She glanced downward, and the last person she expected to see was curled underneath the empty copper frame of Sonja F. Rellingsworth.
“Jonas? What are you doing here?”
He looked up, and when his eyes reached her they seemed to soften. “Hey,” he murmured. “I just wanted to see you.”
Alex was blunt. “Why?”
She was too distracted to care about tact. “Because you’re Jonas. And you haven’t really spoken to me in weeks.” She took a seat on the floor beside him. “Why is that? Why do you always have to put on such a tough act?”
He remained quiet for several moments. “I’m not so tough. I just don’t wear my heart on my sleeve.” He leaned his head against the wall. “Like some other people.” He reached for her hand and flipped it over to run his finger along her palm.
Alex stared down at it, remembering how she used to analyze the lines, wondering why her life line was so long if her future was so bleak. Seeing it now, she knew it was only a projection her mind had created, but it was funny how the lines of her palm were frayed, a warning that life would try to rip at her seams.
“Do you remember that day we skipped school and went to the carnival at Earleigh Heights?” Jonas asked.
Alex nodded. All five of them planned to cut class that day, since it was the final day of the fair. Gabe, ever studious, opted out to take a quiz that morning; Kaleb’s flavor-of-the-week had convinced him to go elsewhere; and Chase couldn’t slip past the school’s strictest teacher. Alex and Jonas had been the only ones to escape to the carnival.
Alex stretched her legs in front of her. “I remember you let me drive. You were the only person who would ever have let me do something crazy like that.”
Jonas fought a smile. ”You’re a horrible driver.”
“No kidding.” Alex had barely been able to reach the pedals of the station wagon. The massive steering wheel had blocked her view of the rain-slick road. To make matters worse, they’d taken a twisting back road to avoid getting caught. Unfavorable odds, even for a good driver.
Alex had been tentative until Jonas barked at her: “Quit living like you’re already dead!” No one spoke to her like that. “Just live.”
She’d pressed her foot against the gas pedal as hard as she wanted to kick Jonas, and the car roared in response. With the windows down, the rain soaked them, but they didn’t care. Jonas never scolded her when the tires squealed. He never told her to slow down. He merely turned up the music. Alex had never felt such freedom before.
“Remember that funhouse?”
Alex nodded again. It was full of mirrors that made them look skinny, wiggly, chubby, all sorts of distorted. “I remember being scared,” she admitted. “It was disorienting.”
“But you know, I remember standing in front of those mirrors and thinking that no matter how warped my image was, yours always seemed clear. And your hand in mine just felt right.”
Alex watched him in bewilderment. “Jonas, you’ve had people trying to reach for your hand your whole life, and you smack them away.”
“You wouldn’t understand.” His tone was so hostile Alex could taste his resentment in her mouth like she’d bitten into a lime.
“Then help me to. I’m listening.”
“Anything I do, they do it better. Anything I want, they get it first.”
Jonas shook his head and stood up. Alex followed suit. Arguing with him was a lost cause, and she was too tired to unlock the chains around his ego. But for some reason, the door to her room didn’t open. Evidently, she wasn’t supposed to go in yet. Then she noticed that Jonas had stopped in the middle of the hallway, staring back at her. “What?” she demanded.
“He kept you to himself for sixteen years, Alex. And he never even acted on it.”
So that’s what this was about.
“Have you ever even considered the possibility of someone else?” he added.
And then, the door to her room swung open with ease. Alex stumbled into the darkness, half expecting Chase to be waiting there. The lights came on to reveal an empty room, but she could have sworn she saw a figure disappearing from her balcony. A new pillow waited on her bed, and the room she’d neglected to clean that week was now free of feathers. She ran to the balcony but found no one. And Chase never came back to her room that night.
As children, the Lasalles would frequently gallivant around town playing out their own rendition of cops and robbers. Although the boys adopted interchangeable roles, Alex was typecast as the damsel in distress. The dramatic theatrics of screaming for help and pretending to faint were exciting at first, but one day she changed her mind. Following a debate during which Kaleb failed to convince Chase that Alex couldn’t be a robber, Gabe finally swayed the vote. Jonas had scowled, and Kaleb had thrown his hands into the air while Chase and Alex shared defiant grins.
In the midst of the heist, the plan went awry. Officer Gabe apprehended and arrested Kaleb in the Parrish shopping center, and Officers Jonas and Chase were detained by batty old Mrs. Morrison in the Hallmark store for waving their toy guns outside her window. Alex seized the opportunity to retrieve the loot from the trash can where Kaleb had stashed it. The filthy sack of “treasure” reeked of rotten onion rings and mayonnaise, but it was gold to Alex, and she clutched the neck of the bag so fiercely that her knuckles turned bleach white.
She was going to win.
She reached the old grandfather tree that Kaleb had designated to be home base and searched for something to hang the bag from the thick trunk. It was then that she felt a cold object jabbing her in between her shoulder blades.
“Pass over the loot, you crook,” Jonas commanded, pushing the barrel of his Nerf gun into her back.
Alex cursed loudly and spun around to face him with her hands in the air, still gripping the treasure tightly.
“Not smiling now, are you?” Jonas said. His cheeks turned pink with excitement.
“How did you know we’d take the treasure here?” Alex choked out in an attempt to buy time.
“Kaleb hasn’t won here yet,” Jonas replied, pointing to the old tree with his free hand. At that point, the trunk bore the tattoos of only three sets of initials: GML, JML, and CML. The Lasalles always marked their territory.
It was then that Alex heard a click.
“Put the gun down,” a new voice ordered. The barrel of another toy gun appeared from behind the grandfather tree. Jonas’s eyes widened first in disbelief and then in anger when Chase emerged from behind it.
“What are you doing?” Jonas gasped. “You’re supposed to be my partner!”
Chase smiled. “I’m secretly in cahoots.”
“Those aren’t the rules.”
“Since when do we follow rules?”
Jonas’s jaw jutted out and swayed. His cheeks flushed.
“Come on. You always find loopholes when it comes to boundaries. You should have seen this coming.”
Jonas pouted. “But I should win. You’re going to choose her over me?”
“Yes,” Chase said matter-of-factly. And he handed Alex his Swiss army knife to mark her victory.
Since both Chase and Jonas were avoiding her, Alex was hesitant to spend so much time at the ball fields, but when she wandered around campus, she’d find herself there anyway. She remained on the outskirts of the stands with her homework, looking up occasionally to watch them. It was the perfect hiding spot until Jack Bond showed up one night.
“What are you doing here?” she asked.
“Detention. Duvall punishes me at least once a week. Believe me when I say this is much better than scrubbing the floors of her classroom.”
Alex was mortified. “Does she make you do that a lot?”
Jack nodded and extended his arms to either side like an airplane, balancing on one of the benches. He pivoted and began to walk away.
“To get an Ex. Then I’ll go to the far end of the fields by the skate park. Reuben should already be over there.”
“Your little sidekick,” Alex said, s
tanding up and gathering her things. “I’ll come help you.”
At the Ex kiosk, the vendor slid the cups across the counter, avoiding Jack’s touch. The boy regarded Jack with the same disgustful expression Alex had received when she was dying. In the final months of her life, she became a skeleton. Even the other loony patients at the institution stared in revulsion at her sunken appearance.
“Thank you.” Jack said, either oblivious to the rude treatment or ignoring it. He ordered an Ex for Reuben, as well.
“What did Reuben do to land cleanup duty?”
Jack frowned. “I think he volunteered.”
“Why would he do that?”
“I think he does it just to get out. He doesn’t have a lot of friends.”
“Maybe he should resign as president of the ‘I heart Jack Bond’ club, and then more people would want to hang around him.”
Jack handed her two cups. “He’s trying to fit in.”
“The only things he’s trying to fit in are your shoes.”
Jack always denied the worship that Reuben exhibited towards him. “People would like him if they tried.”
“You might be right—that is, if he’d actually talk to someone besides you and Calla.” Earlier that week, Alex had attempted to sit with Reuben at the Ex House. He’d regarded her scornfully, swept up his books, and stomped away. He’d left Alex sitting there, dumbfounded.
When they reached the skate park, a small maze of half-pipes, railings, and ramps, Alex was happy to find that from this area of the fields she had a clear view of the games. If she couldn’t be there with the Lasalles, at least she could watch them. The game of choice that night was soccer, Gabe’s favorite, and no sooner had she begun to search the faces of the players when she saw him skidding across one of the fields, sliding to save a ball from the goal. Her stare must have nudged at him because Gabe stopped to glance over his shoulder in her direction. She spun around and faced Jack.
“So, what are you supposed to be doing?”
Jack pointed to a ball of paper on the ground. “Cleaning. We take care of any littering or sticks or leaves.”
“That sounds easy enough.”
Alex searched for a place to set down the drinks and spotted Reuben on the ground, crawling around on all fours like a bloodhound sniffing for clues. He certainly seemed to be taking his job seriously. He noticed Alex, but didn’t acknowledge her until he found Jack.
“Hey!” he shouted a little too enthusiastically. It was like he’d been caught doing something wrong. He itched his neck furiously.
“We brought you a drink,” Jack said. “And stop scratching.”
Reuben scrambled to his feet. His round cheeks puffed into a grin. He grabbed the drink from Alex without a word to her.
She gave Jack a sardonic glance. “Do you guys ever play the games?”
“I’ve never really been one for organized sports,” Jack admitted, lifting a hand to shield the lights from the stadium. “I was always picked last in gym class.”
“But that doesn’t mean you wouldn’t be good at it here.”
“And give those guys an excuse to pound me into the dirt? No thanks.”
Her eyes were drawn to a vacant area of the field moments before Chase appeared from nowhere, using his body as a roadblock to send a boy and the ball catapulting through the air. She wondered about the legality of such aggression, but the referee didn’t blow his whistle. No wonder the Lasalles loved the games. Kaleb leaped up to retrieve the ball, scissor-kicking it downfield to another teammate.
Alex leaned down to pick up an empty cup and tossed it into a trash bag. “You’re a mover, Jack,” she realized aloud. “Why don’t you just pick up all this trash with your mind?”
“I can’t because Calla isn’t here.”
“What does that have to do with anything?”
Jack’s brow furrowed. “It’s a twin thing, I guess. I can’t really do much without her.”
“Is that why your sister is so quiet?”
“I wouldn’t call her quiet so much as … ” He searched for the right word. “Cautious. She’s paranoid about what people are going to do to her. Spirits around here are lemmings and just follow the Darwins. We have to watch our backs.”
“But you aren’t afraid of the Darwins,” Alex said. “It seems like you ignore them pretty well.”
“The Darwin family has a substantial history here, a history with powerful spirits who still hold office in Eidolon.”
“Aren’t you a multigenerational family too?”
“Sure, we’re as blue blooded as they are, maybe even more so, but you don’t see them inviting us to their little get-togethers, do you? We have much different histories.”
Alex opened the bag to dispose of a bit of paper but stopped when she noticed the writing scrawled across the top: “Initiation.” Alex scanned the page.
Alex turned the paper so he could see the checklist. She blinked several times to be sure her eyes weren’t playing tricks on her. But she read:
1. Worthiness
2. Notable trickery
3. Battle the insane
4. Harrowing
Alex looked up at Jack. “What is harrowing?”
“Battle the insane,” she read again. Her eyes drifted to the top of the page. “This says initiation . What do you think this is?”
Jack sniffed. “Honestly, if it was important, do you really think some idiot would leave it lying around?”
Initiation. There were so many little cliques on campus, and it could be any of them. Alex had even heard that the newburies in Duvall’s ABC club used to haze new members.
“Trickery,” Alex said loudly. “That’s the pranks. And the insane? Does that mean banshees?” A thought occurred to her. “Is that why Duvall’s stock of bladderwort was stolen?”
Jack dropped his bag and trash littered the ground at his feet. “How did you know about that?”
“Skye told me.” She studied Jack skeptically. “How do you know about that?”
“Please don’t hate me.” He wrapped his spaghetti arms around his face. “I was partially responsible for that altercation between you and the banshee in Moribund. I didn’t know the flowers would attract banshees when they were concealed.”
“Flowers?”
He peeked through his arms. “Bladderwort flowers. I took them from Duvall.”
“You stole them?” Alex pointed to the list. “Are you a part of this?”
Jack raised an eyebrow. “Who would invite a Bond into anything important enough to need initiation requirements? If for some odd reason that”—he pointed to the note—“is not a joke, I have nothing to do with it.”
“Then why would you take Duvall’s flowers?”
He laughed coldly. “Because I hate the woman, Alex. Every spare second of her afterlife, she is either trying to embarrass me or she’s sending me to detention. I knew she was going to need the flowers for an upcoming lesson, so Calla and I stole them to get her back for punishing us all the time.” He glanced at Alex apologetically and then diverted his attention to his toes. “And banshees don’t live around here, so I didn’t think anything bad would happen.”
Alex crossed her arms. “How did you steal the flowers?”
He shrugged. “It was easy. She was always making us clean her classroom. We didn’t know the flowers would be so obvious, though. They aren’t your average flowers. They’re giant and bright yellow. We threw them in a backpack to try to keep them hidden.”
Alex felt her stomach do a swan dive. Bright yellow flowers in a backpack? She’d seen that before. No wonder Jonas’s backpack had stunk like a rotten bog that night at the Ex House. It had been filled with swamp flowers.
Initiation … initiation …Was Jonas trying to become a part of some group on campus? It made sense. He would be free of his brothers.
“Should we show that to someone?” Jack offered, pointing to the paper.
“No,” she said firmly. “I’ll hold on to it.” At least until she could speak with Ellington again.
Alex nodded, thinking the note might come in handy if she confronted Jonas. Jonas and his backpack of yellow flowers.
Chase continued to avoid Alex during the next few days, and she had no clue why. She searched the campus, the Ex House, and the fields, but they all led to dead ends. She couldn’t hear anything in his head, and if she tried, the fortress around his mind only tightened. After class, she was trudging back to Brigitta when she spotted Gabe sitting at a table in the courtyard, and everything that was bothering her imploded. “Well, you are just the guy I needed to see.”
Gabe pretended to look scared, but he didn’t look up from what he was reading. “Uh oh.”
“Would you get your nose out of that book? I know why you’ve been so worried about Jonas,” Alex exclaimed loudly. “And I can’t believe you didn’t tell your brothers what he’s been up to!”
Gabe yanked her down onto the bench beside him. “Geez, Alex, could you be any louder?” He glanced over his shoulder and lowered his voice. “What are you talking about?”
“You’ve known all along that Jonas was up to something. What’s he doing? Is he trying to weasel his way into the legacy group or something? I found the flowers in his backpack. The ones missing from Duvall’s stockroom? The ones that attract banshees! He let us all think he was a hero when really the attack was his fault!”
Suddenly, sunglasses appeared over Gabe’s eyes. Alex felt so angry that he was trying to hide something from her that she snatched them from his face.
“Easy, Alex. He didn’t use the flowers.”
“I know it’s for an initiation or whatever, and you’re probably well aware because you always know everything. And you’ve kept such a close eye on Jonas recently.”
“All right, sleuth.”
“This isn’t a joke. Why didn’t you tell your brothers? Why haven’t you told me?”
“Look, you know how badly Jonas wants to make something of himself. If Kaleb knew about it, he’d figure out a way in. And that’s exactly what Jonas doesn’t want.”
“And what about you?”
“You know that Kaleb and I don’t necessarily think the same way.”
“What about Chase?”
“Chase is so close with Kaleb he would probably tell him what’s going on.”
Alex couldn’t argue with that. “Is it the legacies?”
It couldn’t be Duvall’s earthly kids, the way Jonas ridiculed them. He wasn’t a depressed choker or one of the movers. But ancestry and fighting were two things the Darwins favored.
“I’ve checked it out,” Gabe said. “On paper, it seems fine. They’re a bit rebellious but harmless. So do both of us a favor and keep quiet about it for a while. There’s something in it for you, after all.”
“If Jonas is a part of some exclusive group, something that will get him ahead, he won’t care so much about you and Chase.”
Alex slouched in her seat. Why did Gabe have to be so damn smart?
Gabe traced the lettering on his book. “I need you to keep this a secret, Alex. Chase can’t know.”
She couldn’t deny that something about it felt wrong. “You really think the group is fine?”
“The requirement wasn’t to have the banshee attack someone else. They were supposed to face it themselves. I’ve read plenty about initiations, and their list isn’t anything drastic. A lot of the smaller cities even list requirements or initiate spirits before they can live there. Please just don’t tell Chase.”
“I wouldn’t be able to tell him even if I wanted to. He’s been avoiding me.”
“I figured he was off with you.”
“You haven’t seen him either?”
Gabe shook his head.
“He’s mad about all this, I know it.”
“All the more reason for us to let Jonas do this quietly. Let him have this. One time,” Gabe said softly, “let him actually win.”
Lazuli Street was decked out in holiday cheer. Not the kind Alex had been accustomed to in life, however. She had learned in Madame Paleo’s history class that spirits celebrate the winter solstice, the longest night of the year. It was yet another excuse to have a party. Decorated sunstones lined the streets while umbrellas of white lights clustered like clouds overhead. Garland accompanied the ivy on the lampposts, and snow speckled the lollipop trees and shops. It had yet to actually flurry in the city, so Alex questioned how fake snow could feel cold to the touch. “Didn’t you expect it to be cold?” Skye had scoffed when Alex voiced her surprise.
No, she didn’t expect any of this, and so she chose to explore the city alone one afternoon. She still didn’t prefer to be by herself, but at least she was able to absorb the magic of what the imagination could create without being told what to see. She had nearly reached the end of Lazuli Street when warped music flooded her ears. She couldn’t tell if the music leaked from the cracks of the last door on the street with a rickety sign that read Stauffer’s Pub , or if the music was indeed spilling into her mind from Chase’s thoughts as she suspected.
The old wooden door swung aside before she could even think to push it open. The first thing Alex noticed was an extremely low ceiling. If she were to stretch her hands above her head, they would graze the boards. It smelled a bit like a basement—the good kind full of old treasures. At the far right corner of the bar, she found Chase.
Alex almost didn’t want to disturb him. She considered turning and running out the door. Even without reading his thoughts, she could feel his dejection. He had his right elbow on the bar, running his fingers through his hair. The other hand was a clutching a drink, which he swirled absently. She came to a stop behind him. “You look like an old man.”
As he turned, his wrinkled brow smoothed and his tightly set lips turned up slightly. “Guess I can’t hide from you, huh?”
“Guess not,” Alex said, pulling up a stool. She leaned in close to him. “How did you get in here?”
He let out a little laugh and his blue eyes twinkled. What was in that drink?
“When are you going to realize we’re dead? Age is irrelevant now. Besides, this is a Cluricaun bar. They invented alcohol, and this stuff”—he pointed to his drink—“was made for spirits anyway. It’s more like a stronger version of Ex.”
“How come no one hangs out here?”
“It’s not exactly lively.”
Maybe that’s what she liked about it. Alex followed Chase’s gaze to the man who was haphazardly wiping the bar with a dirty dishrag. He noticed Alex and raised his bushy eyebrows.
“Can I get you anything?”
“Sure.” Alex peered into Chase’s glass. “Whatever he’s having.”
“Deribatine Ale. Coming up.”
Chase leaned his temple against his fist and grinned adoringly at Alex.
“How much have you had?”
“Doesn’t matter. But are you willing to catch up?”
“I never back down from a challenge. You know that.” Alex rubbed her hands together.
Stauffer returned with a coaster and a small glass shaped like a boot. He placed them in front of Alex, and when she took a sniff, she winced at the pungency.
Chase chuckled. “A word of advice? You might want to drink the first one quickly.”
Alex tossed back the glass, allowing the fiery mist to sear through her. After a quick moment of regret, her entire body became warm and reenergized. “Oh,” she murmured in surprise.
Chase nodded. “Good, right?” He ordered another round.
Alex watched the bartender shuffle away. “Why are you here?” She watched Chase toy with his drink and avoid her question. “You were waiting in my room the other night, weren’t you? Why did you leave?”
Chase ran his fingers through his hair again and sighed heavily. “You know why I left.”
So he had heard the conversation. “How did you know Jonas was out there?”
“I could hear him in your mind. He’s right, you know. About what he said. Why should I deserve you now after all this time?”
“That was a decision we both made.”
“I should have fought for it.”
“You can’t listen to Jonas, Chase. You’ll go crazy. I don’t see things the way he does and neither do you. I’m sure it never occurred to him that anything you did or didn’t do was to protect yourself. And me.”
“I didn’t protect anything. What good did it do us?”
“We never could have predicted how our lives would end.”
Chase rubbed his brow. “You’re unsure of me.” The sleeves of his sweater were rolled above his elbows, and while he clasped his hands on the bar, Alex stared and wondered how projections could be so intricate. She saw the scar on his chin from when he tumbled off his bike, the muscular curve of his forearms, and the strength in his hands.
“I’m not,” Alex insisted firmly. “I just don’t understand you.”
“What if,” he sighed, resting his cheek on his hand, “after all my efforts, I haven’t done right by you?”
“You care about him.”
“If that’s what you interpreted from the conversation in my mind, then you read it wrong. Maybe you should ask before you snoop. I’m worried about Jonas, yes, so maybe that’s what you felt. Maybe now I see why Gabe is worried too.”
Chase shook his head, staring down at his drink. “Alex, he’s my brother.”
Chase took a sip. “Tell me honestly. Do you think his feelings for you are real?”
If this was why he’d been avoiding her, he should know better. “Jonas’s priority is himself. You know that. So there might be selfish intentions there. Beating out one of his brothers for something.”
“It’s more than that,” Chase argued. “He’s been acting so strangely.”
There was another reason for that. She wished she could tell Chase what she knew, what she’d promised Gabe she wouldn’t share, but she was bound by her word. “I’m sorry.”
“I wouldn’t put myself through this if it wasn’t worth it.” He reached up and tucked a strand of hair behind Alex’s ear. His fingers lingered there. “I never thought Jonas was capable of real feelings at all. I guess time can change things.”
“Or death.”
“Does that make me a bad person?” He lifted the glass and downed the contents, wincing. “Shouldn’t I want my brother to be happy?”
Alex repeated the words that Gabe had said to her the day she died. “Have you ever known Jonas to be truly happy?”
They were quiet for a few minutes, allowing Stauffer to fill their glasses.
“Have you been happy?” Chase asked. “After all this. Did I just make things more difficult? Do I now?”
Happy. She considered the meaning of the word. “If you’d felt the same or if you hadn’t, if we’d died, and if we hadn’t, I would have been in love with you anyway. Nothing could have changed it.”
She couldn’t believe she’d said it. She’d actually allowed the word ‘love’ to leave her lips, to dance across the space between she and Chase and land on his own lips as he repeated it.
He reached out and held her arm gently.
He didn’t answer. Instead he leaned toward her, and she felt a sensation in her stomach like she was about to leap from a twenty-story building. Like she was about to fall. He was going to kiss her. She’d wished for it, prayed for it, dreamed of it for so long that she could barely stand it. The feeling lifted her up, twirled her around, and placed her right back on that stool. It was the most wonderful euphoria, and in that split second, whe
ther it struck her from his mind or hers, fear engulfed her. For the first time, she realized perhaps why he refused to kiss her. They couldn’t go back after they fell. The overwhelming intensity of their friendship would only deepen. And part of her hoped he wouldn't kiss her now. Not yet. Not while things were perfect as is. His lips passed hers and kept going, grazing her ear, leaving her with nothing but her dizziness.
“I love you.” His voice danced against her. “There was never a time when I didn’t love you.”
She knew that. She’d always known.
“Let’s go home.” Chase smiled, holding her face in his hands.
“You just called this place home.”
Chase slid off his stool and slung his arm over her shoulders. “Home is wherever you are, Al.”
Who would have thought the holidays would be better dead? In life, Alex never had the Christmas morning she’d longed for—the breakfast, the stockings, the tree. She’d always woken up early to eat stale Corn Pops at a dirty kitchen table while she watched the parade alone and waited for the Lasalles to invite her next door.
In Eidolon, the celebration of the winter solstice meant carolers, the Ex House version of eggnog, cozy fires, and preparations for another Lazuli Street festival. On the morning of the twenty-first, Alex awoke to the sugary aroma of hot chocolate flavored Ex wafting from the vestibule. Above the balconies, words drifted through the air: Here’s to the solstice, rebirth, and new beginnings. It was a much different holiday welcome than the rancid scent of her father’s whiskey sweat and the sound of his drunken snores.
Outside her door, Alex found a heap of presents. The previous night, she’d made her rounds, hoping she was leaving gifts on the appropriate doorsteps, since of course there were no doors. Something told her the presents would end up in the right place even if she made a mistake. The building would see to it.
From Jack, she received a book entitled How to Use Your New Mind Effectively: A Spirit’s Guide to Success . She wondered if self-help books were as popular in death as they were in life. Skye deemed the book to be “overly anxious,” whatever that meant.
Skye’s present to Alex had been a very poorly wrapped lump. She complained for weeks that she’d never gift-wrapped anything in her life because her colony didn’t believe in it, and she didn’t understand the purpose of doing so now. The box was filled with anise seeds and a note instructing Alex to place half of them under her pillow to keep away nightmares. The rest of the seeds were to be planted because the leaves warded off evil. Alex was starting to think that Skye’s superstitions were out of control.
From Gabe, she received a device to transcribe her notes. Kaleb gave her a rulebook about Invisiball games. He’d scribbled a note that she needed to learn how to play since she wasn’t the “crippled girl on the sidelines” anymore. And from Jonas, she found a small box that housed a blue and black butterfly. She touched the wings gingerly, surprised to find the creature was made of something hard and resilient. It sprung from the box and circled the room three times before perching on the tip of her clock. Its wings slowly fluttered up and down in rhythm to what should have been the ticks of the silent clock. The gift she saved for last was from Chase. He had explained that due to his prior record, he needed quite a bit of help obtaining the gift, which had made her furious with curiosity. She ripped through the paper impatiently, and when she saw what was hidden inside, she realized that she had been missing something with all of her heart.
Though she and Chase had been in hundreds of photographs together, Chase had gone back for their first. Alex had kept the picture in her bedroom in Parrish Park, so there was no telling how Chase could have retrieved it. It was a black-and-white of her mother and Danya, two swollen pregnant ladies standing belly to belly. Danya clutched the arm of someone who was squirming to get away, out of the frame. Alex figured the arm belonged to Jonas, since tiny, devious versions of Gabe and Kaleb were in the background stuffing their fingers into a large cake. On Erin’s face was a coy half smile like she had a secret. Her arms cradled her belly like Alex was her greatest treasure.
Holding the picture, Alex with filled with an oddly comforting sensation. The safety of a mother’s arms.
Things became quiet in the months following the solstice. Alex and Chase continued their tango of indecision, holding back because of fear. Sometimes, though, it seemed that he couldn’t help himself, and he’d reach over and grab her hand, interlacing his fingers with hers and holding it over his heart while they walked.
Jonas was like smoke, less visible with each passing day. Alex was starting to believe that Gabe was right. Because of his preoccupation, Jonas wasn’t so concerned with Alex anymore. She kept her promise to Gabe and continued to keep quiet about Jonas’s recruitment despite the tugging at her conscience.
At first she checked Eviar’s letters for new ink every day, but come spring, there was still nothing. Alex lost interest and the box sulked in the corner of her room, swallowing dust bunnies like a frog catching flies.
For the most part, death was peaceful. Chase called it normal; Alex called it unnerving. The calm before the storm.
On a night when the world felt heavy, Alex spent hours in study hall. Although it had been months since her arrival, she still played catch-up in some areas. She probably would have passed out face down in her books if Chase hadn’t come to find her. He gathered her belongings in his arms, and they exited the Hall.
“I think you overdid it,” Chase mused, eyeing her weary face. “Do you need me to carry you, too?”
Alex pretended to think this over. When he stepped forward and readied himself to scoop her up, she laughed and backed away. “You don’t have to carry my books, Chase.”
“I think I can handle it.” But then, the thick text on the top of the pile slid to the ground. “Whoops.” He bent down the retrieve it at the exact same time Alex did, and they collided. Everything in his arms tumbled down.
Alex gave up and collapsed into the mess. “Maybe I’ll just sleep here with my books.”
He stared at her for so long she waved a hand in front of his face. “I love that smile,” he murmured.
She spoke without thinking. “That’s because it’s yours.” He began to shake his head, but she kept going. “I don’t know why you think you’ve done wrong by me.”
“Maybe I kept you from living the way you wanted to.”
“No. When I was with you, I was living exactly the way I wanted to.”
Chase held out his hand and lifted Alex to her feet. He pulled with unnecessary vigor, and she found herself pressed against him nose to nose. A breath caught in her throat as she realized the moment was absolutely perfect. She waited for him to pull away since they were in the middle of the hallway, but before she knew what was happening, he had tilted his head to the side and ever so softly, his lips brushed against hers, asking for permission. She nodded her assent, and he hesitated long enough to grin before giving in.
And then he kissed her.
Finally. Finally . She melted into him, pressing her lips against his, opening her mouth to swallow the happiness which inevitably consumed her. Their lips, their heads, their hands moved in faultless rhythm like a choreographed dance. She could feel his fingers combing through her hair, and she looped her arms underneath his, clutching his shoulders. How could they have been afraid of this?
The space around them began to crack and sizzle. Chase lifted his head for a moment, but Alex yanked at his shirt to pull him back in. Nothing had ever felt so right to her in her entire life. It was like nothing around them existed anymore. It was just Chase and Alex together, as it should be, and the world could wait.
The moment was interrupted by a loud thud from above them. Alex’s eyes flickered upward. “Wha—” Chase shushed her and cradled her face in his hands, allowing their lips to tangle again until a series of thumps thundered over their heads. They broke apart.
“Wait here,” Chase said. He softly kissed her nose and made his way up the staircase. He stopped halfway to look around.
Alex leaned against a pilaster. “Do you see—”
“Shhh.” He held a finger to his lips, his head cocked. And then Alex heard it too. It was a muffled whimper. “Hello?”
“Chaaaase.” The long wail echoed off the walls.
“Jonas?” Chase bellowed. He took off, flying up the staircase until he remembered he could think himself to the top.
Alex began to panic. Had Jonas seen them over the railing? Had he fallen in surprise? Thrown something in anger?
She tried to flicker and project herself to the top of the stairway, but she couldn’t concentrate. When she reached the third floor, Chase was huddled next to two crumpled figures outside Van Hanlin’s classroom. One was cradling the other, rocking back and forth. Jonas. He was holding someone with a head of curly blonde hair.
“What happened?” Chase demanded.
Jonas’s face was etched in agony. “He followed me. I didn’t know!”
Gabe’s head lolled back and smacked against the floor. His mouth hung open like the hinges of his jaw were broken.
“Gabe?” Chase cried. “Gabe?”
But his brother didn’t stir.
“What’s all over his face?” Alex’s terrified voice was barely above a whisper. Streaks of grayish-black whiplashes indented Gabe’s temple, cheek, and neck. Alex had seen similar markings before, though they were fainter and weathered, when Professor Darby had lifted the sleeves of his shirt.
Alex didn’t need to wait for an answer. “Did it scream?” she asked in horror. Chase gasped.
“No,” Jonas wailed. “It was bound when they brought it to us.”
“Brought it to you?” Chase exclaimed.
Battle the insane . Whoever was in charge of this “harmless” group had brought the banshee to the recruits.
“Why isn’t he conscious?”
“He was beaten. We need to go back. He wasn’t the only one.”
Jonas shook uncontrollably. “P-Professor Van Hanlin.”
For a moment no one moved. Alex couldn’t feel anything. She was weightless, treading on a breeze of foreboding.
“They needed to weaken the banshee, so … ”
“So, what?” Chase was looking between Alex and Jonas, flabbergasted. “Why would anyone mess with a banshee?”
“So others could fight it,” Alex whispered.
Jonas’s face showed no expression, no shame that Alex knew where he’d been and what he’d been up to. It made her feel disgusted.
Chase was shaking his head in confusion. “Van Hanlin had you fight it?”
“No,” Jonas snapped. “He was attacked!”
“Home. Gabe must have followed me. I didn’t know where I was going. I was just told to take the emergency exit out of the city.”
“What emergency exit?”
“There. In the corner past Van Hanlin’s classroom. You have to want to see it to actually find it.”
Alex blinked, and a stairway appeared in the wall. It twisted upward like the ramp in the vestibule.
“We weren’t supposed to know where we were going. There were others there, and I couldn’t see anyone else besides Van Hanlin and Gabe, but I recognized the woods. It was home. Parrish home.”
Chase pried Jonas away from Gabe. “Alex, go tell someone about this,” he commanded, hoisting Gabe into the air. “We need to go to the medical center. Try not to jostle him too much, Jonas!”
But Jonas couldn’t stop shaking.
“Who do I tell?”
“Anyone. Paleo is in the Grandiuse, right?”
“What do I say?”
“Just tell her that I found Gabe, and he’s hurt. That’s all.”
“And Van Hanlin?”
“We can’t leave him out. What if he’s still being attacked? Just tell her that we found Gabe here. We don’t know why or how, and the Patrol should be able to go through the stairway to find Van Hanlin.”
Alex glanced nervously at the twisting stairway. If Jonas had gotten to the meeting that way, the others probably had, too. Every inch of her being tingled in urgency, afraid a mob of young pledges were about to come spilling out after them.
“Are you hurt?” Chase asked Jonas, who limped under one of Gabe’s arms.
“I had to enter the ring because I hadn’t battled yet.” His response was directed more to Alex than Chase. He clutched his head with his free hand. “I didn’t know they’d already weakened the banshee until we reached the clearing. And then I saw it. And I saw Gabe at its feet, and Van Hanlin crumbled off to the side. I scooped up Gabe, and I just ran!”
“Wait, someone used my brother for bait?” Chase accentuated the word, my , staring hard at Jonas. “Who?”
“I don’t know.” Jonas wailed. “I couldn’t see any faces, and I was told not to try.”
It seemed like someone else was moving Alex’s lips for her when she uttered, “Will he wake up?”
No one answered.
“Go, Alex,” Chase ordered again. “Please.”
She nodded and took one last look at Gabe’s lifeless body before she projected herself down the staircase and ran as fast as her fear would carry her.
The night seemed never-ending. While Alex and Chase paced in the waiting room, Jonas became strangely calm and finally informed them of the details involving his recruitment process. He’d received a bid to join an alliance of spirits who would eventually leave Eidolon to move on to bigger and better opportunities together. Membership was exclusive and secret. He didn’t know the name of the group because he was still in the initiatory stage and not everyone would survive the process. He had found the invitation written in his law notebook one day, the words promising him a place amongst the elite if he was initiated. Even though he was not a multigenerational spirit, he hadn’t had to prove himself worthy because he was a sibling, a rarity in itself.
It seemed too good to be true. When the banshee mission was proposed, he grew slightly unnerved, but figured the tasks had to be challenging, right? Then, Alex was attacked. He hadn’t been following her that night in Moribund. He’d been stalking the banshee. He didn’t want anyone to get hurt, so when he found the backpack of bladderwort flowers, he took them so no one else could accomplish the task. Whoever was writing in their law notebooks would have to assign another mission. He thought wrong.
For the duration of the story, Chase slouched with his elbows on his legs, refusing to look at his brother.
The buzz had died with the night, and the morning only brought dread and uncertainty. About Gabe, about Van Hanlin, about Jonas. The blame for this would fall on someone, and there was only one newbury who had witnessed the crime, a newbury who was affiliated with an attack on a professor.
Alex feared Jonas’s punishment and wondered when the Patrol would come for him. She was surprised they hadn’t arrived already. Hopefully that meant they’d found Van Hanlin.
“I’m not going to wait around to find out,” Jonas informed her when Chase left for an update on Gabe. “I’ll run.”
“That will make you look guilty.”
“Aren’t I guilty? I was there.”
“You didn’t attack him.”
“I didn’t save him, either.”
Even though it was against the laws of this utterly strict afterlife, she couldn’t find a voice to discourage him from running. If they took Chase away just for leaving the city, what would they do to Jonas for leaving, returning with a near dead brother and without a missing teacher?
Jonas stared at Alex, his eyes refusing to allow too much emotion to escape. “Unless you want me to stay.”
“If you tell me to stay, I will.”
“You’re putting this on me?”
He leaned on the railing of Gabe’s bed and repeated himself. “If you tell me to stay, I will.”
Her response took too long. Chase returned with a frown, no news, and an order for Alex to keep quiet about the ordeal.
Jonas agreed. “Just go about your normal day.”
“How am I supposed to do that?” she demanded. She felt Chase’s touch on the small of her back, and calmness flowed through her.
“They haven’t asked us anything yet, but I’m sure they’ll come soon. You shouldn’t be involved in this. You have enough attention already.”
“And don’t you dare tell Kaleb!” Jonas ordered.
“Kaleb will know about him soon enough. Just give me a few hours.”
She felt helpless, but she did what they asked and headed back toward the campus. The moment she entered the vestibule, she collided with the very person she was trying most to avoid.
“Whoa! Where’s the fire?” Kaleb bellowed.
Alex did her best to appear composed. “It’s just, oh, never mind.”
“Nothing,” she said quickly. Think of something to say . “What are you doing with all these books? You look like”—the name stuck to her throat in a thick wad—“Gabe.”
He jutted his chin at the stack of notebooks in his arms. “Finishing touches. My project for Paleo is due tomorrow. On the time period with the Anovark girl. Actually, I was looking for you.”
“Me?” she yelped. “Why?”
Kaleb quickly surveyed the nearly empty vestibule. “Let’s sit down for a second.”
Alex glanced hastily at the clock and then fleetingly at the exit.
“Believe me. You want to see this.”
He chose a secluded table in the far corner of the room, tucked under the first tier of balconies. He sat and began to scrutinize her face, so she threw out her arms in emphasis. “What?”
“Chill out.” Kaleb crinkled his nose. “I went back through my research one last time just to be sure I didn’t miss anything good. You know I like to put on a good performance.”
“Not you,” Alex murmured sarcastically.
“I found something. It was strange because I’d gone through the notes a million times, and I never thought to look for a picture. I mean, why would there be a picture of a ghost? But then I thought maybe I could show off and try to project something like the teachers do, and well, it just appeared last night.”
Kaleb was shuffling furiously through the files. “Where is it,” he grumbled to himself.
“What would you need me for?”
“Hold your horses.” His voice dropped to a whisper. “I think I’ve discovered why the teachers look at you like you have five heads.”
“Because of my mother.”
Kaleb snickered. “No offense, Al. Yeah, you look like her, but she was here in town for maybe a decade, and her impact was about as resounding as a toothpick dropping to the floor.” Alex opened her mouth to argue but Kaleb held up his hand. “Before you make some argumentative Alex-y comment, think about it. Why would Ellington tell you to keep quiet about your family history? And when the banshee attacked, you said Westfall tried to block you from the Patrol, right? Have you thought about why?”
“Of course I’ve thought about it. I’m guessing it’s because of my mom.”
“You’ve been worried about the wrong person.”
He pulled a photo of a girl from an envelope. Alex immediately noticed the shape of the girl’s eyes. They were large and round with sadness weighing down the outer corners. With her delicate chin a
nd porcelain doll features, she was Alex. The only difference was her stark white hair.
She flipped over the picture and felt her mouth fall open. Josephine “Sephi” Anovark 1849–1865–1901.
Alex’s mind spun. “This is the Parrish Cove Ghost,” she said, just to be sure.
“That’s her.”
“Her nickname was Sephi?”
The pieces of a befuddling puzzle melded together. Josephine, the Parrish ghost, was Sephi. She had to be the recipient of Eviar’s letters. Same name, same time period. But that also meant she was murdered. Sephi would die. Eviar wouldn’t protect her.
And she looked just like Alex.
Kaleb waved the photo. “You are the spitting image of Eidolon’s most famous government advisor. And it girl.”
“You showed this to everyone?”
“Hell, no. Even if I’d wanted to, Paleo flipped her lid and stopped the presentation the second I mentioned Josephine’s name. We weren’t supposed to research people, just advancements. I asked her how in the world I was supposed to leave out a story like this. She said the project was about technology. I told her that was boring and—”
Alex interrupted his rambling. “How did she die again?”
“Some escaped mental patient killed her.”
Was this why her mother disappeared? Was this why Ellington had said not to mention her? Why would her name matter if Alex’s face gave away the secret? “The guy who killed her—do you know where he was from?”
Kaleb nodded. “Some place called Paradise.”
The walls in the psych room pulsated. Ellington eyed them warily. “Why the tension?”
Alex wondered if they were feeding off of her anxiety. About Gabe. About Sephi Anovark. “Better than that other time, right?”
During her session with Ellington following Chase’s return, she’d been so happy that the room had become smaller. The walls had closed in to try to get as near to Alex’s energy as they could, and Ellington, being claustrophobic, dismissed Alex immediately.
He gazed around the room. “How are you so strong?” he wondered aloud. “Your mind is quite extraordinary.”
“There are plenty of people who are smarter than me.”
“This isn’t about intelligence. It’s about brainpower, the energy your thoughts create. For goodness’ sake, you somehow withstood the shriek of a banshee.”
Alex grimaced. The word ‘banshee’ stung her entire being. The image of Gabe’s tattooed face flashed in her mind. “I don’t think that was because of me.”
“Don’t be so sure.”
“I told you about the dreams. About how Chase is there in my head.”
“Dream sharing is not unheard of; surviving a banshee is, however.” The walls jolted, knocking into a side table and sending a vase smashing to the ground. “And furthermore Chase does not have this effect on my room.”
“Dream sharing,” Alex repeated. “You mentioned that before. What is it?”
“Simply how it sounds. Visiting the dreams of others.”
“And speaking to them there?”
“Sometimes, but that is much more difficult to do.”
She chose her words carefully. “What about outside of dreams? Can spirits ever visit each other when the mind isn’t drifting?”
“You mean mentally? No, that’s impossible.”
Alex bit her tongue, and the walls shuddered.
Ellington eyed her suspiciously. “Why?”
“Just curious. But, how can I see the walls shiver like that , and believe that anything is impossible?”
“That’s just energy. Everything has energy, and in that there is life.”
“Can thoughts themselves be energy, then? Can they generate power?”
Ellington scrunched his lips, contemplating the idea. “Yes, I believe so.”
Alex watched the reverberating walls, wondering if perhaps the energy of Chase’s thoughts combined with hers explained how she survived the banshee. If there was double the amount of energy in her head. For a world so entirely mental, it was really hard to get solid answers.
“Why are you suffocating your notebook?”
Alex was inadvertently wringing a notebook like it was a dishtowel. Three seconds ago, she hadn’t had anything in her hands. Where had that come from?
“What’s bothering you?”
What wasn’t bothering her seemed to be the more appropriate question. She tossed her notebook to the floor.
“What happened to my mother?” she asked bluntly.
“I think you hold out on me.”
“As do you,” he replied without missing a beat.
“I know about Sephi Anovark.”
“And my mother?”
He sighed. “There is no possible relation to Sephi. Her relatives were extinguished. Her family tree was ignited at the base, cremated to prevent more prophets from branching out into the world. Sephi was the only one known to have risen from the ashes to become a spirit.”
“But then why was my mom killed?”
“We will never know that for sure.”
“I don’t believe you.”
Tap, tap, tap . Ellington’s pen slammed into his legal pad with unnecessary vigor. “Your mother was given answers, and she still went searching for more. Eventually it killed her.”
“Erin was a spirit for barely a week before she knew about Sephi Anovark. Spirits lined the sidewalks in our city, just waiting for Erin to pass by, to catch a glimpse. They celebrated her like royalty. Truth be told, there is no explanation why there is such a strong resemblance. She found no genetic connection. It still wasn’t enough. She wanted proof, and we all know how that ended up.”
“Why? Who killed her?”
“Sephi worked with the Ardor Service to help imprison spirits. She could predict a crime before it happened. She was also responsible for the destruction of the losing side of the Restructuring war. Anyone on the opposing side, anyone who shared the beliefs of the opposing side, would fear her.”
“You think the same people who killed Sephi went after my mother?”
“Impossible. They’re dead.”
“The inmates from Paradise? What about the other prisoners? Why are they being questioned?”
Ellington raised a small eyebrow. “Have you considered detective work for your future?”
“I’m not joking.”
“Why do you think I was so alarmed when you began asking questions about Paradise?”
Alex leaned back in her chair. She hadn’t realized she’d been gravitating toward Ellington during the conversation. It was too much to be a coincidence that she would find letters written to someone who could be her twin, letters only she could see.
Ellington finally stopped tapping his pencil and pointed it at Alex. “This stays in this room, but the pranks occurring in the city have the Patrol up in arms.”
Alex felt a draft in the room without windows. It crept up and settled behind her. “Why?”
“Because if someone is trying to copy the Paradise crew, your life is no safer than your mother’s was.”
Alex rushed back to the medical center as soon as she could. Something was wrong. In her thoughts, she was Chase. She could see his shoes crunching through the underbrush, passing an old familiar tree with five sets of initials carved into the bark, Alex’s included. And at that grandfather tree where they’d always hid their treasure, she heard Jonas say, “We’re almost there.”
And in her thoughts Alex heard, I can’t believe we’re back here.
She didn’t understand, so she picked up the pace. But the only one in Gabe’s room at the medical center was Skye. “Gabe’s hair looks a bit curlier,” she murmured in greeting.
Alex wasn’t in the mood for Skye’s offbeat remarks. Things weren’t right. The Lasalles wouldn’t have left their brother here like this unless it was for a really good reason. And even with Skye in the room, Alex felt very much alone.
Chase? Alex called in her head.
No answer. Usually if he attempted to block her intrusion into his thoughts, she could still sense him there, but he’d locked the deadbolt of his mind.
“How did you know Gabe was here?”
“Jack Bond.” Skye twisted her beautiful face distastefully. “He told me to give you a message from Chase.”
“What message?”
Skye pointed to the table next to Alex. There was a scrap of paper folded in messy fours. “He left that for you. Where did Gabe find a banshee?”
Alex ignored her question. “How did you know I would be here?”
“I guess Chase told Jack.”
Alex snatched up the note, her eyes scurrying across the page. “You didn’t read this, did you?”
“I didn’t want to touch it any longer than I had to,” Skye said, recoiling and wiping a non-existent contagion from her fingers. “Why?”
“Because you would have come to find me,” Alex said, hurrying out the door.
“What does it say?” Skye rushed to keep up. “Is it okay to leave Gabe?”
“You should stay,” Alex suggested. She threw open the door to the stairway with a little too much force. She heard a cracking sound, but didn’t turn around to see the damage she’d caused. “Ugh!” she groaned, jumping down the stairs. “Why can’t I just think myself out of this building?”
“Because you have to be able to see where you’re going. If you could think your way somewhere we wouldn’t need radio waves to travel.”
“I was being rhetorical,” Alex hissed, bursting out of the building. She waved the note above her head. “I still don’t get this. Jack saw Chase leaving campus this afternoon, and Chase told Jack to tell me that he was going home.”
“Home? Like Brigitta?”
“No. Home , home. Parrish, Maryland. Where Gabe was attacked.”
“Why would they do that?” she asked. “There’s a banshee on the loose.”
Because Alex never gave Jonas an answer to his question. She should have told him to go, to run away. He’d be better off away from his brothers. But if even a small part of him wanted to stay, he needed to find some evidence of his innocence. A way to clear his name. And he’d taken Chase with him, banshee or not. She couldn’t talk to Kaleb right now, and Gabe was unconscious. Without any of them, she felt helpless. Alone. Just like after they’d died. She wouldn’t put up with the hopelessness again.
Alex stopped abruptly, and Skye ran into her. “How do I get to Gramble station?”
“What are you expecting to happen there ?”
Alex looked at her incredulously. “Travel.”
“Are you crazy? Everyone knows we’re not old enough to travel alone. There are rules about newburies. We won’t last ten minutes in the Gramble.”
Alex could feel her anxiety rising like a heat. “Do you know about the stairway by Van Hanlin’s classroom?”
“The exit? Sure. But it only works in emergencies.”
If this wasn’t an emergency, she didn’t know what was. She took off, racing across campus, so determined and lost in her thoughts that she was surprised to find Skye next to her when she reached the third floor of the learning center.
They turned the corner, and there, outside Van Hanlin’s dark room, sat an impatient-looking Professor Duvall. She stood quickly, jewelry jingling, shawls billowing, and her hands placed authoritatively on her hips.
“Professor.” Skye gulped. “What are you doing?”
Duvall huffed, placing one hand on the back of each of their necks, spinning them around and leading them to the opposite end of the hallway. “Helping you,” she whispered. “What took you so long? And what would you have done if the exit worked, huh? How would you have controlled where you ended up?”
Alex’s response caught in her throat. She hadn’t thought that far. Jonas had said he’d entered the stairway with urgency on his mind, and it had transported him home.
“There’s a reason why a roof parapet isn’t an approved form of travel. It’s only an emergency exit. Very dangerous indeed. Let’s go to my office quickly, shall we? We don’t have much time.”
Alex shot a questioning look toward Skye, who promptly raised a confused eyebrow.
Duvall’s office was a mess of books, lab tools, jars of unidentifiable substances, cages covered by blankets, and shelves congested with tiny vials. She scrambled up a rolling ladder, browsing through the inhabitants of the shelves with her bone-thin arms, mumbling quietly about organizing.
Skye’s mouth had formed a large O , astonishment glistening in her eyes. Alex followed her gaze to a large broomstick resting in the corner. There were tracks of dirty footprints trailing from the window to the resting place of the broom.
“Professor!” Skye sputtered. “You didn’t leave the city, did you? I thought it was too risky. What about the witches?”
Duvall followed their gazes to the broomstick. “I’d like it if you referred to them as the gifted, and I can handle myself. It’s been centuries. I doubt they still employ round-the-clock spies to sniff out my whereabouts.” Duvall cut Alex off before she could speak. “So, have either of you ever traveled by power lines?”
Both girls shook their heads.
“Of course not,” Duvall grumbled. “Because this school has become so prehistorically prude in its teachings. They foolishly assume if they give you too much freedom you’ll become troublesome.” She bit her lip. “You need alternate means of travel.”
“Do you mean … ” Alex couldn’t stop herself from gawking back at the broomstick in the corner.
Duvall cackled. “Oh dear me, no! That would be quite a sight in broad daylight!”
Alex crossed her arms and scowled, wondering how in the world she was supposed to know that they couldn’t just douse the broom in Thymoserum to make it seem invisible.
“So how are we going to get there?” Skye asked, glancing out the window nervously. “Electrical wires?”
Duvall shook her head. “Not if you’ve never done it before. You could easily get lost due to the frequent stops, and that would be unfavorable. Too much can go wrong if you don’t know what you’re doing.”
“Well, there aren’t any other ways to travel, are there?”
“You’d be surprised how many of the gifted in this day and age are solely technological.” Duvall spun a computer monitor around to face them. “What signal travels just as quickly as a cell phone?”
Alex inspected the computer. “We’re going to travel through the internet? Is it safe?”
“Of course it’s safe. You’re dead!” Duvall barked. “Your body is comprised of energy. Sometimes the monitor flickers, and I wonder if it’s them trying to find me. Spyware has nothing on pure energy. It isn’t comfortable like cell phone travel, so spirits don’t use it often. Alex, do you know anyone in the Parrish area who might provide us with a connection right now?”
Alex nodded. What teenager wasn’t constantly connected to the internet? She was willing to bet that right now Liv Frank was lounging on her bed with a bag of Oreos and a Diet Coke, scrolling through her phone and ordering her brother out of her room. In that moment, Alex missed her friend desperately. During the past few months she’d been so preoccupied she hadn’t had a chance to think about Liv.
“All right,” Duvall said, shoving aside some odd drawings on her desk. “Give me a phone number or log in name of any social media for whomever you’re thinking of, and you can travel through the connection.”
Skye reached out and grabbed her hand, but that didn’t make Alex any less nervous. “I don’t think this is a good idea.”
Duvall let out an indignant huff. “You doubt me? There is no other way for you to get there.”
“It’s up to you, Alex,” Skye said. “Do you really think they need our help?”
Yes . She couldn’t allow anything to happen to Chase. She’d only just gotten him back. And for him, she’d do anything. “Professor, why are you helping us break the rules?”
“Because you’re supposed to be there. And sometimes fate needs a little nudge.”
Alex didn’t quite understand, but she placed her free hand on the computer before she could chicken out.
“Allow it to pull you in,” Duvall ordered.
Alex tightened her grasp on Skye and leaned into the computer.
To say it was uncomfortable was an understatement. Alex didn’t know if the constricting dizziness in her mind was a result of the form of travel or a reaction to her panic. She never did anything crazy like this unless the Lasalles were there to catch her if she fell.
She mentally clung to Skye’s presence. They zipped around the bends of the roller coaster ride, yelping each time the electricity zapped them. They jolted and jerked through a silver tunnel of sparks, and Alex concentrated with all her might, picturing herself and Skye as one to avoid losing her friend. Finally, Alex saw a rainbow of colors, and she braced herself as they picked up speed and burst through the screen.
They landed awkwardly in a heap on the floor, which was smothered in a Pepto-Bismol pink carpet. Sitting up, Alex inhaled the familiar scent of Febreze and Abercrombie perfume and smiled at the room where she’d spent so many of her childhood sleepovers. Liv’s phone had been left on the floor next to a binder predictably sprinkled with black cookie crumbs. No doubt she was retrieving more snacks from the cupboard where her mother kept an endless supply. Posters of teenage celebrities and pictures of high school cluttered the walls: scenes from football games, dances, field trips, and boat rides. All with Alex. More than she remembered, and in most of them, Chase stood beside her. Liv had captured snapshots of a life lost, framing a note scrawled amongst the photos. Where did you go? she asked of the memories haunting her.
“Alex,” Skye whispered.
Right. No time for this. Skye leaped through the window, which revealed a murky sky concealed by a veil of clouds. Alex climbed onto the sill and took one last fleeting glance at the room before plummeting into the flowerbeds below.
Liv’s backyard bordered the Parrish woods. If they trekked far enough, they would be in the Eskers territory, and that’s where they would find the old asylum, the one Alex knew Chase was searching for.
“Are you ready?” Alex asked, preparing to dart in the direction of the woods.
Skye nodded, but her eyes grew wide as a voice drifted through the yard. “Alex?” It clung to the air around them like a prayer. Liv Frank craned her head around the windowpane and squinted into the darkness.
“She can see us,” Alex whispered in surprise.
“Alex,” Skye said with warning in her voice. “We need to go.” She glanced at Liv guardedly. “That could get us into more trouble than we can handle.”
She was right. Alex desperately wanted to see her old friend and wondered how Liv knew she was there, but there were more pressing matters at hand.
The girls hurried off into the trees which seemed so undersized to Alex compared to the redwoods she'd grown so used to seeing. They didn’t slow their pace until they reached a narrow road snaking its way through the underbrush.
“Okay,” Alex said. “It’s off this path somewhere.”
Skye had one hand closed around the nearest branch, and she used her free hand to hold Alex in place. “Do you hear that?”
“It sounds like … ” Skye tilted h
er head towards the darkness. “It sounds like bells.”
Fear still had the ability to make Alex’s throat tighten.
A child’s voice twisted through the air around them like an exhale of cigarette smoke. “Does she remember me? No screams this time?”
Alex spun around, but it was impossible to tell where the voice was coming from.
“Who is that?” Skye asked.
The bells jingled again. “Answer my question and I’ll show you who I am. He who makes it sells it. He who buys it doesn’t use it. He who uses it doesn’t know it. What is the object?”
Skye shrugged. She didn’t seem fazed by their present company at all. “It’s a coffin,” she replied easily.
“Smart girl,” the voice noted. “You look like a Gossamer.”
A figure appeared between two distant trees, and he was far less intimidating than Alex expected. He was stick-figure thin with white hair and young laugh lines. Alex had assumed the squeak in his voice was due to insanity, not adolescence. He didn’t wear the jester’s hat, but it hung from his waistband. His defiant eyes curled up at the edges like he’d been caught doing something wrong. He reminded Alex of Huckleberry Finn.
“You’re the Jester?” Alex asked.
“I knew you’d be back here.”
The boy shrugged, shooing the air with his hand. “Once you’ve been a spirit as long as I have, you get a sense for the soon-to-be deceased.” He grinned widely at Alex. “You stank of death.”
“Thanks for the flattery.”
“You’re quite far from the others.” The Jester tut-tutted. “Lost, are you?”
“No, the old Eskers building isn’t far, right?” Alex asked. “The west end?”
“Oh.” The boy pursed his lips. “Yes.” He glanced in the opposite direction, narrowing his eyes suspiciously.
“Have you seen two boys?”
“Only two? Yes,” he replied in a sing-song voice. “They look the same, similarities misleading, one is so honest and the other deceiving.”
This kid has lost his mind , Alex thought.
“Can you show us where they are?” Skye asked.
“I wouldn’t go near that building if I were you. Insanity isn’t something to meddle with.”
“They’re our friends. We’re going to find them.”
For the first time, the Jester’s smile faded. “Okay, fine, have it your way. I was hoping you’d stay and play awhile.”
“Wait,” Alex said, remembering the rumors. “Are there other spirits living there in that building? Will they hurt us?”
“They’re hiding right now,” he replied, “for obvious reasons.” He pointed to the left. “Follow the sounds of screaming.”
Alex watched him float away to the ringing of bells. “What a whack-job.”
“I thought he was interesting,” Skye said.
They turned in the direction to which he’d pointed. Within minutes, they came to a large, rusty steel gate labeled The Eskers .
“It looks like a concentration camp,” Skye commented, wrinkling her nose.
No birds chirped, and the light even kept its distance, tucked safely behind the darkening clouds. Alex’s residence had been the newer version of the facility, which was built on the opposite end of the woods. This side of the Eskers had an entirely different vibe. Half the building remained intact. The leftovers, however, comprised a mountain of singed bricks and blackened debris. Alex could smell the burning of the rotten embers like charcoal sitting for hours after the grill had died.
“Charming place,” Skye noted, slipping through a hole in the gate.
“I don’t hear any electricity, do you?”
Skye shook her head. “But that’s only when spirits move at an exhaustingly fast pace. Banshees aren’t reasonable enough to know better, so it wears them out, but you might not know it’s there until it's hovering behind you.”
Alex shuddered and glanced over her shoulder, half expecting to see a set of soulless black eyes piercing through her. “So we shouldn’t just start shouting out Chase’s name, huh?”
“Probably not the best idea. I don’t feel good about this place.”
Neither did Alex. Who would? But they needed to hurry before they lost the dim light from the cloudy sky. Skye followed Alex through overgrown weeds, jagged stumps, and random furniture scattered throughout the yard, a chair here, a blackened file there. The building was like a stroke victim—from one angle the structure seemed perfectly healthy, unscathed, and from the other side it slumped lifelessly.
Alex didn’t want to tell Skye how scared she was. Rumor had it that during renovations, the builders became frightened after a series of accidents. They abandoned the project, labeled the building “damned,” and left it alone to rot. No one cleared the dirty surgical rooms for lobotomies or the beds with shackles for electroshock therapy treatment. Or so she had heard.
“Is there a door?” Skye asked. “I don’t want to go through the wall. I don’t want to touch anything.”
“I’ve never gone through a wall,” Alex admitted. “And I’m not sure I could think my way through it right now anyway.”
They found a side entrance where a door dangled askew, hanging by a hinge. One at a time, they ducked into the unknown.
Skye stumbled over the threshold and caught herself by grabbing the doorframe. She shivered violently and ripped her hand away. “Oh God,” she choked. “What’s wrong with this place?”
“Ironically,” Alex said, “people say it’s haunted.”
They weaved through the rickety end tables and metal hospital beds of an old infirmary, complete with bloodstains in the outlines of human forms, and Alex couldn’t help but wonder if the hospital was flooded with lunatics and banshees lurking around every corner.
Alex tried to make her voice sound determined, but it shook uncontrollably. “Let’s just find the boys and get out of here.”
A greenish glow tinted the hallway. The overhead lights flickered like dull strobe lights and buzzed at them in warning: Someone had been here. It stunk like a science lab, acidic and pungently chemical.
Alex trembled, and her pride blamed it on the chill, not her fear. They floated down a hollow hallway, passing dozens of identical black doors with tiny rectangular windows. Solitary confinement.
“Look,” Skye whispered, pointing to the ground. The dust they were sifting through had already been disturbed. Unfortunately, there were not footprints lining the dirt, but two solid lines. Alex pictured the way banshees traveled, dragging the tips of their toes, and the hairs stood up on her arms.
The hall seemed to stretch behind them for a mile. Each time the lights sputtered out, they were momentarily engulfed in darkness, and each time the hazy glow flooded them again, Alex was terrified there would be a monster standing before her. The horrible stench of burnt embers became stronger the more they walked, and Alex concentrated so hard on ignoring it that she almost didn’t notice Skye stop.
“Do you hear that?”
It sounded like flapping bed sheets, but it was impossible to tell from which direction it came. Suddenly, the lights zapped, and they were swallowed by blackness.
“Alex ,” Skye whimpered, clutching her.
“Shhh.”
The lights pulsed on, slowly reappearing and going out again. In and out, in and out, like a morbid game of peek-a-boo.
Lights on. Alex saw Skye, her chin quivering.
Lights out.
Lights on. Skye’s eyes were darting every which direction.
Lights out. Flapping …
Lights on. An open door down the hallway.
Lights on. Shadows dancing. Alex’s breath escaping in short gasps.
Lights out. The sound of something dragging softly across the floor.
Lights on.
Alex slapped her hand over Skye’s mouth before the bloodcurdling scream could erupt from her throat. A dead-still form of a banshee slumped like a cat held by the skin of its neck. Strings of hair covered most of its sallow face while it cocked its gruesome head in question, no doubt wondering what they were doing, though it never completely lifted its black eyes.
Lights out. The bone chilling sound of its toes dragging across the dust covered floor.
Lights on. It was several feet closer. Its pallid hair fell back, and it slowly lifted its head. It was a little girl. Alex could see the purple circles under her macabre eyes, which rose and seemed to stare directly through Alex’s pupils and into her terrified soul. The corner of the banshee’s mouth sagged in a way that made Alex picture her pleading for mercy during her last few moments of sanity. Alex kept her hand over Skye’s mouth and began to back up slowly.
Lights out. Alex could feel the girl’s presence, her charge. It was moving with them, creeping closer.
Lights on. She was inches from their faces. Alex could hear the dulled hum of energy. The girl’s eyes rolled back in her head as her mouth opened in a wide O . Alex could practically see down her throat into the depths of hell. And then her head snapped up straight, narrowing those devil-black eyes. She lifted one hand, and Alex braced herself.
Lights out. ZAAAAAP ! The electricity was so painful that Alex couldn’t hold on to Skye. A blue current erupted between them, and her ears were filled with Skye’s agonizing scream. The icy fingers of electricity grabbed Alex’s mind and twisted it, suffocating whatever life was left in her.
Somehow it hurt all over. She didn’t have a heart, but it constricted. She didn’t have a torso, but it burned. She didn’t have breath, but it stuffed her throat, asphyxiating her. And then blackness.
Lights on. The banshee’s bony hands were still lifted, ready to shock the girls again.
Lights out. Skye whimpered. Alex heard the stomping of feet against the unforgiving metal floor.
The girl electrocuted them again, and in the brilliant steak of the blue lightning, Alex could see shadows running towards them.
Lights on. Whooooosh ! Boom ! The banshee slammed into the wall and collapsed to her knees, lifting her head to snarl.
Chase jumped high into the air, his leg flying out directly in front of the banshee’s mouth. The force of it created a sickening thwack . Before the banshee could retaliate, Jonas swung his right arm down on her, immediately followed by his left fist. He ducked so Chase, behind him, could push the full force of his energy at the girl.
The banshee fell into the nearest room and bellowed in surprise while her body began to convulse in spasms of electricity. Chase slammed the door shut, containing her.
Jonas cursed loudly. “What are you doing here?”
Skye shook so violently it was like her body was seizing.
“You shouldn’t have come here,” Chase murmured, but he pulled Alex into his arms. His embrace was like a drug, injecting courage into Alex’s soul.
“We need to get you two outside,” Jonas replied, looking around frantically, maybe waiting for another monster to appear. “Now.”
“What about you guys?” Alex asked.
Boom !
Alex jumped away from the door.
Boom ! Boom ! The banshee hurled herself into the metal door. The hinges creaked and popped. They heard a screeeeech of electricity from inside the room.
“Why doesn’t she just go through the wall?”
“She isn’t that smart,” Jonas murmured.
“Is she smart enough to use the knob?”
And then they heard a tiny click .
“Run!” Chase commanded, already in motion, yanking Alex behind him. The others were close at her heels.
She heard a squealing roar of rage. Alex didn’t know exactly where she was going, but the hallway twisted and sloped upward and sooner or later there wouldn’t be anywhere to go. The stench from the charred debris ahead burned her senses. When would the damaged structure give way?
At the peak of the rising ramp several yards ahead, finally, Alex could see the murky, gray sky above, but a mountain of rubble guarded the gateway to freedom. Crooked metal wheelchairs meshed together into a grisly jungle gym. They rusted against jagged piles of floorboards and fragmented doors speckled with chips of paint, slashes of wallpaper, and shards of broken glass. It stretched beyond what would have been the ceiling if the building still existed.
“Up!” Chase yelled when they reached it.
Alex’s fear hindered her concentration. She tried to climb the remains but couldn’t focus away her weight. The objects teetered under her. Her hands grasped pieces that crumbled or clattered, and her feet slipped against the glaze of ashes.
Jonas projected himself to the top of the mound, and he circled his hands, urging them to hurry.
Alex couldn’t stop gravity from pulling her down. She turned to see the banshee climbing the ramp of the hallway on her hands and knees, thrashing her body around in rage so violent her features blurred. The whips of hair lashed about in nightmarish snaps. She opened her mouth, preparing to shriek.
Chase reached for Alex. What do we do? They might be able to save each other again, but what about Skye and Jonas? How could they possibly survive this?
A flash of red whipped past them. Skype slid down the mountain of junk. She held out a handful of smooth, gray rock. She curled it into her fist and winked at them somberly.
“What is she doing?” Alex tried to grab her, but it was too late. Skye launched herself back down the ramp, skidding toward the banshee.
“Skye, no! Don’t touch it!”
Alex lifted her arms, but she couldn’t shove the space between them to separate them, as she had with Jonas in the clearing. The hallway was too narrow. Skye connected with the banshee, and the impact cracked like thunder before they flew apart. The banshee crumbled at the foot of the ramp and lay on her belly, blubbering in aftershocks of voltage. She began to drag herself away and disappeared into the abyss of darkness.
Alex rushed down to Skye.
“What was she thinking?” Jonas asked.
“She was thinking of us. She saved us. Darby said he lived through his banshee encounter because he ran at it. You tried to the run at that banshee in the clearing!”
“No. I was trying to get that banshee to chase me from the clearing. Touching a banshee is like hugging a bolt of lightning.”
“But Chase kicked it!”
“I never actually touched it,” Chase said. “I just aimed for it. An actual punch can’t hurt it, only the energy from it can.”
“She’s not dead , right?”
“We’re all dead, Alex,” Jonas said dully. “Believe me, Gabe withstood much more than that. The doctors at the medical center said the mind shuts itself down for protection.” He pulled Alex to her feet. “You need to take Skye back to Eidolon.”
Chase scooped Skye from the floor and cradled her in his arms. They didn’t dare go back the way they came, but luckily they turned a corner to find a crater in the wall, leading to fresh air. They stood in the middle of ruins, on what was formerly the roof, collapsed to the first floor. A step to the left and Alex would be out in the overgrown lawn again.
Jonas nudged her in that direction. “If you want Skye to be okay, you need to go.”
“Are you coming, too?”
His gaze shifted into the darkness. “Yes. After we either find Van Hanlin or find some other sort of witness.”
“The Jester said everyone is gone.”
“Jester?” Chase’s head snapped up. “You saw him?”
“Maybe he knows something about last night.” Jonas said hopefully.
“Don’t be ridiculous,” Alex said. “You guys are coming back with us.”
“No, we’re not.”
“Jonas—” Chase began.
“I’m not leaving.” Jonas’s eyes darted around at their surroundings.
“What are you looking for?” Alex shouted. “You’ll hear it before you see it. That thing is pissed off.”
“Get out of here Alex,” Jonas urged her, but Alex remained rooted to the ground.
Chase stepped closer to Alex, holding out Skye. “I’ll stay here with Jonas. But I need you to go. You’re too much of a distraction.”
“If that’s true, then you shouldn’t have told me where you were going.”
“Why would you tell me where you’d gone if you didn’t want me to follow?”
Chase glanced at Jonas, who shrugged. “Al, I didn’t tell anyone where we were going.”
“You told Jack! He left me a note.”
Three things happened at once. Chase shook his head. Alex felt several warm snaps of electricity. And a sharp cry of pain erupted from behind them. Jonas’s body arched back, suspended in midair before plummeting down to the dirt and ashes.
“What the hell?” Chase shouted.
Lights began to appear at various points atop the debris. Was it the Patrol again? Here to save them from the banshee? The logical part of Alex’s brain knew better. The Patrol wouldn’t have attacked one of them.
Dread filled her as, within seconds, they were surrounded.
Despite Alex’s inability to pull her attention away from their invisible company she couldn’t quite look at them. She wouldn’t. It would inevitably show her what or who they really were, and she wasn’t prepared for it.
Alex!
The desperation in Chase’s voice startled her back to reality. She watched him place Skye’s hazy form behind what was once a nurse’s station. Alex was sure it wouldn’t protect Skye if a spirit wanted to attack her directly, but it would keep her out of the line of fire.
Jonas had managed to pull himself to his feet, pressing his palms against his temples. He and Chase stood on either side of Alex.
“Can you see them?” Chase asked, but Alex shook her head. “I know you don’t want to. I don’t blame you. But you need to try.”
She didn’t want to know, but she opened her mind to see them nonetheless. Silhouettes appeared one by one, turning into full projections. They were children, newburies. They were her peers. Joey Rellingsworth sat on the top of a demolished wall. A large boy named Hecker Smithson, who never spoke a word to anyone, folded his arms and glowered at them. He stood next to Reuben Seyferr, and … Jack? Alex’s initial reaction was to call it a hoax. A test orchestrated by Ardor Westfall perhaps, to punish them for leaving campus.
Chase inched closer to Alex. “What’s going on?”
Alex couldn’t help herself. “Jack?” she exclaimed, lifting her palms upward in question.
His name acted as a chain reaction. One by one, the heads of the attackers turned to gawk in surprise at those who joined them.
Jack stood proudly and squared his frail shoulders. “Is it gone?”
Alex looked to Chase, who looked to Jonas, who opened his mouth to respond but hesitated, evidently surprised that Jack was addressing him. Finally, he offered a stiff nod.
Please get behind the desk with Skye, Chase commanded again. His head shifted slowly, scanning the disadvantage of their unfortunate positioning with trepidation in his eyes.
Joey Rellingsworth swung his feet back and forth on the wall. “Why is there an extra?”
“Jonas,” Chase murmured, “what is he talking about?”
“She came on her own,” Jonas responded loudly. “I tried to get her to leave.”
“No, not her.” Joey pointed to Chase. “Him.”
Jonas frowned. “What?”
Hecker Smithson leaned down to Joey. “You know who that is, right?” He pointed his f
at finger in Alex’s direction.
“Of course I know. I think that’s the whole point.” Joey glanced over at Jack apprehensively, and he wasn’t the only one. Many of the attackers didn’t look quite so confident now that they’d opened their eyes.
“That’s her,” Jack affirmed. “That’s who they want.”
“Hold on.” Jonas took a step forward. “I thought I was supposed to bring my brother.”
Chase cursed. “This is why you didn’t want to tell Kaleb where we were going?” He glowered at Jonas. He led me here.
Chase shook his head in disbelief. I can’t believe he did this.
Jack studied Jonas’ face with interest. “The only reason you needed to bring your brother is because we needed Alex to follow. You didn’t think she’d come all this way to follow you , did you?”
Something inside Alex chilled.
Jonas’s mouth hung open for a mere second before his expression turned colder than Alex felt. “Why do you need Alex?”
“The message appeared this morning, but you probably can’t see it anymore. I’m guessing you no longer want to see it considering you ran way last night.”
Alex wondered why all these spirits weren’t running away now , now that they’d seen Jack among themselves. Everyone hated Jack! They ridiculed him! It felt like some alternate universe. But glancing at their faces, she realized that everyone hovering above her was similar to Reuben and the Bonds. They were each quiet, or meager, or misfit, or eager to get ahead.
“There is much knowledge to be had when you have ancestors to tell you what teachers will not.” Jack beamed proudly at Joey Rellingsworth, who shifted uncomfortably. “Blood runs thick, Jonas, something you don’t understand.”
Alex’s head was spinning. Why did Jack need to arrange this rendezvous at Eskers? He could have set her up easily at school.
Because he needed you off campus , Chase answered for Alex. He has no power there, but here it’s a different story.
“You’re absolutely sure she’s the one they want?” Hecker whispered to Jack.
“Oh, it’s her. The ghost of a prophet. I’m definitely right. And so”—Jack pointed to Chase and Jonas—“you two may go.”
“You expect us to just leave her?” Chase asked.
Jonas stood statue-still, his face blank, staring at nothing.
Hecker spoke quietly. “You have to do what you have to do. And so do we.”
“Am I supposed to know what that means?”
“We don’t have a choice anymore. If you won’t step aside, we will force you aside.”
“Step four,” Jack added quietly. “Harrowing.”
What is harrowing ? Alex thought to Chase.
Chase’s voice came out steady and confident. “Harrowing? Do you realize how long it takes to break a mind?”
“Of course,” Jack muttered. “We were witness to it last night.”
He’s dead . Chase’s voice pounded in her mind. Van Hanlin is dead.
“You’ll have to beat us for hours? Do you realize what the repercussions are?”
Jack huffed through his horse teeth. “There won’t be any.”
“You aren’t exactly charmed,” Chase said. Alex agreed and wondered why the newburies around them, who knew the Bonds were hardly a symbol of good luck, remained at his side now. Her bewilderment must have leaked into Chase’s head because he pointed at the halo of attackers who stood above them. “What about the rest of you? You would sacrifice your morals, your afterlife , to be a part of this group?”
“The groups on campus are encouraged,” Jack replied. “They’re designed to rally those who are similar. And this is greater than all of those combined.”
Is that why he was doing this? Alex wondered. Was this his way of fighting back? Of reversing the curse he’d been betrothed with? “And you don’t worry at all about the consequences of your actions?”
“What do I have to lose?” Jack crouched down on the jagged wall on which he was positioned. “We’re damned now. We can’t go back to Eidolon.”
“Did you know about this, Jonas?” Chase asked.
Although his brother asked the question, Jonas faced Alex when he replied. “I thought it was like signing myself over to the military.”
Jack threw his hands in the air. “Exactly! Do soldiers fighting a war return as murderers or heroes?”
Alex couldn’t believe his logic. “It depends on what you’re fighting for. This isn’t revolutionary. This isn’t honorable. You’re acting under orders like a bunch of obedient dogs.”
“Jack has a point,” Joey said, ignoring Alex. “Don’t soldiers act under orders?”
”Soldiers know who and what they’re fighting for,” Chase scoffed. “Do you? I bet you don’t. Jonas, did you?”
Jonas did not acknowledge his brother.
“We’re fighting for each other. Because no one else will.” Jack’s eyes traveled the length of the area. “Did you know that after two years they sort us out anyway? If we haven’t made an impression, if they haven’t seen something they can use us for, we don’t get to stay in the city.”
That didn’t make sense. “But the curfew and the rules?”
“Oh, the rules still apply. Why do you think the Patrol exists? This might be an afterlife, but it certainly isn’t heaven. This place is far from perfect. They don’t tell you that after you die.”
Yes, they do , Alex thought. That’s why this life was a choice, she realized. There wouldn’t be a choice at all if the world were perfect.
“And Eviar is for the elite.”
Alex took a step backward because she thought the ground shook below her. “What did you just say?”
“Eviar. This is an old brotherhood, an esteemed one.”
Eviar? How? It couldn’t be the same, could it? Eviar was a person. Dread began to tug at her mind.
“Jack,” she said in a low voice. “I don’t think this is going to turn out well.”
“I don’t want you to get hurt. I don’t believe the league itself wants to hurt you either. But if you’re in the way, I can’t protect you.”
“Are you listening to yourself? You tried to convince me that the Darwins are the enemy.”
He shook his head. “The Darwins know about all this, I’m sure. Just because they play on the opposite side doesn’t mean their side is the right one.”
“How is this going to help you?”
“We’re already here,” Jack said, glancing at Joey, who nodded and stood up.
“We’re already implemented.” Joey seemed to be trying to convince himself of his own argument.
“It’s not worth arguing anymore,” Chase said to Alex. “These spirits have found a niche. Even if they were willing to jeopardize it, they’ve seen what happened to Gabe. And Van Hanlin.”
Jack stretched a hand to Alex. “We only need you. We don’t have to hurt anyone.”
“No,” Chase said. “Prophets are hunted, Alex. Your mother was killed. There is no way I’m letting you go anywhere with them. We fight. They can’t beat us.”
Hecker guffawed and stuck out his chest, but Alex knew his towering size meant nothing. It didn’t exist anymore.
“This is my fault,” Jonas whispered.
“Yeah, it is. Tell me one thing, though.” Chase took his eyes off their captors. His exterior stayed strong, but Alex could feel something cracking. She reached out her hand, as though to hold him up, to keep him from crumbling. “You thought you were leading me here. Do you really hate me that much?”
Time seemed to stop. There was no danger of attack, only the danger of betrayal. Alex couldn’t bear to look at Jonas, who had no response for his brother.
Chase turned away from Jonas. “We aren’t giving them what they want.”
“Ten to three,” Jonas said. “There’s no guarantee. And I’m sure there are more of them waiting somewhere. We’re outnumbered.”
Alex didn't want Jonas to speak. She hated his voice, hated that he'd put them in this situation. But her hatred didn't change their predicament. She considered the newburies standing above them and knew someone was missing. Jack wouldn’t go anywhere without Calla. She had to be waiting somewhere, and Alex doubted she was alone.
“We can take it,” Chase insisted.
“What if Jonas tells everyone what he saw here?” a girl said in a low voice. “Or his brother, what if he tells?”
“We can’t go back. We can protect each other,” Hecker said. “Isn’t that what this is all about? Maybe that’s our test. There are plenty of other cities.”
Reuben shifted from foot to foot nervously. “I don’t know.”
Joey glared at Reuben disdainfully.
“It’s her choice to come with us willingly or not.” Hecker began to push at the air around him.
Alex could feel it like a gentle wave in the ocean, preceding the more vicious one looming. She watched in the horror while the others mimicked him.
Chase’s voice was confident in her mind. Blast ’em .
Alex had enough enmity bottled inside her to take out an entire town. She could feel the energy gearing, and she cringed in discomfort. Jack saw her face and there was a split second of panic in his eyes, but it was too late. The pressure in her head became too much. She couldn’t hold on any longer. Her hands flew to her head, but she wasn’t foolish enough to think she could actually grab hold of it. The force of her fury escaped and crashed to the ground.
She was liberated, no longer stifled by the fear of harming someone. The effect of the energy was an earthquake shaking the world.
The ground rippled, and spirits flew in various directions, but those who managed to remain on their feet shot blasts back. Before Alex knew it, she was knocked face down by the force of the blow. There was a pain shooting into her neck like she’d been hit with a fifty pound dumbbell.
She rolled onto her back and shoved against the air in another burst of energy, though much weaker than the first. The attackers scattered like ants, making a break for it.
Chase grabbed Alex’s hand and yanked her to her feet, dragging her from the wreckage. Jonas followed, blocking several blows.
“Skye,” Alex reminded them.
“She’ll be better off where she is,” Chase said, sprinting across the yard. “We’re leading them away from her.” He skidded to a stop.
A perimeter of attackers appeared, encircling the yard. Alex’s heart dropped. She was right. A second wave had been waiting, Calla among them.
Chase had a firm grasp on Alex’s hand, and he used his other arm to shove fiercely at the air. He threw the remnants of blackened furniture, which whizzed across the yard, knocking into the attackers. Jonas and Alex followed his lead.
Alex concentrated her energy into each object, holding her hand steady before flicking her wrist like she was tossing a Frisbee. The debris obeyed and shot toward her targets with the velocity of a bullet leaving a gun.
Each time a desk or a bed took out one of their fighters, two more seemed to reappear in their place. Alex felt a blast to arm, a smack to her head, a shot to the leg. Too many hits came at once, and the circle was closing in on them. Alex centered her anger into her core, ready to explode again.
Suddenly, a wind yanked her feet from under her and fell forward. “Oomph,” Alex groaned, landing flat on her face in the dirt. Before she could move, she was jerked backwards across the overgrown weeds, bouncing off the rocks and stray bricks mercilessly. She zigzagged feet first through the bodies of the attackers, screaming in protest. She was leaving Chase and Jonas to fight alone. She clawed at the grass and flailed her arms, but it was useless.
When she finally came to a rest, she was slumped, belly down, on the outskirts of the fray, and Calla was at her side. Calla’s hands opened over Alex’s face, pushing pressure against her. Why wasn’t she fighting? Why was she trying to save Alex?
Then she noticed Jack there, too. “We can’t let her back in,” he ordered.
Alex tried to stand up, but she couldn’t. It was the strangest and most agonizing feeling she’d ever encountered. She knew what she wanted to do, but she couldn’t do it. She wasn’t numb, but she had no control over her movements. It felt like a vise held her in place.
“Just concentrate on keeping her between us. She won’t be able to move,” Jack told his sister icily.
They weren’t trying to protect Alex. They were trying to contain her. She was helpless, useless. Calla and Jack had paralyzed her; how? She could only listen to the sounds of battle. The wind whistled erratically through the air and collided with its targets louder than claps of thunder. If she had closed her eyes, she would have believed she was listening to a hurricane.
“Al-ex?” Chase’s horrified voice climbed above the chaos followed by a muffled groan of pain. “Alex!” he bellowed again.
Alex’s heart began to crumble into a million pieces. She wanted to curse at Calla, scream at her. If she was strong enough to have a gift like this, whether she needed Jack to make it work or not, Calla didn’t need to be a part of a group. The city would have kept her in Brigitta anyway. Then again, maybe that was Calla’s fear. That she’d be forced to stay in a town that ridiculed her.
Chase , Alex gasped inside her head.
Where are you? Even in his thoughts, his voice was choked. Strained.
The Bonds are holding me out here.
Blast through them and run!
I can’t. They’re stronger than me. She couldn’t believe the words even as she thought them.
He growled in fury. You’re not hurt?
Not physically . Alex willed Calla to break her focus, but she didn’t falter, not even when the crowd began to shift toward them. Alex could see Chase and Jonas back to back, holding their own against so many spirits, kicking, shoving, punching at the air, attempting to beat them to death. Thankfully, none of the attackers seemed brave enough to get too close. Instead, they fought equally, waiting for someone else to strike the hardest.
It was Reuben who marched formidably on the outskirts of the group. He side-stepped around the fighters, his doughy face etched in concentration, waiting. And then a crash erupted above Chase and Jonas. They ducked to avoid the impact. When they stood up, whoosh ! The blast of the force propelled Chase away from his brother and Alex could only watch in horror. Chase gyrated through the air before crumpling at the crowd’s feet.
Before Chase could recover, Reuben lifted his arms, pausing for only a moment to glance defiantly at the others who had underestimated him. Chase rose like a marionette only to be smashed into the ground again.
Alex screamed silently in her head, trying to thrash, bite, kick, scream, anything, but her body refused to move. It was like crying at the top of her lungs in a soundproof bubble. Chase rose and fell, and rose and fell, flopping around like a lifeless rag doll. The mob scurried to Chase, and Alex could only watch in revulsion. Seeing his disadvantage, they all began to take hits at the body Reuben continued to control.
Alex tried to claw at the ground and fight for what she had lost once before. No, she was sobbing in her head, not him, not him . And her own mind began to ache, to succumb to the pain of it all and try to take some of it away from Chase. And then out of nowhere came the shattering of glass. Kaleb flew from the ruins of the asylum and zipped across the open the field. He rocketed through the mob and the attackers were blown off their feet. Confusion and fury corroded his blue eyes, and in one violent shove to the space around him, he eradicated half the crowd. How could he have so much force in his mind? His mind . Kaleb was fighting without touching anyone, using the force of his energy to knock them aside. Calla and Jack couldn’t paralyze her, because she no longer had a body. They could only be holding her here in her mind. She could still think, and her thoughts were active, so she could still move.
Move something , she commanded herself. She used every ounce of her concentration to elevate a nearby tree branch. She spun it in circles and released it, and the trajectory led directly over Calla’s head.
It broke the twins’ concentration for only a millisecond, but that was all Alex needed. She flung her arm through the air like a right hook, allowing its haste to pummel Calla’s freckled face into the dirt. Alex jumped up and lifted her elbow, slamming all of her anger into the hit.
Calla doubled over. She fell to the ground and began scooting away and searching for her brother, but Jack was already gone. Calla yelped fearfully at Alex before ducking her head and crawling into the woods.
Kaleb was fighting what seemed like five spirits at once, his arms whipping so rapidly his movements blurred. Jonas darted around quickly so no one could strike him. There were spirits sprawled across the battlegrounds, but none of them were Chase.
A large body came rushing toward her. Reuben. Her mind reacted, flashing the image of Kender Federive battling the banshee, and the rest of her acted accordingly. Without knowing how or what she was doing, she spun into the air like a tornado and then scissor-kicked her legs, connecting with the air around his piggish face. The force of it sounded like smacking an open palm on bare skin, but it was enough to knock him on the ground. She leaped over him, and in the fray she found Jack, splitting his shoves between Kaleb and Chase. Alex sprinted into the mass, pushing aside everyone in her way. She stopped several feet from Jack and concentrated, allowing her disappointment and hatred to spiral inside of her.
Something that felt like fire shot Alex between her shoulder blades. She fell forward, crying out in pain.
Jack noticed and he screamed out, “Use the rest of it!”
Joey Rellingsworh held a jagged rock the size of a paperweight. He turned it around in his hand, indecision on his face.
“Do it!” Jack yelled moments before Kaleb slammed into him. Jack’s eyes bulged before he fell. Kaleb lifted his arms and aimed a jolt square into Jack’s chest. Without his sister, Jack was no match for Kaleb.
Behind them, several spirits flocked together. Alex didn’t need to question why. If these newburies were birds of a feather, they were vultures. She ran to them, knowing she would find Chase at their feet. There were at least ten spirits on him, pummeling him with hit after hit, not afraid anymore. Some were throwing pieces of jagged rock. There were too many for Alex to take on alone.
Alex fell to her knees before Chase. For a moment, she held out her hands helplessly, and a sob shot up through her before she slammed herself over him, trying hopelessly to shield him from all angles.
She felt a stinging shot into her back, then her neck. She couldn’t stop her body from convulsing with each strike. But nothing was worse than the silence telling her that Chase was gone. She shut her eyes tight, trying to withstand the agonizing pain, and let out a long, low scream. It lifted into the air and carried through the trees and into the depths of the world.
And then everything went silent.
It didn’t feel like her physical death at all. It was like the ending of a fabulous dream, the kind where you don’t dare open your eyes, thinking that maybe if you fight consciousness, the
movie reel will resume. And yet you can’t even remember what the dream was about.
In that split second between sleep and awake, all Alex could feel was Chase. It wasn’t like she could feel him lying beside her. It was like he was everywhere . If his smile could become a physical feeling, this would be it. Despite everything Miss Petra had told Alex about the erasing of memories, Alex didn’t doubt for one second that she was tasting Heaven, even if only a spoonful.
Before she could tighten her grip, the comfort was ripped away like pulling the sheets from a warm bed. Alex felt numbed, barren, empty. Her sore head felt heavy, but she could still feel , so that was something, right? So where exactly was she? What exactly was she?
The thought of opening her eyes terrified her. Alex expected she might find herself back in Miss Petra’s classroom with a fresh set of decisions waiting for her, but the scent she caught was not of freshly sharpened pencils and blackboard chalk but hospital smells: starched bed sheets, bleach, and sadness. Her body was stretched out on a stiffly padded cushion.
Had she never died? It was possible that her brain had completely invented Eidolon in some insanely torturous dream, and now she was going to awake in the institution to find a nurse ready to dope her living mind with medication and psychoanalysis. The only good news was that when the true reality hit, it would kill her for sure.
Abruptly, in the midst of her frenzy, a slice of her mind pieced away, opening a space for Chase. He wasn’t far from her.
She opened one eye first. Clipboards lined the wall outside the doorway, and spirits in white coats scuttled past them. Movement from the far corner of her room caused her to jerk upright. Alex focused her eyes only to find a stranger, a boy clutching the seat so tightly his arms trembled. Alex was about to ask him who he was and why he was in her room when he shot up into the air as though the ceiling were magnetic. He slammed mercilessly like a bug on a windshield before crashing back to the ground.
He scrambled back into his chair and glanced at Alex furtively. Alex thought she could have kissed him. He was the very proof she needed. “Are you all right?” she asked, unable to contain the excitement in her voice.
“Go ahead, you can laugh,” he murmured. “The docs say it’s a mental virus spirits can contract, so maybe you’ll be lucky enough one day to experience how much it sucks.”
Alex made a face and covered her nose with her shirt. Thank goodness this time there was no hospital gown, but her head was covered in bandages.
“They put me in here because space is limited, and you’ve been out cold for a while. They didn’t think I’d bother you, but I guess I did,” he said sheepishly. “Sorry about that.”
“No problem.” Alex watched him grip his chair again. “How often do you … uh?” She pointed from the boy to the ceiling and back down again.
“Every few minutes. Good thing there’s a roof. Who knows how far I’d fly if I was outside.”
“How’d you get here then?”
“I projected myself and ran.” He grimaced. “Really fast.”
Alex couldn’t wipe away her smile. She was still alive, well, dead … whatever. She looked at the boy sympathetically. “Can they fix you?”
“They said they’ll just inject something into my head.” He craned his head to look through the doorway. “Do you want me to go get your nurse?”
Alex shook her head. She still existed in this afterlife, yes, but what about Chase? Why could she feel him if he wasn’t here? “Has anyone been here to see me?” she asked the boy.
“No, but I’ve only been here for a few boring hours.” He rested his head against the back of the chair.
Alex began to worry.
“Oh wait; there was one girl who popped in for only a second. She didn’t tell me her name.” He seemed upset by this.
“Was she pretty?”
He looked at his lap. “Well, yeah.”
Alex smiled. “Tall with really long red hair?”
“Skye Gossamer. That’s her name.”
That meant someone had remembered to pull Skye from the rubble. Jonas must have escaped the battle because besides Chase and Alex, he was the only one who knew where she was hidden.
“A Gossamer, huh? I should have known. I think she said she was going to check on your friend.”
“Do you know which direction she headed?” Alex asked, swinging her feet over the edge of the bed.
“Um, I think that way.” The boy pointed to the right, looking alarmed. “Are you sure you’re okay to get up? From what the nurses were saying, you were pretty much comatose.”
“I feel fine,” Alex assured him. “If the nurse comes while I’m gone, just tell her I didn’t want to catch—” Alex waved her hand at him “—whatever it is you have.”
He might have objected, but instead he rocketed straight up out of his chair again. This time his feet flew up behind him, flipping his body upside down so his toes smacked into the ceiling first and sent him nose-diving back down.
Someone should tie him to the chair , Alex thought merrily.
She padded down the hallway a bit clumsily, a sailor without land legs. She had a slipper on one foot and a sneaker on the other. Her mind must be all sorts of frazzled. Moments from the battle blazed into her head like flashes of lightning: Kaleb bursting through the glass, Reuben thrusting his arms in the air like an insidious puppeteer, Chase’s face coated in black ash.
Alex desperately needed to find him. In that field, they had both been losing what they had left of life—of that she was sure. She didn’t know what had saved them, what had kept them here, but she wouldn’t be here if he wasn’t. She had succumbed to death in those final moments, allowing her mind to think it was suffocating since her heart could no longer feel him, because she believed that Chase was doing the same and she refused to let him leave without her again.
Alex roamed the hallway, keeping her head down. She turned a corner, and warmth overcame her. She took a few more steps before her mind was completely revived, and suddenly she was encased in Chase’s arms. He tucked her deep into his chest, wrapping himself around her again and lifting her from her feet.
The pain in her mind floated upward like the dried seeds of a dandelion. Wishes she didn’t need any more. “I thought you were gone.”
Alex could feel his chin moving back and forth when he shook his head. “You saved me. I don’t know how. I was there, and then I wasn’t. I was alone. Then a second passed, and everyone came back,” he said. “And the pain returned with them. I heard you scream, and I don’t remember anything after that.”
Alex blinked, surprised. “Me too. How long do you think we’ve been here?”
Chase didn’t get a chance to respond before Alex heard familiar voices echoing against the walls. “They’re awake!”
Alex turned to see Gabe and Kaleb frozen in shock, each with an outstretched arm holding back the other, before slinging into motion, barreling down the hall, shoving visitors and dodging patients in their hurry.
Alex ducked inside the huddle so they could embrace her and Chase together. Kaleb stepped back to beam at them, and Gabe lowered his head to his hands, covering the scars the banshee had tattooed on the projection of his face. “Do you know what you’ve put us through? And it would have been my fault if you guys were gone.”
Kaleb smacked Chase playfully. “You have no idea how horrible it was for me to have to peel your lifeless bodies off one another to carry you here.”
“You carried both of us?” Chase asked.
“You didn’t weigh anything, and besides, Alex was wrapped around you like a koala bear.” He shook his head as if to discard the memory. “But, eventually Jonas took Alex.”
Chase’s eyes narrowed. “Where is Jonas?”
Gabe and Kaleb mirrored identical expressions of reservation.
“We’ll talk about it later,” Gabe said, gently pushing them all back down the hallway.
“No,” Chase insisted. “We’ll talk about it now.”
Kaleb began to walk. “Let’s at least head back to your room.”
Chase didn’t budge. “Where is he?”
Kaleb sighed. “He’s gone.”
“What do you mean, gone ?”
“He took off.” Kaleb shoved his brother into movement. “I’m sure he didn’t want to face the Patrol. We can start looking for him now that you two are okay.”
“I’m sure he didn’t want to face us,” Chase said in a low voice.
Gabe scrunched his brow, and the scar on his forehead bunched together. “What do you mean?”
“It was because of him that we were there in the first place. He admitted that he led me to that field willingly, knowing those newburies would arrive.”
Gabe took a clumsy step back as Chase’s words struck him. Kaleb said nothing but his expression showed no surprise.
“He thought they were taking me, not Alex.”
“No way.” Gabe shook his head adamantly. “He couldn’t have known that.”
“He didn’t deny it,” Alex added gloomily. “He just kept trying to get me out of there.”
“Do you know that for sure?”
Alex stared at Gabe wide-eyed, gesturing to the three of them, who had been victims of the “innocent” experiment to give Jonas his own clout. Now who was naïve?
“Maybe he brought you there to join the alliance,” Gabe said softly, but it sounded like he didn’t even believe his own words.
Kaleb pursed his lips skeptically. “Why would he think that after what happened to you, Gabe?”
“Maybe he thought it would protect you.”
“You’re reaching,” Chase said, shaking his head.
Gabe rubbed his finger over one of his scars absently. “The Patrol didn’t take Jonas with the others, though.”
“They came?”
Kaleb smirked. “Yeah, right after you decided to use yourself as a shield.”
Alex couldn’t help but think that the Patrol had absolutely horrible timing. Again, they arrived after damage was already done.
“How long have we been out?” Chase asked.
“A few weeks.”
Alex gasped. How could so much time have passed? Her fatigue implied the battle had happened only yesterday.
“Yeah,” Kaleb grinned at a passing nurse and twisted to watch her leave. “You woke up once. Both of you, on the same day, but neither of you regained complete consciousness, and then at exactly the same time, you both went out again. Some of the doctors went all berserk about it, and others seemed really excited.”
“You were doing everything in synchronism. Kind of like when you were little. If one of you moved, the other one moved. I overhead the doctors saying that your brain waves were identical.” Kaleb stopped in front of a doorway. “Do you remember anything?”
“No,” Chase replied, and she wondered if he was lying too, if, like her, he couldn’t explain the feeling with words.
Gabe’s curls were standing on end. He put a hand on Chase’s shoulder. “I’m going to go see about getting you guys out of here.” He hurried away, but he stopped halfway down the corridor and leaned against the walls, resting his hands on his thighs.
“He always wants to believe the best in people, doesn’t he?” Kaleb said.
“At least the best in Jonas.” Chase held out a hand to indicate that Alex should enter the room first. “Gabe wasn’t the only one.”
Jonas used to joke that Alex’s innocence, though he deemed it stupidity, would be the death of her, not her disease. He’d used it against her.
“I can’t deny what happened there in that field,” Chase said. “Or the look on his face. I know it’s hard to believe. I don’t want to believe it, and I was there.”
Alex stopped at the center of the room, not quite sure where to go. With one strong scoop, Chase swept her up and placed her on the bed. He fluffed the pillows behind her and kept one hand around her arm as if someone might snatch her away.
Kaleb loitered in the doorway, staring at the floor, like he needed permission to interrupt them.
“Sit down, Kay,” said Chase, and chairs appeared by the bedside. “So, how did you know we were in Parrish?”
Kaleb shrugged. “I didn’t know, but I knew someone had used the parapets on the roof. I was told if I got up there, the waves would take me to wherever you were.”
“How did you know that?”
“The Darwins.”
“What?” Chase and Alex exclaimed simultaneously.
Kaleb shook his head and plopped into one of the chairs. “Believe me, I was shocked, too. They found me wandering around wondering where everyone had gone, and I almost told them to shove it, but something about them seemed so genuine it made me stop and listen. They knew what had happened to Gabe, and they said they wanted to warn me about the rest of us.”
“Wait a minute. Do you think that means they were in the league, too?” Alex asked skeptically. “Why else would they know all of that?”
Kaleb shook his head. “They weren’t a part of that. The way they were talking sounded like they were disgusted by the league. You know what I think? I think their family knew, and I think a lot of other people knew what was going on. I couldn’t believe my eyes when I got to the Eskers. I thought it was another prank or something but then I saw them attacking you.”
Chase scooped his hand under Alex’s. “If you think the Patrol or whoever knew what would happen, why weren’t they there? Why wouldn’t they stop it?”
“You’re missing my point. I think they were there.”
“Watching?”
“Maybe.” Kaleb sat back in his chair, crossing his arms angrily. “Waiting to see how bad it would get.”
“How did the fight end?”
“It ended right after Alex fell on top of you.” He laughed humorlessly. “Do you remember screaming like a damn banshee, Al?”
Alex stared into nothing, tasting the moment of hopelessness again. “Kind of,” she whispered. “But I don’t remember anything after that.”
Kaleb tugged at his ear. “That scream was awful. I knew you had a loud mouth, but that was insane. Your damn yelling was so loud that most of the spirits fighting had to stop and cover themselves. That gave me a clear shot at the newburies who were still jabbing at you. I dove into the air and tackled three at once, and I just started wailing on them.”
“Throwing punches?”
“I was so, so angry. I lost my head. I don’t know what I was thinking, because once your scream ended, I was like a deer surrounded by hunters. I blocked some blows, but most were aimed at my head. I was the new target. And they had those stones.”
“What were those?” Alex asked, remembering the stings and flinching.
“Copper. Thankfully, they split the rock into small pieces, the morons. It wasn’t too powerful. And then the Patrol came flying in like a meteor shower. I don’t think you understand how loud you were. Scream isn’t even the right word for it. And they didn’t pin down those newburies until after you stopped.”
“I really don’t remember doing it, so I have no idea if I could ever do it again.”
Kaleb’s hands flew to his ears. “Don’t try it,” he warned her. “I think I have permanent hearing damage. It’s been horrible trying to listen during workshops because it feels like one ear is pressed against the wall.”
He stood. “Brigitta’s been nuts since the fight.” He walked to window, glancing out.
“Everyone knows?” Alex asked in surprise.
“Well the Patrol arrested twenty-five newburies. Someone was bound to notice. People were asking so many questions that some spirits even starting writing gossip columns and positing them electronically in the vestibule. Guess whose picture was on the first copy?”
“Sephi Anovark.”
Kaleb nodded. “Cat’s out of the bag. The teachers were pissed, but what could they do? Everyone had already seen it. That first copy really got everyone’s attention. There were all these theories about witchcraft and mind control.”
Alex didn’t miss the knowing glare Chase gave her.
Kaleb leaned back against the windowsill. “I was there when they were questioning the Eskers kids. They took me back to the Dual Tower to report my statement. Every single one of those kids mentioned ink appearing in their law notebooks.”
Alex suddenly felt nauseated. Was that why Duvall had been circumspect when she’d questioned the ink? And Jack had mentioned Eviar. Her thoughts rearranged themselves over and over, searching for a solution.
“The messages told them what to do. Joey admitted to the copper in the fountain. Jack and Calla admitted to luring in the banshees.”
The door creaked open, and Gabe entered with a grin. It made the scar on his cheek look like a half-moon. “Doc is on her way,” he announced. “Dr. Blaise will take good care of you.”
The doctor who had treated Gabe burst through the doorway with her white coat billowing behind her. “Well, you certainly gave us a scare.”
“You went missing! You!” She gawked at Alex. “Almost had to pull the alarm. We’ve had Ardor Service members, teachers, and government officials breathing down our necks for weeks!”
“Government officials?” Chase asked.
The doctor peered over her glasses and nodded. “The case was turned over to the Service.”
“I just went to find Chase. That’s all.”
The doctor attached something to Alex’s temple before moving over to Chase. “Whatever you do, just don’t scream.”
Kaleb screwed up his face and pulled at his ears.
“Not that I was planning on it,” Alex said sardonically, “but why?”
“You started wailing one night about a week or two ago in your sleep. Thankfully no one was in your room at the time, but you broke every piece of glass within a twenty-foot radius. The joke around here is that you’re half banshee. I had no idea you were the girl who survived the scream.” Dr. Blaise tipped her pencil towards Chase. “You started screaming at the same time. I suppose I shouldn’t be surprised that you both woke up simultaneously. I’ve never seen anything like this. The research staff is going ballistic.”
Chase tightened his grip on Alex. “Does that mean we’re going to be here for a while?”
“We do need to make sure that you’re allowed, er, I mean strong enough to leave. Not to mention that legally, we cannot let you go until the Ardor Service clears it.”
“Because you were found at the scene of a crime, that’s why. They need your statements.” Dr. Blaise turned to Gabe. “I need to run a few tests on these two. Visitors are going to have to leave. And I’m sure you’re sick of being in this building.”
“It’s like home,” Gabe stopped in the doorway. “Do you have an idea of when they may be discharged?”
“You can come back tomorrow. I’ll have more news for you then.”
“Good to see you two conscious,” Kaleb said, smiling faintly. They exited, and he began to whisper heatedly in Gabe’s ear.
Thankfully, Dr. Blaise allowed Alex to remain in Chase’s room. They wouldn’t have been able to sleep even if they’d wanted to. A continuous stream of doctors bustled in and out, interrupting their recounts of what had happened during the battle, and in the middle of the night, they were visited by Ardor Westfall.
“Has Van Hanlin been found?” Alex asked quietly.
Westfall let out a sigh. “He’s neither turned up dead or alive.”
“Jonas said he saw his body.”
“If that's the case, he's still alive. Without a mind, a spirit can't formulate the projection of a body. We can’t exactly question Jonas Lasalle, but, we’ll keep searching. You’ll make us aware if he tries to make contact, I’m sure.” He glanced at them warily. “None of the other newburies we detained claim to hav
e seen Professor Van Hanlin attacked.”
Alex shared a look with Chase. “What will happen to those newburies?”
“They’ll be detained for a while. Questioned. Analyzed. That ink didn’t appear in their notebooks exclusively. The residue of the ink is actually in every single law notebook on campus.”
“What?” Alex exclaimed.
“The only spirits who could see the words were the ones who were looking for it. I’m sure you’ve discussed this during your therapy sessions, but young spirits are often searching for acceptance, and those particular spirits needed it more than others. And they found it. They found camaraderie and a sense of belonging within their recruitment.”
“How is ink like that possible?” Chase asked, shooting Alex a look that screamed I told you so . “Sounds dangerous.”
“The mind is a fascinating thing. There’s much we can’t see even when we know what we’re looking for … and there’s much we’re blind to when we don’t.”
“Do you have any idea who the group may have been?” Chase asked, digging his elbow into Alex’s side.
“I’ve seen this kind of ink used before, and the user had the ability to sway the decisions of others. The recruits who read the ink were not possessed. They never blacked out doing the things they did. They knew what they were doing when they did it, but they didn’t understand why.”
Alex felt a headache creeping in. “Jack said the group was called Eviar.”
Westfall didn’t immediately respond, and that in itself was confirmation. “Eviar is a group of inmates. They were ingenious, but they didn’t quite know how to control their minds.”
“Inmates?” Alex asked.
“From Paradise, yes.”
“Then how come Ellington didn’t know about the name?”
Westfall raised an eyebrow. “They didn’t adopt that name until after they were released from Paradise, a release that I approved but Van Hanlin ordered. He thought they could be of use. I thought they could be watched, tamed, useful during the war. We were arrogant. And wrong.”
“Van Hanlin,” Chase said. “And the ink showed up in law notebooks. You think Van Hanlin is responsible for all this?”
“No. He was working with us.”
“You knew what was going on?”
“Bits and pieces.”
Alex remembered his entrance in Moribund. “You knew the banshee was near the haunted house.”
Westfall nodded.
“And you and Duvall were talking about Eviar that day during her ABC group. Did you know she was going to send me to Parrish?”
“We needed to track the group. And we needed to see the extent of what the recruits would do and how you would handle it. We wouldn’t allow anyone to get hurt.”
“Van Hanlin is missing.”
“His mistakes continue to haunt him.”
Chase balled his hands. “We’ve been passed out for a month!”
“Newburies are tested throughout their entire stay at Brigitta. You’d better get used to it,” Westfall replied.
Alex placed a hand over one of Chase’s fists. She didn’t particularly like Westfall, but if he was giving out answers, she’d take all she could get. “Was Eviar named after one of its members?”
Alex closed her eyes. So Eviar had found Paradise, after all.
“I was convinced they would help us to win the war, but I should have realized they had a different agenda. Eventually Eviar was dismantled with the help of a friend of mine, a prophet I’m sure you’d heard of by now. Sephi Anovark sacrificed her life to end the antics of that godforsaken brotherhood.”
“Sephi found them?”
Westfall nodded. “Sephi was responsible for the detainment of many spirits. You understand now why people wanted her dead. Why they might want you dead, if they think you can see their crimes before they happen?”
“So Eviar was responsible for what happened to us?”
“Seeing as how the founder of Eviar—not to mention the rest of the inmates released—are dead, we can’t say for sure. It might still be a copycat situation.”
Alex wanted to sink right through the mattress of the hospital bed. Eviar had died. And Sephi had died. That was the ending to the letters.
“So we may never know who would want to rebuild an army?” Chase asked.
“My concern,” said Westfall “is not so much who, but why .”
On the morning Chase and Alex were to be released from the Medical Center, Kaleb and Gabe arrived to escort them home. Alex couldn’t understand why Kaleb insisted it was necessary until they left the building to find crowds gathered, bordering the sides of the street. Most spirits watched her in fascination, others waved, and some held photos of Sephi. Alex spotted Ardor Westfall patrolling through the spectators, and she couldn’t decide if this made her feel safe or not.
She was relieved to reach the seclusion of the Brigitta campus and immediately excused herself to visit the learning center. “I have someone I need to talk to.”
Chase glanced in the direction of the school and made a face. “Do I need to remind you that Duvall led you to the Eskers that night? She put you in that situation.”
“I know. That’s the whole point.”
Alex entered the abandoned school and only heard her hollow footsteps after she wondered why she made no noise. Most of the doors to the classrooms were closed, but something told Alex that the one she was headed for would be wide open, the steam from a mind-bending concoction wafting into the hallway. Sure enough, the closer she inched to the ABC room, the thicker the smell of rotten eggs and gasoline permeated the air.
She hesitated in the doorway, watching Duvall lift her arms over a line of flasks. She was like a bat with wings of crocheted yarn. “Awake finally?” Duvall asked.
“You knew that though, right?”
“Not of my own accord.”
Alex hoisted herself up onto the nearest desk. “Did you know who we would be fighting that night?”
Duvall’s voice was low. “There are ways of knowing the pictures that fate has already painted on her canvas. I wasn’t sure of anything but the scene itself.”
Duvall click-clacked around the lab table. “I think you’ll discover the answer to that question in due time.”
“If you knew what was going to happen, why would you let us go?”
“Because that was the plan.”
Alex twirled her hair nervously. “I want to ask you about a student you had a little over a hundred years ago.”
Duvall chuckled. “What makes you think I’d remember a child from so long ago?”
“Just a hunch. Sephi Anovark?”
Duvall’s bony fingers clenched the edge of the table. “No doubt you saw that blasted column.”
“I already knew about her. You knew I looked like her. Why didn’t you tell me earlier? It would have explained a lot.”
“That isn’t what made me curious about you,” Duvall replied. “But the staff thought it was best if you remained unaware about your appearance at least until you became adjusted to this world.”
“It isn’t easy being a prophet or to be associated with one. Much like it isn’t easy to be a witch. You see, prophets and witches are categorized together as the gifted. Sephi was an instant target. Witches and prophets are not safe in the spiritual world, which is why I never leave this campus.” Duvall studied Alex with a look of determination. “Your mother learned that the hard way.”
“My mother? So was she a witch? Or a prophet?”
Alex threw her hands in the air, exasperated.
“But she resembled Sephi Anovark enough for the spiritual world to become hysterical. People thought she lied about her abilities. Right away, the government assumed she was gifted and employed her to help them. She went digging for answers about her ancestry and it led her back to your hometown. She never came back. Ardor Westfall thought it best that you remain ignorant so your fate would not mirror hers.”
“Sephi’s family was killed, right?”
Duvall responded quietly. “Yes.”
“So let me get this straight. My mother had no prophetic talent and no possible relationship to this girl, but she was killed simply because she looked like her? That doesn’t make sense.”
“Magic scares people. Enough people were terrified of Sephi Anovark to want to keep any piece of her out of this world forever.”
“What’s to fear?”
“Prophets can see things about people, things that they might want to keep concealed. Many people believed that events occurred because she predicted them. Witches know better. Some aspects of fate are written in lead, some in ink.” She paused for several moments, allowing Alex to mull over what she’d said. “People are afraid of those who are different from themselves. I’ve been alive a long time, and that is something that never seems to change.”
But one person had never been afraid of Sephi.
“Professor, do you remember Sephi’s best friend here at Brigitta?”
Duvall puckered her lips in a sour expression.
“You didn’t like him,” Alex added.
“Who was it?”
Duvall’s eyes flashed angrily like the reflection of an unforgiving sun. “The very person who murdered her.”
Alex recoiled, dread seeping through her.
“He went after her. No one wants to believe it, but evidence of Eviar has been resurfacing all year.”
“Eviar,” Alex squeaked.
“That was the name of his alliance. He certainly was not humble, was he, that Syrus Raive.” Duvall snickered. “Using his own name to label his group only implicated him in twice the number of crimes.”
“His name?”
“Spell it backwards.”
RAIVE. EVIAR.
If Alex had a body, she would have vomited all over the floor. His brotherhood. His name backwards, a nickname Sephi herself had inspired. Backwards thinking.
“Syrus Raive,” Duvall said his name like a curse. “He could infest a mind like a locust. I’m sure he’d heard that Sephi had predicted his death.”
“Was that why he left?”
Duvall reached into a desk drawer and extracted a green plant. She held it next to Alex’s face. “Unfortunately, sometimes we cannot control who we are connected to.”
She placed the plant back in the drawer before pointing a bony finger at Alex’s head. “She could hear him. Even if he wasn’t speaking. She had no control over it. She had to listen to the thoughts that made him a monster, and he could hear her prophecies. After class one day, she came to me wanting some sort of solution, but unfortunately I had none. She distanced herself, but she couldn’t get Raive out of her head even then. What a cancer. We need to keep our minds closed lest we desire insanity.”
Alex was feeling more and more lightheaded, and she reached out to stabilize herself against the counter. There was no explanation why she was so similar to this girl.
“Sit down,” Duvall ordered. “You just came back to the land of the somewhat living.” She patted Alex’s arm and continued to mix ingredients. “Raive heard Josephine’s thoughts when she went into hiding, and that’s how he found her. She tried to run from it, and she tried to fight it, but the world wouldn’t let her. Some things are just bigger than us. It’s foolish to think that we can manipulate that.” She bit her lip. “I couldn’t predict Syrus Raive’s future as she could, but I could taste his betrayal.”
Alex felt the desire to tell the truth. “I found letters that he wrote to Sephi. He never said his real name. He signed it Eviar. I had no idea it was him.”
Duvall rested her elbow on the edge of the table and leaned towards Alex.
“He seems pretty young. It’s mainly about school. But I can’t read half of them because they’re written in some strange ink.”
“The ink you questioned me about?” Duvall asked. She analyzed Alex like it was the first time she’d ever laid eyes on her. “When did the ink disappear?”
“After I tried to let Chase read them.”
“Hmm, yes, magic is unforgiving sometimes.”
“I can still see half of them.”
“Peculiar,” Duvall whispered. “May I have the opportunity to look at the letters?”
“I don’t know,” Alex said warily. “The last time I tried to show them to someone else, they disappeared on me.”
“I might be able to find a loophole. Where did you find these letters?”
“In Moribund.”
“Isn’t that interesting?” There was dry humor in her tone. “Were they in a box?”
“Yes. How did you know that?”
“If you were able to see the contents of that box, you must have some connection to Sephi, by relation or not.”
“You said it was impossible.”
“I’m a firm believer in the impossible.”
“Didn’t you say before it could be a glitch? If the person didn’t know what they were doing.”
“Oh, they knew what they were doing.”
“Because I created that box.”
“Of course. I designed it. And that box wouldn’t have shown itself to you unless it felt some sort of allegiance. Whoever put it there wanted to know if you could see it.”
Alex shifted on the desk.
Duvall mumbled under her breath, raking her fingers through her erratic hair and causing it to stand on end.
“Professor?”
She waved her hand towards to door. “I think that’s enough. Go enjoy being awake for a change.”
The fumes in the ABC room, mixed with her confusion, made Alex woozy. She gladly escaped, picking up her pace the closer she came to the exit. Outside, the sun fell over the town like a spotlight. She’d never seen the city so bright.
Chase’s feet dangled from the edge of the picnic table. He lay sprawled in the sunshine with his eyes shut tightly. The light radiated from him so brightly he could have been an angel. He looked so young. She’d never understand how it was possible to love someone so much that she could ignore how terrified it made her.
Chase turned his head and opened his eyes, finding Alex with a smile. When she reached him, he braided his fingers in hers, and pleasant zings of electricity shook her body.
“How was your chat with Professor Crazy?”
Alex blinked against the glare of the sun. “You weren’t listening?”
Her mind ached thinking of Duvall’s warnings about keeping one’s thoughts to one’s self. “I have a lot to tell you.”
Chase jumped off the picnic table. He slid his arm around her, leading her away from the shade of the towers and into the rays of the sun. “I have a feeling it won’t be a light conversation.”
“It may take a while.”
Chase let out a small laugh and pulled her in close. “Let’s save it for later. We have all the time in world.”
Alex nodded and curled her hand around the edges of a small note, the one she’d found in her pocket at the medical center. A scrawling of an hourglass. Had someone placed it there? Had her mind created it somehow? She wanted desperately to know, but she held her tongue and stuffed the note deeper into her pocket, saving it for another time. Chase was right. They did have time. A luxury she might never get used to.
She stepped away from him and stretched out her arms, opening her palms toward the heavens. And then, she did something she’d never done in life. She twirled. She threw back her head, absorbing the energy of the sunlight, and she spun and spun until her mind became the clouds and her vision became the whirling wind.
Alex had once believed that when she died everything that made her weak— her love, her sadness, her pain—would all spill out of her body and into the world. And maybe once she really truly died, whenever that might be, if ever that might be, her emotions would leave her, since there would be nothing to contain them. They would dissolve into the air until they were nothing, or perhaps even find the closest object to cling to. But not love. Love, she believed, would ride the wind until it found the sky, shining its beauty on the world below.
Perhaps that is the only thing truly immortal.
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← China builds Gulag-like prisons for Muslims, calls them ‘political re-education centres’
Germany Reportedly Mistakenly Deports Uyghur Man To China →
In new admin error, Germany expels Uighur man to China
PUBLISHED: 10:42 BST, 6 August 2018 | UPDATED: 10:42 BST, 6 August 2018
Demonstrators holding Uighur flags demonstrate in Berlin on July 9, 2018, prior to a meeting between German Chancellor Angela Merkel and Chinese Premier Li Keqiang
German authorities wrongfully deported an Uighur man to China due to an administrative error, local media reported Monday, in a fresh scandal as the country seeks to step up expulsions of failed asylum seekers.
Officials were due to hold a hearing with the 22-year-old Uighur, who was not named, on April 3 over his asylum application, said regional public broadcaster Bayerischer Rundfunk (BR).
But a fax announcing the hearing from the Federal Office for Migration and Refugees (BAMF) apparently failed to reach local authorities in Bavaria, who, in the early hours of April 3, put the Uighur man on a plane to Beijing.
“We were unable to find the fax despite an intensive search,” Munich authorities told BR.
“We regret greatly that the deportation took place even though a valid asylum application had been made. It was never the intention of the immigration authorities of Munich to infringe on the rights of the foreigner affected by the expulsion.”
The BAMF would not give details on individual cases but told the broadcaster that expulsion would be “inadmissible” under such circumstances.
The Uighur asylum seeker’s lawyer Leo Borgmann said he has had no news from his client since the deportation.
“There is no sign of life. We fear that he has been detained,” Borgmann told BR.
– Secretive network –
Many of China’s mostly Muslim Uighur minority say they face cultural and religious repression.
Members of the Uighur diaspora say relatives have been arrested for seemingly innocuous acts such as sending Ramadan greetings to friends or downloading popular music.
Chinese authorities are also believed to have detained hundreds of thousands of Muslims in a secretive network of extra-judicial political re-education centres, where inmates are given language and ideological training and forced to participate in military-style drills.
The case surfaced after a series of administrative errors that led to illegal deportations by German authorities.
In a further controversial case, a German court in July ordered that a man who allegedly worked as a bodyguard for Osama bin Laden be returned to Germany only hours after his deportation to Tunisia, saying the expulsion was illegal as he risks torture there.
The 42-year-old, identified by German authorities only as Sami A. and by Tunis as Sami Idoudi, had lived in Germany for more than two decades, but outrage over his presence grew in recent months.
Although he had won a court ruling against his deportation, the decision reached federal authorities by fax a day later — hours after his flight to Tunisia had taken off.
Also in July, the interior ministry was forced to repatriate an asylum seeker who had been deported to Afghanistan even though his legal appeal against expulsion was ongoing.
In June, another Afghan man who was allowed back into Germany after he was illegally deported from the country was officially granted asylum.
http://www.dailymail.co.uk/wires/afp/article-6030887/In-new-admin-error-Germany-expels-Uighur-man-China.html
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FTT Wonders: Who Really Aired the First Asianovela in the Philippines?
Tag Archives: Ruby Rodriguez
comedy, drama, entertainment, humor, Philippines, television
Kalyeserye Returns After One-Month Absence
October 17, 2016 ralphierceAi Ai delas Alas, Alden Richards, Allan K, Eat Bulaga, Eat Bulaga GMA, Eat Bulaga TAPE, GMA, GMA Network, Joey de Leon, Jose Manalo, Kalyeserye, Kalyeserye 2nd chapter, Kalyeserye comeback, Kalyeserye conclusion, Kalyeserye Eat Bulaga, Kalyeserye end, Kalyeserye return, Kalyeserye revived, Lola Babah, Lola Nidora, Maine Mendoza, Massachusetts, Paolo Ballesteros, Patricia Tumulak, Philippine Arena, Pia Guanio, Rogelios, Ruby Rodriguez, Ryan Agoncillo, Ryzza Mae Dizon, Sa Tamang Panahon, Sa Tamang Panahon anniversary, Sa Tamang Panahon Eat Bulaga, TAPE Inc., Tidora, Tinidora, Tito Sotto, Tito Vic and Joey, Vic Sotto, Wally Bayola 10 Comments
The apparent end of ‘Eat Bulaga”s Kalyeserye segment last September proved to be a premature proclamation.
Last Saturday, ‘Eat Bulaga’ decided to revive the long-running ‘reality’ skit, with a new arc that focuses on the ‘engagement’ of main stars Maine Mendoza (formerly known as Yaya Dub) and Alden Richards. The episode also marked the return of Paolo Ballesteros’ Tidora character, which had been absent since March.
Also present on the skit were Lola Nidora and Tinidora, the famous alter egos of Wally Bayola and Jose Manalo respectively, along with their bodyguards known as the Rogelios. During the segment’s hiatus, they were said to be ‘residing’ in Massachusetts alongside Tidora, who had long been on vacation.
To spice things up further, Ai-Ai delas Alas reprised her role as Lola Babah in a special guest appearance. Babah was said to be the ‘landlord’ of the mansion now owned by Lola Nidora during her recurring appearances in the skit.
Talagang isinilang kami para sa tabi este sa TV. Ang TVJ may TV. Our producer Tony TuViera!
A post shared by Joey de Leon (@angpoetnyo) on Oct 14, 2016 at 8:55pm PDT
All of that took place while Sen. Tito Sotto, Vic Sotto and Joey de Leon were on vacation to celebrate the latter’s 70th birthday (see above). With the celebrated trio off for the weekend, it was up to the other main hosts (notably Allan K, Ruby Rodriguez, Ryan Agoncillo, Pia Guanio, Ryzza Mae Dizon and Patricia Tumulak) to pick up the slack.
The return of Kalyeserye on ‘Eat Bulaga’ couldn’t have come at a better time. This week will mark the first anniversary of the immensely successful ” live event at the Philippine Arena, which by all accounts marked the pinnacle of the skit’s success.
But even if ‘Eat Bulaga’ decides to bring back the celebrated segment on a full-time basis, it may no longer have the hype of episodes past. Still, for loyal viewers of the show, the return of Kalyeserye should be memorable in more ways than one.
comedy, entertainment, humor, Philippines, television
A History of Vic Sotto Sitcoms (Part 1)
June 16, 2016 ralphierce1 For 3, 1 For 3 GMA, 24 Oras Weekend, 24 Oras Weekend GMA, ABS-CBN, Ai Ai delas Alas, Aiza Seguerra, Alice Dixson, Allan K, BJ Forbes, Charito Solis, Charlene Gonzales, Cindy Kurleto, Daddy Di Do Du, Daddy Di Do Du GMA, Danica Sotto, Dawn Zulueta, Eat Bulaga, Eat Bulaga GMA, Eat Bulaga TAPE, Enteng Kabisote, Enteng Kabisote franchise, Enteng Kabisote movie franchise, Ful Haus, Ful Haus GMA, Full House, Full House Asianovela, Full House GMA, Full House Koreanovela, GMA, GMA Network, Hay Bahay, Hay Bahay GMA, IBC-13, Imee Marcos, Intercontinental Broadcasting Corporation, Isabelle de Leon, Jinky Oda, Joey de Leon, Joonee Gamboa, Jose Manalo, Keep on Dancing, Keep on Dancing ABS-CBN, Larry Silva, M-Zet Productions, Marissa Delgado, Maxene Magalona, Mickey Ferriols, Mitoy Yonting, Nanette Inventor, Nida Blanca, Nida Blanca death, Nida Blanca murder, Okay Ka Fairy Ko, Okay Ka Fairy Ko ABS-CBN, Okay Ka Fairy Ko GMA, Okay Ka Fairy Ko IBC-13, Paolo Ballesteros, Pia Guanio, Redford White, Rosanna Roces, Ruby Rodriguez, Sugar Mercado, The Voice of the Philippines, The Voice of the Philippines ABS-CBN, The Voice of the Philippines Season 1, Tide detergent, Tide Tolits, Tito Sotto, Tito Vic and Joey, TVJ, Tweetie de Leon, Vic Sotto, Vic Sotto filmography, Vic Sotto sitcoms 3 Comments
The cast of ‘Okay Ka, Fairy Ko’ nearly 30 years after it first aired. Tweetie de Leon was the second actress to play the role of Faye. (Photo credit: Allan K Official Instagram)
It has been nearly 30 years since Vic Sotto left the shadows of TVJ and became a star himself.
On Sunday, June 19, his newest sitcom ‘Hay, Bahay!’ will officially premiere on GMA. This will mark Vic Sotto’s eighth sitcom as a solo artist, and ninth overall.
While he was better known as 1/3 of the fabled trio TVJ alongside Tito Sotto and Joey de Leon, and the host of ‘Eat Bulaga’, it was his individual comedic brilliance on television and film that cemented his legacy. Without further ado, let’s look back at his solo sitcoms over the years (in chronological order), starting with the first four on the list.
1. Okay Ka, Fairy Ko! (1987-97)
Aired on: IBC-13 (1987-89), ABS-CBN (1989-95), GMA (1995-97)
Notable co-stars: Aiza Seguerra, Alice Dixson, Tweetie de Leon, Dawn Zulueta, Charito Solis, Jinky Oda, Ruby Rodriguez, Larry Silva
The sitcom that started it all, ‘Okay Ka, Fairy Ko’ introduced viewers to Enteng Kabisote, the mechanic-turned-husband of the fairy Faye. The character then went on to star in nine box-office hit movies based on the sitcom.
2. 1 For 3 (1997-2001)
Aired on: GMA
Notable co-stars: Ai-ai delas Alas, Charlene Gonzales, Rosanna Roces, Nanette Inventor, Imee Marcos, Allan K, Mickey Ferriols
Believe it or not, ‘Hay, Bahay’ is not the first sitcom to star both Vic Sotto and Ai-ai delas Alas. When Charlene Gonzales left ‘1 For 3’ to host ABS-CBN’s ‘Keep on Dancing’, Ai-ai was introduced in the sitcom as one of Gene’s (Vic) housemates.
3. Daddy Di Do Du (2001-07)
Notable co-stars: Danica Sotto, Maxene Magalona, Isabelle de Leon, Cindy Kurleto, Redford White, Ruby Rodriguez, Joonee Gamboa, Jose Manalo, Paolo Ballesteros, Nida Blanca
The first sitcom to feature Vic and daughter Danica, ‘Daddy Di Do Du’ was the second in Vic’s sitcom filmography to feature a mystical theme. Unfortunately, just a few months into the sitcom’s run, Nida Blanca was murdered, and her character was written off afterwards.
4. Ful Haus (2007-09)
Notable co-stars: Pia Guanio, Jose Manalo, BJ Forbes, Joonee Gamboa, Marissa Delgado, Mitoy Yonting, Sugar Mercado
Based on the Koreanovela ‘Full House’, ‘Ful Haus’ marked the debut of child star BJ Forbes, whose claim to fame was via the Tide detergent commercials as ‘Tolits’. This was also the first project for Mitoy Yonting prior to winning season 1 of ‘The Voice of the Philippines’ several years later.
For Part 2 of A History of Vic Sotto sitcoms, click here.
Note: ‘Hay, Bahay!’ will air every Sunday after ’24 Oras Weekend’ on GMA. All of his sitcoms are property of M-Zet Productions.
June 16, 2016 ralphierce24 Oras Weekend, 24 Oras Weekend GMA, ABS-CBN, Ai Ai delas Alas, Allan K, Ang Darling Kong Aswang, Anjo Yllana, Bea Binene, Buboy Garovillo, Ces Quesada, Daiana Menezes, Derrick Monasterio, Dianne Medina, Enteng Kabisote, Erika Padilla, Glaiza de Castro, GMA, GMA Network, Hay Bahay, Hay Bahay GMA, Jackie Lou Blanco, Jimmy Santos, Jin-ri Park, Jinky Oda, Joey de Leon, Jose Manalo, Kakai Bautista, Kristine Hermosa, M-Zet Productions, Mcoy Fundales, Miguel Faustmann, Miriam Quiambao, My Darling Aswang, My Darling Aswang TV5, Niña Jose, Okay Ka Fairy Ko, Oyo Boy Sotto, Pilita Corrales, Rhea Nakpil, Ritchie d'Horsie, Ruby Rodriguez, Ryzza Mae Dizon, Sugar Mercado, Tetchie Agbayani, The Jose and Wally Show, The Jose and Wally Show Starring Vic Sotto, The Jose and Wally Show Starring Vic Sotto TV5, The Jose and Wally Show TV5, Tito Sotto, Tito Vic and Joey, TV5, TVJ, Vampire ang Daddy Ko, Vampire ang Daddy Ko GMA, Vic Sotto, Vic Sotto filmography, Vic Sotto sitcoms, Wally Bayola, Who Wants to Be a Millionaire Philippines, Who Wants to Be a Millionaire?, Who Wants to Be a Millionaire? TV5 1 Comment
Vic Sotto’s eighth solo sitcom, ‘Hay, Bahay!’, will mark his second collaboration with Ai-ai delas Alas. (Photo credit: GMA Network/Hay, Bahay! Official Facebook)
On Sunday, June 19, his newest sitcom ‘Hay, Bahay’ will officially premiere on GMA. This will mark Vic Sotto’s eighth sitcom as a solo artist, and ninth overall.
While he was better known as 1/3 of the fabled trio TVJ alongside Tito Sotto and Joey de Leon, and the host of ‘Eat Bulaga’, it was his individual comedic brilliance on television and film that cemented his legacy. Without further ado, let’s look back at his solo sitcoms over the years (in chronological order), concluding with the final four on the list.
5. My Darling Aswang (2010-11)
Aired on: TV5
Notable co-stars: Daiana Menezes, Tetchie Agbayani, Ces Quesada, Sugar Mercado, Jose Manalo, Wally Bayola, Ritchie d’Horsie, Miguel Faustmann, Kakai Bautista, Rhea Nakpil
Based on the movie ‘Ang Darling Kong Aswang’, ‘My Darling Aswang’ was the first Vic Sotto-starred sitcom in 15 years to not air on GMA. Instead, it aired on TV5, where Vic also happened to be the host of the game show ‘Who Wants to Be a Millionaire’.
6. The Jose and Wally Show Starring Vic Sotto (2011-12)
Notable co-stars: Jose Manalo, Wally Bayola, Jimmy Santos, Mcoy Fundales, Erika Padilla, Dianne Medina, Buboy Garovillo, Miriam Quiambao, Niña Jose
While Jose and Wally were the headliners of this variety show within a sitcom, Vic was also added to the mix as its ‘director’. Like ‘My Darling Aswang’, ‘The Jose and Wally Show’ was aired concurrently with Vic’s other show on TV5, ‘Who Wants to Be a Millionaire’.
7. Vampire ang Daddy Ko (2013-16)
Notable co-stars: Oyo Boy Sotto, Pilita Corrales, Jackie Lou Blanco, Anjo Yllana, Jimmy Santos, Ryzza Mae Dizon, Bea Binene, Derrick Monasterio, Glaiza de Castro, Jin-ri Park, Allan K, Jinky Oda
‘Vampire ang Daddy Ko’ was the third Vic Sotto-starred sitcom to feature a mystical theme. It was also his first project alongside son Oyo Boy, and the first comedic role for young child star Ryzza Mae Dizon.
8. Hay, Bahay! (2016-present)
Notable co-stars: Oyo Boy Sotto, Kristine Hermosa, Ai-ai delas Alas, Jose Manalo, Wally Bayola, Ruby Rodriguez
The premise of ‘Hay, Bahay’ is similar to ‘1 For 3’, in which the characters share the same house owned by a landlord. The sitcom marks the television comeback of Kristine Hermosa, and it will be her first show outside of ABS-CBN.
Indeed, Vic Sotto has come a long way since he was introduced as the iconic Enteng Kabisote in ‘Okay Ka, Fairy Ko’. After nearly 30 years as the ‘Bossing’ of Philippine sitcoms, he is still going strong.
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Samsung Galaxy Tab Pro 8.4 - Hands On (CES 2014)
what's up guys Texas is back again and today we're going to be looking at the new samsung galaxy tablet pro 8.4 the new tablet from samsung brings some interesting software improvements as well as hardware the new samsung tab pro 8.4 is Samsung's answer to Apple's iPad Mini with Retina display which was also recently launched with its high resolution display new software improvements and killa internals does the new galaxy tab stand up to its competition we'll find out once you get this tablet in-house for review Samsung has managed to give the new Galaxy Tab a 2560 by 1600 super clear LCD and to power all those pixels Samsung has put its own Exynos 5 octa-core chipset that will be clocked at 1.9 gigahertz other countries that probably include the United States will get a Snapdragon 800 chipset that will be clocked at 2.3 gigahertz the samsung galaxy tab pro 8.4 will have only 16 and 32 gigabytes of storage but it'll be expandable by a microsd up to 64 gigabytes the tablet will also come with 2 gigs of RAM which is kind of weird because we've already seen Samsung implement 3 gigs of ram into their no 3 device other than that the device feels really good in the hand and uses the same pleather material backing that can be found on the Galaxy Note 3 line the tablet is also slim but has good weight to it you shouldn't really have any problems carrying this throughout the day the new galaxy tablet also come pre-loaded with magazine interface samsung says his experience was specifically designed for a larger form factor devices allowing users to further tailor the experience of the galaxy tablet to their own needs the interface enables users to organize the content the way they want in a dashboard our automatically pulled new data from servers as well as organizing apps that you more frequently use on the top this will also be Samsung's first device that runs 4.4 kitkat officially for the one guy who actually uses the tablet camera you'll be pleased to hear that the Galaxy Tab comes an exceptionally good tablet camera we actually compared it to an iphone 5s which arguably has one of the best shooters on a mobile device at right now and as you can see it could hold its own against the Apple iPhone center wraps up the video thanks again for watching we saw the few other Samsung to go over as well as other products to cover so make sure you guys are subscribe so you guys don't miss any cool videos
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Geek BitsTV/Movies
Back to the Future: The Musical Confirms World Premiere In 2020
It’s time to go back, back to 2012 when plans were made by Back to the Future director Robert Zemeckis and co-screenwriter Bob Gale announced their plans for a musical based on 1985’s Back to the Future.
The musical which was originally slated to be released in 2015 clearly did not happen but fast forward to the present, and tickets to the Back to the Future musical has actually already gone on sale.
#Manchester played host to two #BackToTheFuture Heroes and cinema’s most famous car at the iconic #AlbertSquare.
Say hello to our Marty McFly (@ollaaaay) with Trilogy co-creator and all round @BTTFmusical Godfather #BobGale! In 2020, you’re gonna see some serious sh*t 😎 pic.twitter.com/te86YaD5br
— Back to the Future (@BTTFmusical) May 21, 2019
The first official musical theatre adaptation for Back to the Future is scheduled to run for a 12-week season from February 20 to May 17 2020 at the Manchester Opera House, before moving to London’s West End. Zemeckis will be working with Gale and theatre producer Colin Ingram to produce the musical.
The 1985 film centres around Marty McFly (Michael J. Fox), a teenager who is accidentally transported to 1955 in the time-travelling DeLorean, an invention created by his friend, Dr. Emmett Brown. Whilst in the past, Marty has to make sure his high school-age parents fall in love in order to ensure his own existence when he goes back to the present.
Olly Dobson (Matilda, Bat Out of Hell) will be taking on the role for the musical, with Tony Award-winning director John Rando directing. Additional casting, including who will take on the role of Doc Brown, will be announced at a later date.
READ ALSO: Mobile MMORPG World Of Dragon Nest Launches January 8, 2020 In Southeast Asia
Gale, who penned the play, shares his excitement for the musical,
“Bob Zemeckis and I have been trying to get this project off the ground for years, but good things take time and finally, the time is right. Our cast is outstanding, the songs are fantastic, and director John Rando is doing an amazing job ensuring the show truly captures the magic of the movie. We’re thrilled that we can retell our story on stage in a brand-new way, and we’re certain that Back to the Future fans all over the world will share our enthusiasm. In the words of Marty McFly, ‘your kids are gonna love it’ — and so will you and your parents.”
Tickets for the musical go on sale from May 24, priced from £19.55. You can purchase them from the ATG Ticket website.
Germaine is a fun-sized introvert who loves nothing better than sleeping in on rainy days. She can be found reading fanfiction and manga while still waiting for her Hogwarts acceptance letter. It’ll come eventually.
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Massive Metal Monday: The Atlas Moth “The Sea Beyond”
By Ides Bergen | @ | Monday, August 17th, 2015 at 3:00 pm
There must be something in the water in Chicago that is causing it to be America’s new heavy metal capital. The list of insanely great bands hailing from the windy city is as long as your arm, and growing seemingly by the minute. At the forefront of that movement is a doomy, post-metal band that call themselves The Atlas Moth. Their sound manages to be both ethereal and crushingly heavy, while always maintaining an element of (dare I say it?) beauty.
Today’s Massive Metal Monday track “The Sea Beyond” is taken from The Atlas Moth’s third full length album The Old Believer. It is a concept album that deals with the emotions surrounding the death of singer/guitarist Stavros Giannopoulos‘ mother.
The rest of Atlas Moth’s talent are Alex Klein (Bass), David Kush (Guitar, Vocals), Dan Lasek (Drums), and Andrew Ragin (Guitar).
Check out “The Sea Beyond” here below and if you like what you’re hearing I strongly recommend delving into the band’s back catalog. You can thank me later.
Upcoming Tour Dates:
Aug 17 Club Dada Dallas, TX
Aug 18 Empire Control Room Austin, TX
Aug 19 Rudyard’s British Pub Houston, TX
Aug 20 Siberia Nola New Orleans, LA
Aug 21 Masquerade Atlanta, GA
Aug 22 The Orpheum Tampa, FL
Aug 25 Saint Vitus Bar New York, NY
Aug 26 Great Scott Boston, MA
Aug 27 Metro Gallery Baltimore, MD
[Source: The Atlas Moth FB]
When I was growing up in rural Indiana in the early ’80s, there was very limited access to heavy music. These were the days before MTV blew up with the whole hair metal, Headbangers Ball phenomenon. But on Sunday nights, there was a two-hour radio show that came from WOXY, just across the state line in Oxford, Ohio (home of Miami University of Ohio). It was called Massive Metal for the Masses, and I would wait all week for it to air. It was through this show that I was introduced to bands like Venom, Bathory, WASP, Michael Schenker Group, Slayer, and countless others. This Monday weekly column is my tip of the hat to that show. I call it Massive Metal Monday. Every week, I will pay tribute to defining moments by the artists that laid the groundwork for heavy metal to become the worldwide cultural bond for all of us metal heads.
Topics: Features, Massive Metal Monday, Music, News
Tags: Brutal Panda, Candlelight Records, Heavy Metal, Profound Lore, Stavros Giannopoulos, The Altlas Moth, The Old Believer, The Sea Beyond
Preview ‘The Bastard Executioner’ With The Cast!
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TV Review: Dimension 404 1.1 “Matchmaker”
By Maximus Prime | April 4th, 2017 at 3:00 pm
Episode 1.1 “Matchmaker”
Directed by Stephen Cedars and Benji Kleiman
Written by Will Campos and Dez Dolly
Starring Robert Buckley, Lea Michele, Joel McHale, Matt L. Jones, Karissa Staples, Mark Hamill
Air Date: Tuesday, April 4, 2017
Warning: Minor spoilers for Dimension 404 below:
Imagine if Doctor Who and The Twilight Zone had a baby; the result would be Rocket Jump’s new Hulu series, Dimension 404. Each installment of the six episode anthology show is inspired by the internet’s all too familiar “404†error code, and focuses on the deeper, darker, and stranger depths of the World Wide Web — and did I mention that Mark Hamill is the narrator?
But is the show itself a success, or does it deserve its own “error†mark? Find out below in this review of episode one, “Matchmaker.â€
Tags: Benji Kleiman, Dez Dolly, Dimension 404, Hulu, Joel McHale, Karissa Staples, Lea Michele, Mark Hamill, Matt L. Jones, Robert Buckley, Rocket Jump, Stephen Cedars, Will Campos
‘Dimension 404’: Watch A Trailer For Hulu’s New Sci-Fi Anthology Series
By Maximus Prime | April 3rd, 2017 at 6:00 pm
We’ve all seen it before: you click on a link to a page you’d really like to view and that annoying “404†error is displayed across your screen. But why? Where could the page have possibly gone? What happens beneath that website mistake, in the dark depths of the World Wide Web?
A trailer has been released for Dimension 404, a new science fiction series premiering on Hulu from Rocket Jump, the production company behind the popular web series, Video Game High School. An anthology show that taps into the scary, weird, and humorous aspects of the internet’s expansive unknown.
Read the synopsis and check out the trailer below!
Topics: News, Television, Trailers
Tags: Ashley Rickard, Constance Wu, Dimension 404, Hulu, Joel McHale, Lea Michele, Lorenzo Izzo, Malcolm Barrett, Mark Hamill, Megan Mullally, Patton Oswalt, Robert Buckley, Rocket Jump, Sarah Hyland
Check Out The Teaser For Hulu’s ‘Dimension 404’
By Olympus Athens | @ | March 22nd, 2017 at 4:37 pm
A new supernatural anthology series is set to hit Hulu next month. Dimension 404, airing on 4/04, is a 6-episode series, where each episode is its own self-contained story. Lea Michele (Glee, Scream Queens), Robert Buckley (iZombie), Joel McHale (Community), Sarah Hyland (Modern Family), Constance Wu (Fresh Off The Boat), Patton Oswalt (Agents of S.H.I.E.L.D.), Megan Mullally (Will & Grace), and Tom Noonan (12 Monkeys) are some of the names set to star. The first 3 descriptions of this show created by Dez Dolly and Will Campos, and co-created by Dan Johnson and David Welch, have been released.
Check out the teaser, synopsis and episode descriptions below.
Topics: News, Television, Videos
Tags: Constance Wu, Dan Johnson, David Welch, Dez Dolly, Dimension 404, Freddie Wong, Hulu, Joel McHale, Lea Michele, Lionsgate Television, Matthew Arnold, Megan Mullally, Patton Oswalt, Robert Buckley, RocketJump, Will Campos
TV Review: Scream Queens 2.10 “Drain The Swamp” (Finale)
By Dr. Zaius | @ | December 21st, 2016 at 10:00 am
Episode 2.10 “Drain The Swamp”
Written by Brad Falchuk & Ian Brennan
Directed by Ian Brennan
Starring Emma Roberts, Jamie Lee Curtis, Abigail Breslin, Keke Palmer, Billie Lourd, Kirstie Alley, Lea Michele, Taylor Lautner, John Stamos
Air Date: Tuesday, December 20th, 2016, 9pm
Scream Queens concludes its second season tonight with an appropriately titled episode, considering it’s air date is the day after the Electoral College confirmed the Trump ascendancy. There are two Green Meanies left after Wes (Oliver Hudson) was killed off last week in a vat of boiling peanut oil. That leaves Chanel-hating hospital admin Ingrid Hoffel (Kirstie Alley), and vengeance seeking baby in the belly, Dr. Cassidy Cascade (Taylor Lautner) whose mom is even crazier than him, keeping Zayday (Keke Palmer) hostage while her son murders everyone he can in the hospital. The major bone of contention is his love of Chanel #3 (Billie Lourd) and whether or not he will follow through with killing her or run away with her. In other news, Munsch (Jamie Lee Curtis) finally admitted she’s dying of an incurable disease and Chanel (Emma Roberts) could be in line for a major gig, replacing a murdered Brooke Shields on “Loving the Dâ€.
Spoilers for the second season finale of Scream Queens below:
Leave a comment: 1 Comment »
Tags: Abigail Breslin, Billie Lourd, Emma Roberts, Fox, Jamie Lee Curtis, John Stamos, Keke Palmer, Kirstie Alley, Lea Michele, Scream Queens, Taylor Lautner
TV Review: Scream Queens 2.9 “Lovin The D”
By Dr. Zaius | @ | December 15th, 2016 at 1:00 pm
Episode 2.9 “Lovin the D”
Written by Ian Brennan
Directed by Maggie Kiley
Spoilers for Scream Queens…
You gotta love any show that names an episode “Lovin the D.†Last week, things got way too kinky as Jamie Lee Curtis directed her first episode of the show, and her Cathy Munsch quickly became the subject of a love triangle as Wes Gardner (Oliver Hudson) returned and swept her off her feet, which caused huge jealousy for Dr. Holt (John Stamos). It was later revealed that he is also one of the Green Meanie killers since his daughter Grace went nuts after season 1. He left Chamberlain (James Earl) a bloody mess. That gives us Wes, Ingrid Hoffel (Kirstie Alley), the hospital admin out for revenge against the Chanels, and Dr. Cassidy Cascade (Taylor Lautner), the baby in the belly from the premiere as our three (so far) killers. Of course Hester Lea Michele) is still roaming the hospital and she was the killer from season 1. And technically Chanel (Emma Roberts) killed Hoffel’s sister at Kappa house… and Holt has a the hand of a serial killer… and Munsch definitely murdered her husband last season… jeez man, who isn’t a killer on this show!
Tags: Abigail Breslin, Billie Lourd, Emma Roberts, Fox, Ian Brennan, Jamie Lee Curtis, John Stamos, Keke Palmer, Kirstie Alley, Lea Michele, Maggie Kiley, Scream Queens, Taylor Lautner
TV Review: Scream Queens 2.8 “Rapunzel, Rapunzel”
By Dr. Zaius | @ | December 12th, 2016 at 12:00 pm
Episode 2.8 “Rapunzel, Rapunzel”
Written by Brad Falchuk
Directed by Jamie Lee Curtis
Air Date: Tuesday, December 6th, 2016, 9pm
Last week on Scream Queens, the adorable couple of Chanel #3 (Billie Lourd) and Dr. Cassidy Cascade (Taylor Lautner) tried to work through their issues so they can move forward together. Unfortunately, there’s a small problem with their relationship in that he is one of the Green Meanie killers stalking the CURE Institute. We know that hospital administrator Ingrid Hoffel (Kirstie Alley) is pulling the strings and acting as a second killer, but there may be another. The highlight of last week was Dr. Holt (John Stamos) and the ongoing battle with his own hand, which was transplanted from a serial killer as well. It’s impeding his budding romance with Chanel (Emma Roberts) and drawing him into conflict with Munsch (Jamie Lee Curtis).
Spoilers for this week’s Scream Queens below.
Tags: Abigail Breslin, Billie Lourd, Brad Falchuk, Emma Roberts, Fox, Jamie Lee Curtis, John Stamos, Keke Palmer, Kirstie Alley, Lea Michele, Ryan Murphy, Scream Queens, Taylor Lautner
TV Review: Scream Queens 2.7 “The Hand”
By Dr. Zaius | @ | December 1st, 2016 at 11:00 am
Episode 2.7 “The Hand”
Directed by Barbara Brown
Air Date: Tuesday, November 29, 2016, 9pm
Last week, we found out the identity of The Green Meanie… well at least one of the Meanies. Dr. Cassidy Cascade (Taylor Lautner) confessed to psycho nurse administrator Ingrid Hoffel (Kirstie Alley). She was already on her own crusade to kill the Chanels for the murder of her sister, the cook back in season 1. Meanwhile, Chanel (Emma Roberts) won the hospital blood drive and Hoffel’s trip to Blood Island and plans on consummating her relationship with Dr. Brock Holt (John Stamos) very soon. In a hilarious twist, Cascade framed Holt as the “baby in the belly”… leaving 53-year-old Stamos being accused of crimes of the 30 year old. He is of course flattered at first until he realizes they’re serious.
More below for this week’s Scream Queens…
Tags: Abigail Breslin, Billie Lourd, Emma Roberts, Jamie Lee Curtis, John Stamos, Keke Palmer, Kirstie Alley, Lea Michele, Niecy Nash, Scream Queens, Taylor Lautner
TV Review: Scream Queens 2.6 “Blood Drive”
By Dr. Zaius | @ | November 26th, 2016 at 11:00 am
Episode 2.6 “Blood Drive”
Directed by Mary Wigmore
Starring Emma Roberts, Jamie Lee Curtis, Abigail Breslin, Keke Palmer, Billie Lourd, Kirstie Alley, Niecy Nash, Lea Michele, Taylor Lautner, John Stamos
Last week, Chanel (Emma Roberts) devised a plan to recruit new “Chanels†for the purposes of being cannon fodder against The Green Meanie. Plan worked, as the killer struck again. Zayday (Keke Palmer) is convinced that hospital candy striper Chamberlain (James Earl) has something to do with the murders. Munsch (Jamie Lee Curtis) is trying to stay one step of both her illness, and the news that her CURE Institute is housing a serial killer. Back at it…
More below for this week’s Scream Queens:
Tags: Abigail Breslin, Billie Lourd, Brad Falchuk, Emma Roberts, Fox, Jamie Lee Curtis, John Stamos, Keke Palmer, Kirstie Alley, Lea Michele, Mary Wigmore, Ryan Murphy, Scream Queens, Taylor Lautner
TV Review: Scream Queens 2.5 “Chanel Pour Homme-icide”
By Dr. Zaius | @ | November 16th, 2016 at 3:45 pm
Episode 2.5 “Chanel Pour Homme-icide”
After four long weeks, Scream Queens is back! Breaking for both the World Series and the Presidential Election, Scream Queens now reclaims its tuesday night time slot. Frankly after the election produced real horror, I need some good fake horror back in my life. When we last left the hospital, Chanel #5 (Abigail Breslin) was attacked and left for dead by the Green Meanie who also disposed of Denise Hemphill (Niecy Nash) via electrocution. Hester (Lea Michele) has also escaped and may or may not be aiding the Meanie in their revenge killings.
TV Review: Scream Queens 2.4 “Halloween Blues”
By Dr. Zaius | @ | October 22nd, 2016 at 4:07 pm
Episode 2.4 “Halloween Blues”
Directed by Loni Peristere
Air Date: Tuesday, October 18, 2016, 9pm
Sorry this is late, but Tuesday night was Amy Schumer at Madison Square Garden in NYC… but here’s what’s happening on Scream Queens. My poor sweet Chad Radwell (Glen Powell) is dead. I have not, and will not recover. His body fell Suspiria-style through the stained glass ceiling at his supposed wedding to Chanel (Emma Roberts). The CURE Institute has been shockingly successful at finding cures for bizarre ailments, while at the same time being horrible at keeping its patients alive post-cure. The Green Meanie continues to wreak have on the hospital now run by Cathy Munsch (Jamie Lee Curtis). Thirty years ago on Halloween night, a patient was ignored and died thanks to the staff who then dumped his body in the swamp. Now, in order to try to lure the killer out, the current gang are having their own hospital Halloween party.
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Richard Henry J Knowler 1939 - c2000
The child of George Knowler (a farm horseman heavy worker) and Amelia Spelman, Richard Henry, the second cousin once-removed on the mother's side of Nigel Horne, was born in Thanet, Kent, England on 8 Aug 19391,2,3.
He died c. Nov 2000 in Dover, Kent, England2,3 and was buried at Hamilton Road Cemetery, Deal, Kent c. 2000.
George Thomas was born on 2 Sep 1901
Amelia Winifred was born on 11 Oct 1895
https://search.findmypast.co.uk/record?id=bmd/b/1939/3/az/000688/095
https://search.findmypast.co.uk/record?id=us/bmd/billion/5/000027756850
https://search.findmypast.co.uk/record?id=bmd/d/2000/10/83784552
England & Wales births 1837-2006 - Findmypast
England & Wales deaths 1837-2007 - Findmypast
England Billion Graves cemetery index - Findmypast
To be done
Burial date (abt 2000) has no citations
1939 UK register information missing
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Home » Halftime » Halftime Leisure » Trailer Takes: Nancy Drew and the Hidden Staircase, Godzilla: King of Monsters, and Good Boys
Trailer Takes: Nancy Drew and the Hidden Staircase, Godzilla: King of Monsters, and Good Boys
By: Inès de Miranda, Katie Woodhouse and Skyler Coffey
Nancy Drew and the Hidden Staircase: https://www.youtube.com/watch?v=knPrLVBn93w
Sky: Oh man, if this movie had come out when I was 10 years old I know I would have been all over it. The kind-of-scary mystery, the modern rebellious take on Nancy’s (Sophia Lillis) character, and Nancy’s epic girl squad would’ve had me hooked. Now, however, the glaring flaws in this movie are just too prominent for me to look past. As my fellow writers have already pointed out below, in this movie, Nancy’s signature adventurous spirit, playful charisma, and headstrong persona are used to show how much of a not-girly-girl she is. Specifically, a blonde, stylish girl is clearly used as a foil to Nancy in an apparent frenemy relationship, even drawing the comment from Nancy, “Mean girls go first.” @Nancy and all the writers of this movie, please check your internalized misogyny. Also, between an adult flat out listing her qualities and specific scenes that are included just to highlight a seemingly “unique” aspect of Nancy’s personality (like pretending to drop a test tube), this movie seems like exposition central. I actually remember reading Nancy Drew as a kid and generally enjoying the books. While I of course thought of Nancy as an impressive heroine, I cared much more about the actual mystery than the protagonist because the books themselves spent much more time on plot than characterization. In a way though, this method still allowed Nancy to shine: You don’t need someone to say that she’s brave if you can just see her unflinchingly investigate a somewhat-creepy clue, which would be needed to advance the plot anyway. With this movie, as with many remakes, it seems that less (meaning sticking closer to the original) would have been more.
Katie: To start off, I must admit that I’ve never been a huge Nancy Drew fan so my interpretation of this trailer could be missing something, but there is one thing about it that distracted me the whole time—does Nancy Drew (Sophia Lillis) really need to ride skateboards and wear flannels to be badass enough to solve crime? As much as girls don’t need to fit the stereotype of “girly,” there is something to be said for embracing femininity, for lack of a better word, and being smart and badass at the same time, something that Nancy Drew is historically known for. I think by trying to break stereotypes here, this movie is actually falling into the Hollywood trap of the “I’m not like other girls” cliché. Every supporting character other than a shamefully token black friend has long blond or brown hair seemingly in order to emphasize just how different Nancy is, which seems contrary to the statement this film is trying to make. What’s wrong with other girls? Nothing! I definitely will not be putting aside the time to see this movie, but hope that die-hard Nancy Drew fans get the modern day remake they want in this film!
Inès: When I was a kid, I read the books, both the regular Nancy Drew books in English and the French version Alice Roy (don’t ask me how that name translates, I don’t know). I also loved the 2007 film Nancy Drew which starred Emma Roberts and made me look up to her. I learned about the Miranda Rights in that movie, and it was a great blend of child-level thriller and fun. I don’t know whether that movie holds up today, but I know it’s biased me against this new remake because everything in the production of this trailer, the WordArt-level font especially, jumps out at me. I’m not sure I like the premise, I’m not sure I like the supporting cast, and I definitely feel too old to watch this teen Disney-esque film. I will say that I don’t hate the tomboy-style Nancy, but it feels like a cliché that doesn’t reflect 2019 feminine power but 2008 era [insert an iteration of a Cinderella story here] type of character that superficially isn’t a “girly-girl.”
Godzilla: King of Monsters: https://www.youtube.com/watch?v=MnxerBqUZgw
Sky: Alright, I don’t like monster movies and I don’t like apocalypse movies, so I feel like this is just not the thing for me. This movie seems like Jurassic Park (1993)/World (2015)/whatever sequel they’re on now but with much higher stakes. I don’t understand what makes Godzilla so special as a monster when he kind of just seems like a giant lizard? I’m also very confused because Godzilla is not the only monster in this trailer, and the title “King of Monsters” implies that there is some kind of intra-monster conflict that is going to happen. This really confuses me: Am I now supposed to root for Godzilla? Will the monsters destroy each other or will they destroy the Earth first? Was the real Godzilla the monsters we made along the way? While these are all extremely pressing questions, I still don’t think they will actually compel me to pay money for or spend time watching this movie.
Katie: Have there been a lot of Godzilla movies? I honestly don’t know, but it seems like at least a thousand. Of course, I’m also grouping in all of the other massive-monster-destroys-a-city movies. This one seems to have *gasp* MULTIPLE monsters, which from the title I assume are all defeated by this “Godzilla” creature. That is about all I have pulled from this very short trailer. I think there is an audience for this type of movie, but personally I find the whole genre cliché and quite boring. I did look up the cast that is briefly shown and it seems to be pretty solid (Millie Bobby Brown, Bradley Whitford, Thomas Middleditch etc.) and it looks like there will be some promising action scenes and excellent graphics work, but I personally will not be taking the time to go see it.
Inès: Ok, so I have never seen a Godzilla movie before, and have never felt the need to. Not to sound superior, but I just don’t get the appeal of a movie with a monster who is attacking the world and very little plot beyond that. And I will sometimes watch movies with little to no plot, so that’s really not saying much for this franchise. This is a mercifully short trailer which shows that the premise involves there being more than one monster, they’re fighting, and humans are in the midst of this in some way, probably mostly as collateral damage and for the purpose of narration. The sad and dramatic music does not draw me in, and I have basically an abnormally high level of indifference towards this movie and everything about it. I just can’t find it in me to care.
Good Boys: https://www.youtube.com/watch?v=RrE_ujzCm-E
Sky: This movie immediately strikes me as a counterpart to Bo Burnham’s Eighth Grade (2018), except less accurate, more comical, and with a group of boys instead of a solitary girl. I thought that the opening of the trailer with Seth Rogen explaining how the boys could not watch the movie that they themselves are featured in was very clever (reminding me of how eighth graders could technically not watch the movie Eighth Grade), and established the film as both more raunchy and less-idealized than other middle school flicks. Ultimately, this movie seemed very funny and I liked how there were some scenes in which I found myself laughing at the characters, and others laughing with the characters. I definitely caught myself relating a little bit too hard when one of the sixth grade boys pointedly inserted F-bombs into his speech to appear tough as he vindictively explained that a juice box is not a sippy cup. Overall, this movie seems like it will have a lot of laughable bits, even though some of the overarching plots, such as the one with a drone spying on the two girls, seem a little questionable. Out of all of the trailers this week, though, this is definitely the movie I would most want to see.
Katie: Ok, this was funny. Like a really funny, well done trailer, especially the “restricted” opening. I feel like I have seen the whole movie, but even if this is the whole movie, it looks charming and like a sweet celebration of devoted friendships in those awkward, terrible middle school years. I doubt I will take a whole trip to the theater for it, but I hope to catch it at some point on a plane or something. Kudos to the kids as well, because they look both fantastic and professional as well as legitimately funny. On this note, as the hilarious Stranger Things (2016) reference reminded me, I just have to recognize how impressive child and teenaged actors are and how recently they have been showing up their adult counterparts in a big way. When I was 13, I was scared to even see myself in a mirror much less be on camera … it was a dark time. Although that sentiment is probably more relatable than anything these boys do in the movie, I really do hope that it is as good as it looks!!
Inès: I like the way the trailer is meta; the trailer genre could use a glow up honestly. It’s a bit on the nose here, but I like the initiative and the commentary. The movie itself looks like it’ll be funny, a regular fun movie—not one I’d necessarily go to the movies for, but I’ll definitely watch this on streaming. The vibe of the movie is a bit like a cross between The Hangover (2009) and a trope movie about middle school boys. It’s funny because of the sex and drug jokes, and the foul language, but it’s successfully funny because of the boys’ naiveté. So I’m here for it. A smart comedy that isn’t high brow is my idea of a fun movie night with friends.
Image Credits: IMDb
comedy Monsters Nancy Drew Seth Rogan trailer takes
Inès de Miranda is a senior who has no idea what she'll do next year but loves contributing to the Voice in the meantime. She's the current chair of the editorial board. Also, she's French (Editor's note: it comes up)
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2 COMMENTS ON THIS POST To “Trailer Takes: Nancy Drew and the Hidden Staircase, Godzilla: King of Monsters, and Good Boys ”
Dillon says:
03/20/2019 at
You all have terrible taste lol. Godzilla looks fantastic
Godzilla is going to be so much fun!
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Characters, Universal Century characters, Male
Jerid Messa
Revision as of 04:57, January 5, 2016 by Alex0079 (wall | contribs)
MSZG
MSZG Define
Side Story of Gundam Zeta
Mobile Suit Gundam 0087: Jerid Sortie Order
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Ethan Cole
Genetic Type
August 10, 0063 (U.C.)
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Jerid Messa (ジェリド・メサ, Jerido Mesa?) is a fictional character from the Mobile Suit Zeta Gundam series. A member of the Earth Federation's counter-insurgent organization Titans, he is best known for being the archrival of the main character Kamille Bidan.
Personality & Abilities
Jerid has the typical traits of a Titan member: being ruthless, egotistical, overconfidant and an absolute disregard for the lives of civilians. Jerid has the ambition to one day become the Titans leader, but wishes to do so his own way without the help of others. However, despite his pride as an Earthnoid he would ask the help of Lila to better himself as a soldier. On a similar note, he is extremely arrogant to believe that the Titans have the power to deem what they do as right, despite that his arrogance only sparked hatred and mistrust to the public population. His rivalry with Kamille becomes bitter hatred when his comrades die one by one, and he blames Kamille's very existence for his loss. Ultimately, his arrogance and hatred brought forth his demise at the hands of his rival, and puts his ambitions to rest.
Jerid Messa was born into a family of trained soldiers in U.C. 0063. After achieving high results on a military aptitude test, Jerid qualified to join the elite Federation unit, the Titans. He was sent to train at Green Noa I, where he first encountered Kamille Bidan. When Jerid made fun of Kamille's feminine name, Kamille punched him.
Later, as Jerid was training on one of the RX-178 Gundam Mk-II prototypes, he was responsible for crashing into a government building, and causing much damage. He abandoned his mobile suit, and it was later moved to a building where, after a confusing battle inside the colony, the AEUG was able to steal it.
Battle of Green Noa I
After Quattro Bajeena and Kamille Bidan escaped from "Green Noa I" with the two Mark II prototypes, they were retrieved by the AEUG flagship, Argama. In space, Titan's Commander, Bask Om launches Lt. Emma Sheen (with the last Gundam Mk-II) to the Argama with specific orders of retrieving the stolen prototypes. Nearby, Jerid waits in a Hizack and opens his orders, which are to destroy a capsule (that was released to space) if the AEUG attempts to retrieve it.
After the negotiations between the Titans and the AEUG are broken, Kamille launches from the ship with the Gundam Mk-II in a desperate attempt to rescue his mother, Hilda, revealed to be inside the capsule. When Kamille approaches, Jerid starts shooting at the capsule, believing that the capsule is a bomb that would destroy Kamille. Instead, the shots destroyed the capsule, killing Hilda.
Although Jerid later apologized to Kamille and explained what truly happened, their rivalry started once again, because Jerid didn't forget Kamille's arrogant attitude in Green Noa I and because he didn't want to be disgraced by a kid. After a prolonged fight and the defection of Lt. Emma Sheen to the Anti-Earth Union Group, Jerid is forced to retreat.
Quest for the Argama
Back in the Alexandria, Jerid meets Lila Milla Rira, an Earth Federation pilot. Titan's Commander Jamaican Danninghan decides that Jerid will lead the next attack on the AEUG. Shortly afterwards he asks Lila to teach him how to survive in space combat, holding back his previous pride for help. After he fails in his attempt to destroy the Gundam MK-II, Lila tells Jerid to feel the hostile intent of his enemy when fighting in space, since it is not the same as fighting on Earth. Lila defends Jerid from the wrath of Jamaican, stating that the crew of the Argama is composed of Newtypes. By doing this, Lila managed to earn Jerid's both respect and admiration.
In TV version, while pursuing the Argama, the Titans and E.F.S.F reach the Space Colony 30. Once there, Lila and the Federal Forces fought against Kamille and the Anti-Earth Union Group. Jamaican, aware that Jerid was eager to join them and support Lila, refuses to accept any plead of help from the Federal Forces. Thus, Jerid is forced to watch the outcome of the battle from the bridge of the Alexandria; that is, Lila's death at the hands of Kamille. (In the movie version, after Lila's unit was destroyed by Kamille before atmospheric entry, Jerid could feel Lila's death, though he was not sure for that, he said he would get revenge for Lila in atmospheric entry, but he was trying to find Lila when he enter Jaburo.)
Battle of Jaburo
After seeing Lila's death, Jerid swore to avenge her death by killing Kamille Bidan. He gets an opportunity when he is ordered to attack Anti-Earth Union Group forces in satellite orbit. During this battle, he is unable to beat Kamille. Jerid is also shocked to see his good friend Kacricon Cacooler die when his ballute is destroyed by Kamille. This action causes Kacricon to meet a painful death in the Earth's atmosphere.
The battle continues when the AEUG forces landed on earth. They penetrated the defenses at the base, only to learn that a nuclear bomb is timed to explode. Jerid attacks Kamille inside the base, hoping to kill him. Again, he fails, and his Marasai is severely damaged. He is able to escape the base before it's destruction by commandeering a jeep with several Federation soldiers. He then fights his way onto an escape vessel, only surviving because a hand pulled him into the crowded ship. It belonged to another Titans pilot, Mouar Pharaoh.
Operation Apollo
Afterwards, Jerid is seen serving under Scirocco, where he is given the RX-110 Gabthley. During this time, he and Mouar become lovers, and the two of them launch attacks against the Argama. During a surprise attack against the Argama, Mouar is killed trying to protect him from Kamille, in his MSZ-006 Zeta Gundam. Jerid, cursing Kamille for killing people close to him, attempts to attack but gets damaged by Kamille. Mouar's spirit then gives him a Newtype vision, telling him that he is the only one that can lead the people down the right path. After this, Jerid renews his attack in pure rage, doing more damage to the Argama than he has ever done before his mobile suit is disabled by Kamille and Emma.
In TV version, he was then sent to the Earth base of Kiliminjaro. While being treated, he comes across Kamille, who had infiltrated the base and ran into Four Murasame. When Kamille begins to convince Four to get out of the Psycho Gundam and go with him, Jerid in his new model RX-160 Byalant charges toward them with his beam saber drawn, but ends up killing Four when she blocks the strike with the Psycho Gundam. He follows the AEUG to Dakar and attacks the city, in hopes to shut down the communications tower, which Char was using for his address. He retreats when favor sways from the Titans and heads back into space. (In the movie version, he remain in the space after Mouar's death, and the Byalant was assigned to him afterwards.)
Battle of Gryps
During the Battle of The Gate of Zedan, Jerid appears, exhibiting superb battle skills. When Axis is slammed into the Gate of Zedan, Jerid launches to protect the fleeing Titans in the RX-160 Byalant. In the ensuing battle, Jerid shoots down Lieutenant Apolly Bay, who was protecting Fa Yuiry. An interesting note, is that during Jerid's charge towards the Gwadan, Haman Karn senses a psychic pressure from Jerid, which suggests that Jerid has begun to unlock his Newtype potential (In the movies, he was just being shot and retreats). This attests for his ability to later fight in the NRX-055 Baund Doc, a machine created especially for Newtypes. Jerid is seen using the Baund Doc on a raid against the Radish at the Battle of Gryps, and then duels with Kamille. Jerid has the misfortune of challenging Kamille as he goes to rescue Emma, which results in Kamille arriving seconds too late. Instead, the AEUG battleship Radish rescues Emma at the price of its destruction at the hands of Titans ace pilot Yazan Gable. Jerid then attempts to continue the duel, and Kamille dispatches Jerid after a short battle, sending him flying into the remains of the exploding Radish. With his last breath, Jerid curses Kamille's existence, as a barrier to his ascension in the ranks of the Titans.
in Zeta Gundam Define
Notes & Trivia
In SD G Generation DS, if you finish the entire Rival Route, including the Encore Sessions, Jerid Messa will lose his Newtype Ability. This could be an overlooked mistake in the game before publishing.
He is viewed as a joke in a sizable number of the fandom due to how he fails to rise to being a true rival rather than an annoyance that he became at the series' end. The first Dynasty Warriors Gundam game appeared to be aware of this and has him training under Master Asia.
In the show Jerid's rank insignia is very inconsistent, often switching back and forth between lieutenant junior grade and full lieutenant. This is possibly due to a misunderstanding in the illustration team where perhaps one artist always drew him as a full lieutenant and another artist depicted him as a junior lieutenant.
Retrieved from "https://gundam.fandom.com/wiki/Jerid_Messa?oldid=310846"
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Tatuaje The Tiff
December 8, 2019Brooks WhittingtonCigars, Limited Edition, Nicaragua, Reviews, Tatuaje
Earlier this year, Tatuaje released the final two cigars to its most popular and long-running series Monster Series: The Chuck and The Tiff. The Monster...
Tatuaje The Chuck
Tatuaje CQ2
October 27, 2019Brooks WhittingtonCigars, Limited Edition, Nicaragua, Reviews, Tatuaje
By 2013, Tatuaje selling a retailer exclusive cigar had almost become old hat after legendary cigars like the Porkchop, Pork Tenderloin, Little Boris and Tobacco...
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While a good portion of this site is about objectively evaluating cigars, I will admit that I love a good subtle nod in the back...
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September 30, 2019Patrick LagreidCigars, Limited Edition, Nicaragua, Redux, Reviews, Tatuaje
In 2012, Pete Johnson of Tatuaje decided to venture from his generally Nicaraguan-forward cigar blends and release a cigar with a Mexican San Andrés wrapper,...
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Back in 2012, Tatuaje was known for releasing small batches of cigars with little to no warning and even less explanation. That was the case...
Surrogates Eight Baller
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This year has been rather quiet when it comes to the L’Atelier brands, notable because in 2018, Pete Johnson announced that he would be merging...
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July 20, 2019Charlie MinatoCigars, Limited Edition, Tatuaje
Fifty firfth? Fifty oneth? Yes, it says 51th; and no, I have no clue how to pronounce it. This year’s the Tobacconist Association of America...
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Peanut butter and jelly, Bert & Ernie, Tatuaje and the TAA. Some things just go together. Since 2011, Pete Johnson has been creating limited edition cigars for the Tobacconists’ Association of America, an organization of approximately 80 of the largest, highest-volume brick-and-mortar retailers in the industry, as well as about 40 manufacturers. The cigar gets […]
Tatuaje Little Hassell
March 28, 2019Charlie MinatoCigars, Limited Edition, Nicaragua, Reviews, Tatuaje
Earlier this year—and with virtually no fanfare on this website, Instagram or other—a new Tatuaje showed up at stores. While the cigar is new, both...
Tatuaje Anarchy (2010)
March 4, 2019Brooks WhittingtonCigars, Limited Edition, Nicaragua, Redux, Reviews, Tatuaje
While retailer exclusive cigars were not exactly a new concept back in 2010, they were quite a bit more common than retailer exclusive series. One...
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The Hamlin Model of Care
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News from Catherine Hamlin Fistula Foundation
Quentin and Catherine: Two Inspirational Australians
When the Honourable Dame Quentin Bryce met Dr Catherine Hamlin AC in March 2009, it sparked the beginning of a beautiful friendship based on mutual respect and admiration. Leaders in their respective fields, these two Australian women have been inspirations to thousands over the years – and inspirations to one another. Their friendship has seen Quentin lend her voice in support of Catherine’s work and even write the foreword for the updated edition of Catherine’s autobiography, ‘The Hospital By the River,’ co-written with John Little.
Admirer from afar
In 2009, then-Governor General Quentin Bryce visited Addis Ababa to address the African Union. Quentin knew of Catherine’s work in Ethiopia and was keen to meet her and visit the Addis Ababa Fistula Hospital. In an interview with ABC RN Breakfast‘s Fran Kelly in 2016, Quentin discussed her long-held admiration for Catherine’s work eradicating obstetric fistula in Ethiopia. “I looked forward so much to meeting this wonderful women who I held in the highest esteem from afar… I think it’s true to say she is one of the most loved and admired women in our world,” revealed Quentin.
The initial meeting was a success, as the two women shared their experiences over the decades. In her foreword to ‘The Hospital By the River,’ Quentin recalls their first rendezvous: “I was enthralled by Catherine’s storytelling, her strong true partnership with Reg steeped in mutual respect, equality, shared vision, the finest values and intellectual rigour.”
Catherine acted as tour guide for Quentin, introducing the Governor General to the staff, volunteers and fistula patients, and taking her around the grounds of the Addis Ababa Fistula Hospital. “We walked arm in arm in Catherine’s garden… there was so much to share as we talked about the road ahead,” reminisces Quentin in ‘The Hospital By the River.’
Inspiring women everywhere
Quentin’s trail-blazing status as one of the first women accepted to the Queensland bar, the former Queensland Director of the Human Right and Equal Opportunity Commission, and the first female Head of State in Australia, allowed her to raise awareness of the plight of fistula sufferers in Ethiopia.
In 2011, Catherine was among 50 prominent Australians invited by Quentin, to take lunch with Queen Elizabeth II and the Duke of Edinburgh at Government House, Canberra. The two friends spent a few days together, sharing memorable conversations in the verdant gardens of Government House. They proceeded to travel to Perth together for a special event on women and leadership as part of the Commonwealth Heads of Government Meeting (CHOGM). A key theme of that year’s CHOGM was ‘women as agents of change’ – an apt description of both Catherine and Quentin.
Catherine and Quentin’s friendship has spanned continents and years, and inspired thousands of people in Australia, Ethiopia and beyond. Reflecting on her relationship with Catherine, Quentin remarked “I’ve been privileged to enjoy a friendship with her through letters and her visits to Australia.”
Catherine’s work to eradicate fistula in Ethiopia has inspired thousands, including Dame Quentin Bryce. Learn more about the incredible impact of Catherine’s journey in our 60for60 blog series.
A Summit Advocating for the Advancement of Women’s Rights Research
January 17, 2020 On 10th December over 100 stakeholders, advocates and dignitaries attended an advocacy event organised by the United Nations Population Fund (UNFPA), the Ethiopian Ministry of Women, Children and Youth Affairs, and the Ethiopian Human Rights...
2020: International Year of the Midwife Midwives
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The Need to Go Regional Hospital
January 7th, 2020 For her 96th birthday this year, Catherine has one wish: to upgrade and stock urgently needed new equipment for Hamlin Fistula Ethiopia’s five regional hospitals. These hospitals were created to reach and treat as many...
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Home > Our Firm > Media and Press Releases > PIMCO and University of Chicago’s Center for Decision Research Announce Partnership to Guide Wiser Decision-Making
PIMCO and University of Chicago’s Center for Decision Research Announce Partnership to Guide Wiser Decision‑Making
The Center’s Labs, part of the Chicago Booth School of Business, will be renamed the PIMCO Decision Research Laboratories.
This includes plans to enhance research facilities in Chicago to foster greater engagement with the public.
Enables CDR and PIMCO to better understand human judgment and decision making.
Newport Beach, California (September 27, 2018) – PIMCO, one of the world’s premier fixed income investment managers and the Center for Decision Research (CDR) at the University of Chicago Booth School of Business announce a partnership in support of CDR’s behavioral science research. In recognition of this investment in research, Chicago Booth’s CDR laboratories will be renamed the PIMCO Decision Research Laboratories and will include a new “storefront” behavioral science research lab to foster greater engagement with the public and to broaden the reach and increase diversity of participants in the research studies.
PIMCO has been a longstanding follower of the work of CDR and Richard Thaler, winner of the 2017 Nobel Prize in Economic Sciences. Thaler, Charles R. Walgreen Distinguished Service Professor of Behavioral Science and Economics at Chicago Booth, is also a current board member and visionary former director of the Center for Decision Research. Nicholas Epley, John Templeton Keller Professor of Behavioral Science and Neubauer Family Faculty Fellow at Chicago Booth, currently serves as Faculty Director of the CDR.
“This partnership is incredibly exciting to us. From PIMCO’s plans to disseminate CDR’s research findings, to conducting joint projects in behavioral science, the collaboration will have a transformational impact on our research enterprise,” said Madhav Rajan, Booth Dean and George Pratt Shultz Professor of Accounting. “PIMCO’s spirit of experimentation and interest in asking real-time questions about investing and the economy make it the ideal partner for Booth.”
“This support will enable the CDR to take innovative steps to enhance our research infrastructure,” said Epley. “Conducting the highest impact behavioral science experiments requires being able to conduct experiments out in the world where people are actually living and working. PIMCO’s support will give us one of the most sophisticated laboratory operations in the world, running large-scale experiments in locations ranging from elite organizations to science museums to city sidewalks.”
PIMCO, an innovator in applying research to investment decisions, is excited to both support and participate in this academic research. CDR research draws insights from many disciplines – social psychology, cognitive psychology, economics, and neuroscience – to gain a deeper understanding of human behavior and decision making processes. The PIMCO Laboratories for Decision Research will yield scientific discoveries with the potential to improve individual and social welfare.
“PIMCO is always looking for inputs and data that challenge our ideas and assumptions as CDR researchers have been doing for years, so we look forward to building on this legacy together,” said Dan Ivascyn, PIMCO’s Group Chief Investment Officer. “Through this novel partnership, we hope to nurture exceptional insights into decision making behavior that will ultimately help PIMCO make wiser decisions for portfolios, clients and employees.”
PIMCO’s investment process - which includes quarterly investment forums, speaker series and the input of external advisors including industry and academic professionals - provides the firm with a diverse selection of external views and perspectives that guide PIMCO’s investment decisions. PIMCO with its industry renowned platform and reach to clients is excited to help amplify and disseminate the research of the CDR.
“Understanding how we behave and the decisions we make are critical to building on PIMCO’s strong culture of investing excellence and creating a diverse, engaging workplace, so we are excited to partner on this groundbreaking approach with Nick Epley and his incredible team at CDR,” said Emmanuel Roman, PIMCO’s Chief Executive Officer.
About the Center for Decision Research
CENTER FOR DECISION RESEARCH
The Center for Decision Research (CDR) at the University of Chicago Booth School of Business is devoted to understanding human judgment and decision making. Faculty researchers use the CDR Labs to conduct cutting-edge studies and examine the processes where intuition, reasoning, and social interaction produce beliefs, judgments, and choices. Understanding these decision making processes has critical applications in a variety of contexts including management, marketing, health, finance, and public policy.
Michael Reid
Global Head of Corporate Communications
michael.reid@pimco.com
Agnes Crane
U.S. Corporate Communications
agnes.crane@pimco.com
Laura Batty
laura.batty@pimco.com
Jochen Haegele
EMEA Corporate Communications
+49.89.26209.6293
jochen.haegele@pimco.com
Jennifer Spivey
U.K. and EMEA Corporate Communications
jennifer.spivey@pimco.com
Donna Chan
APAC Corporate Communications
donna.chan@pimco.com
About PIMCO
PIMCO is one of the world’s premier fixed income investment managers. With our launch in 1971 in Newport Beach, California, PIMCO introduced investors to a total return approach to fixed income investing. In the 45+ years since, we have continued to bring innovation and expertise to our partnership with clients seeking the best investment solutions. Today we have offices across the globe and 2,150+ professionals united by a single purpose: creating opportunities for investors in every environment. PIMCO is owned by Allianz S.E., a leading global diversified financial services provider.
Except for the historical information and discussions contained herein, statements contained in this news release constitute forward-looking statements within the meaning of the Private Securities Litigation Reform Act of 1995. These statements may involve a number of risks, uncertainties and other factors that could cause actual results to differ materially, including the performance of financial markets, the investment performance of PIMCO's sponsored investment products and separately managed accounts, general economic conditions, future acquisitions, competitive conditions and government regulations, including changes in tax laws. Readers should carefully consider such factors. Further, such forward-looking statements speak only on the date at which such statements are made. PIMCO undertakes no obligation to update any forward-looking statements to reflect events or circumstances after the date of such statements.
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Barb Jungr accompanied by Jenny Carr (8:30pm Doors)
Tickets are on sale now
Barb Jungr accompanied by Jenny Carr - (8.30pm Show)
Friday 31st January 2020
Tickets: £20.00 Seat at a shared Table for 4 /£15.00 Seat – No Table
Show: 9.00pm
One night – 2 incredible shows!
“Please note, this show is not suitable for Children, only 14+ should book due to some of the adult content of some of the material being presented.”
Barb Jungr:
Cult icon performer and singer Barb Jungr joins jazz star, composer and arranger, pianist Jamie Safir to present songs from their 5 star collaboration Bob, Brel and Me and more, celebrating the songs of Dylan, Brel, Cohen, Springsteen, Sondheim alongside original material in these 2 special shows for Hampstead Jazz Club.
Across her 40 year career she has been internationally acclaimed for combining immaculate vocal technique, impassioned performance, piercing insight and beautifully unexpected musical arrangements to reinterpret European and American popular songs in a manner which The New York Times described as ”revelatory”.
What you might not know is that as a live performer, Barb Jungr is always funny, and often hilarious. Like, intentionally. Cabaret Scenes described a performance in November 2016 as “the funniest hour of cabaret I’ve ever seen” from a “world-class raconteur”. Originally emerging from the alternative cabaret scene of the 1970s and 80s, and cutting her teeth alongside the likes of Julian Clary, Alexei Sayle and Arnold Brown, her ability to deliver shows which are utterly alive, and spontaneously respond to the world in and outside the performance space, is second to none.
If you are only familiar with Barb’s work from her albums, you simply have to see her perform live. Even the highest quality mp3 in the world won’t tell you what it’s like to be in a room with her and her musicians.
Jungr received the New York Nightlife Award for Outstanding Cabaret Vocalist, the Backstage Bistro Award for Best International Artist, and Time Out New York’s #1 Top Live Cabaret Act for 2011. Her powerful singing style reaches across musical boundaries.
“It’s as if Edith Piaf and Nick Cave had a lovechild who was adopted by Carmen McCrae!” – Glam Adelaide
Barb Jungr is ”mesmerising” – New York Times, ”casually virtuosic” – Guardian, an ”alchemist among jazz singers” –Telegraph, possessing a voice which is “shockingly expressive, with an astonishing palette of colours” – Observer
“Barb Jungr proves she’s a genuine jazz marvel….A true musical alchemist… who should not be missed” **** – 4 stars The Telegraph
JENNY CARR- PIANO
Classically trained, Jenny arrived in England from Australia in the early 1990s as keyboardist and backing vocalist on Jason Donovan’s world tour.
Her diverse career has included performing and recording with pop artists Julia Fordham, Bliss, Beverley Craven, Yazz, Billy Ocean and Imelda May, comedian/performance artists David Mills and Christopher Green and singer/songwriters Jeb Loy Nicholls and Robb Johnson. As well as freelancing with a myriad of jazz and swing bands on the London circuit, she is known as a sensitive accompanist and as pianist, MD and arranger. Jenny has collaborated with Barb on several albums and theatre productions as well as touring extensively in the UK, Europe and Australia
“breathtaking sensitivity, ferocious attack… Carr’s playing radiates eloquence and intelligence” Robb Johnson -Irregular Records
www.barbjungr.co.uk
www.kristalynrecords.com
Barb Jungr – Vocals
Jenny Carr – Pianist
No dogs allowed in the Jazz Club.
For £20.00 Tickets:
Seats are not numbered and you will be seated at available tables. Please note tables seat 4 people, so for bookings of less than 4 people, you will be seated and share a table for 4.
This is a fully seated event. Seats are not numbered and will be allocated on a first come first serve basis.
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Movie review: 'A Hidden Life' is a miss from Malick
By Al Alexander/For The Patriot Ledger
"A Hidden Life" tells the true story of an Austrian conscientious objector.
It’s called “A Hidden Life,” but Terrence Malick’s latest fever dream is closer to “The Invisible Man.” That’s how vacuous he renders the would-be fascinating tale of a stubborn Austrian farmer proving such a sticky thorn in Hitler’s side that the Fuhrer ordered his head chopped off. Instead of a rousing true tale of strength and conviction, Malick reduces Franz Jägerstätter’s rise to beatified martyrdom to three hours of what look like outtakes from “The Sound of Music.” The hills are alive with the sound of … footsteps.
Yes, footsteps! Malick repeatedly serves up long, ponderous shots of Franz (August Diehl) and his beloved wife, Fani (Valerie Vachner), strolling through the gorgeous landscapes surrounding the couple’s idyllic farm high in the Austrian Alps. Riveting! Or it would be if the pair bothered to stop and engage in a lick of dialogue that might provide a clue about who they are, their relationship, motivations and dreams; in lieu of the usual wispy voiceovers with which Malick has become so endeared. It’s beautiful but monotonous; more travelogue than a movie.
Yet it would be heartless not to be viscerally moved by Franz's fight for principle, a conscientious objector devout in his belief that Hitler’s race-purifying fight for supremacy is not only wrong but immoral. It’s a view he shares with Fani, who instills in him the will to stand for what’s right, even though it reduces them and their three young daughters to pariahs in their tiny village. But it’s equally unnerving to witness such rampant selfishness on the part of Franz, who rejects numerous opportunities to save himself by accepting a non-combat position in a military hospital as an orderly.
Yes, he will still need to swear an oath to Hitler, but as his advisers tell him, an oath is just words; not a sacrifice of the heart and soul. It goes against his Catholic beliefs, he tells them without nary a thought about how his needless death will leave Fani without a husband and their children without a father – forever. Fatherless himself, Franz’s mother (Karin Neuhäuser) beseeches him to remember what it was like to grow up the son of a casualty of World War I.
Still, nothing will change his mind, and Diehl’s perpetual stoic expressions signal his unbending demeanor to the point of inspiration. But you crave more than the cursory examination of Franz that Malick allows, stirring only the minimum of empathy for a good man unjustly jailed for refusing to partake in an unjust war. The larger reaction is one of frustration with an esoteric writer-director insisting on keeping us at a distance, intent on the larger goal of trying to convince us what most already believe: That war is a crime against nature, especially when the chief goal of said conflict is to alter it forever by rendering an entire race extinct.
Message received but did Malick really require three hours to reveal such a simple observation? Director of photography Jorg Widmer makes it worth the while – to a point. An hour or so in, after being exposed to the steady juxtaposition of Franz’ pristine life at home and the ugliness of being subjected to torture and attempted brainwashing behind bars, you grow weary if not bored. It verges on cinematic malpractice.
Sure, Malick doesn’t want to cheapen Franz’s story by sentimentalizing it as most Hollywood productions would surely do. But in going to the opposite extreme, he risks reactions of indifference, which is tragic, particularly at a time when the modern world could use a couple of million men and women like Franz to vigorously oppose the madness of Hitleresque nationalistic politics. That’s an even sadder outcome than what befalls Franz, because, like him, there’s the very real chance we could all lose our heads.
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~~Secrets of our Industry~~
By GTAknowledge, December 2, 2011 in General Chat
GTAknowledge 2
Got the idea from this thread: http://forum.bodybuilding.com/showthread.p...36662521&page=1
Auto Industry, I worked in the collision and routine car services department.
-the company that I worked for was based off of honesty and loyalty, so we never lied about cars having problems. If it didn't, we would tell you and tell you to leave. However, beware of the repair shops that like to lie and take your money. And there are ALOT. A smart thing to do is to take your car to various different shops for free estimates and see what they say
-you do not need to have an oil change every 3000 miles. Try 6000, and for newer cars, even 8000
-learn how to change your own oil. Do it the first time, and you will know how to do it the rest of your life, saving alot of cash. It is retardedly easy.
-my pr for quickest oil change is 8 min on a 99 honda accord, including checking tire pressure. that means I make about 10 bucks in 8 minutes
-most mechanical repairs will require a test drive before being handed back to the customer. I won't take your car out for drag races, but I like to see which of my test cars go from 0 to 40 the quickest.
-i can smell the weed
-hispanics take pride in their car, thus why you see so many of them are riced out. they don't care you are hating on their stickers
-not surprising, but women are generally stupid when it comes to cars
-if your ac is not cold, it costs less than 20 bucks to fix, 80% of the time. People usually don't want to check for an estimate because they think it will cost alot
-if you drive an american car, we will hate you. They are much harder to work on than hondas or toyotas, yet it costs an equal amount to fix.
-Most nurses are incredibly lacking in common sense and are VERY lazy. Many I know don't even quite know who their patients are for the shift until WELL after shift change.
-Operating rooms aren't as clean as you'd think they should be
-Too many regulating agency's affect how well or how not so well a hospital can operate.
-Hospitals that claim non-profit are still doing things for the money. Sure it doesn't go toward typical FOR profit type things, but believe me, they still count every bean and try and push as many patients out as fast as possible to make room for the new
-Dr's order WAY too many diagnostic exams to be done unecessarily. Most of them are doing it to cover their own asses due to the highly litigious society we live in. CT scans do cause cancer. The rate is low, but they still do CAUSE cancer. And MD's order them like they are going out of style. Kid falls and hits his head, you bring to ER even though kid seems fine, BAM CT scan of head.
-Often diagnostic imaging exams are done simply to appease insurance companies. Go to MD about shoulder pain and expect an MRI? Nope, you'll get unecessary x-rays done first to PROVE that you need the MRI even though your symptoms are clearly needing an MRI scan.
-All surgeons are NOT created equal. In fact, some are downright incompetent.
-MD's like their asses kissed at all times the same as officers in the military. And just like those officers, not many of them deserve it.
I'm still a student at the moment, so don't have much to offer. But would be interesting to see the things you've learnt in your jobs/careers.
Viperman 1
Logically Horizontal
Heavy machine working for oil industry (turning, boring, clad welding) tips:
Avoid at all costs. Dirty, mucky environment that completely lacks in health and safety. While your 4ft 11, bald, asshole of a boss cuts about in aston martins, and playing golf.
Sorry, may be a one sided opinion!
GreatGig 532
Stinkfist.
One thing I hate about where I work, and most supermarkets, is the totally unnecessary waste of food. At the end of every shift we waste on average about £67 worth of food that is totally fine. It's all because of the use-by dates so I can understand why but still, a lot of what we throw is perfectly edible for at least a couple more days. There are quite a few things that can be done with this to help people out and it just infuriates me that nothing is done.
GTA_stu 8,365
victim of credit card fraud
Well being a geography student I wouldn't say I work in an industry. But here's something that's kinda in a small way related:
Why would you say the equator is the warmest part of the earth? Becuase it's the closest to the sun right?
It's because of the shape of the earth being a sphere (roughly speaking). When the sun's rays hit the equator they hit it at a roughly 90* angle. The higher latitudes receive the same amount of radiation but it is spread over a larger surface area due to the curvature of the earth. The suns rays also have to penetrate more atmosphere in the higher latitudes.
Edited December 2, 2011 by GTA_stu
GTA 360 27
LIVE WITH IT OR DIE FROM IT.
We have a 56 VW Jetta and the oil in that is one that will do 20000, but it's a pain in the arse to change as they've started to hide the oil filters and make the cars so you can't get to drain it either.
Also, have a look in the manual for your car, if it says not to put additives in the fuel or oil DON'T DO IT! We sent in our M reg Audi to a garage, it came out, worked well until you set off then it would shake the car around, same thing happened to the bosses 4 year old BMW, both cars were saying it was -40 degrees C outside. So don't use fuel or oil additives.
From my industry, Agriculture: If you have the knowledge and you don't mind getting dirty then fine, do it, it's fun, but if you're a dumb pussy that won't touch sh!t then you're not welcome.
Edited December 2, 2011 by GTA 360
Always useful to know this stuff.
Rhoda 6,200
Warm Drink
Most of these seem like generalizations more than anything else. Calling most nurses lazy is like saying "oh, all Americans are fat".
Robinski 11
Under a fluorescent sky
I'm only a second year media student, so I've got no extended firsthand experience of it, but the media at large can't be 100% trusted, but not for the reasons you think. Pretty much everybody signs up to the idea that "Oh well, you can't believe everything you read in the papers". But if you then ask them why, then you'll usually get some line about advertisers or owners pusing their own agendas and censoring their publications to make themselves/their politics/useful associates/etc. look good. In truth, that only really accounts for a very small amount of "bad" reporting, usually in places like the Murdoch press.
The real answer is simulatneously close to that, but also completely different. It is commercialism and business that is making the press more incompetent, but it's not about propoganda and PR but something much colder and scarier: money. The ownership of the press in the last 100 years has gone from inidivudal owners or small groups to massive multinational conglomerates who don't have an agenda other than "make money, f*ck everything else". What's the easiest way to increase profit? Cut jobs. Less journalists are gathering, writing, editing and fact-checking news pieces. Second easiest way to increase profit? Put out more product, to carry more advertising. Publications start carrying a lot more content, but from fewer staff. So now you've got less people doing more work, meaning they literally can't do a good job on stuff like fact checking. You end up with ridiculous amounts of churned out work. Press releases are the biggest offender, they just get re-written and put out as news. As everyone knows, the PR office that puts out the press release will even flat out lie to you rather than say anything negative about their client.
So yeah, you can't trust the media a lot of the time, not because the journalist is trying to brainwash you but because they've got 8 more stories to write before lunch.
If anyone's interested in this sort of stuff and wants to see the news media in a new light, grab a copy of Nick Davies' Flat Earth News. Or watch this.
Edited December 4, 2011 by Robinski
Waddy 45,645,647
Gods foster son.
Politicians sometimes tell lies.
OysterBarron 1,796
You need a Pearl necklace? Hit me up ;)
The trouble with papers today is the journalists dont do buggar all like they used to! in the old days journalost spent months in the field cross checking facts about storys they have uncovered before it goes to print! Nowdays the journalists just wait for the press release from the partys involved! this in turn is how some storys dont quite add up due to the fact they just take the press releases that the companys and people that were involved in the story wrote down themselves and prints them in full in the papers so alot of the stuff you hear is made up by the companys or people involved. a serious lack in journalists abiltys these days if not that then its just pure lazyiness!
you now know why the goverments are so fond of press releases because they pretty much get to spoonfeed you anything they want. The amount of times ive heard an MP say that there will be a full press release soon!
Edited December 4, 2011 by oysterbarron
Tryst 0
Professionally Retarded
Liar.
As a tech guy I can tell you, we don't know how to do everything in the world of the top of our heads. We use google more than you'd think.
mikkenugent 4
Wolf God
All musicians steal their work from past works. From Kanye to Metallica, every musician "steals" but only the greats make such thievery sound original. Looks don't matter in music, drug dealers do. Sad to say it but if you are a female singer most people won't work with you so learn to be a multi-instrumentalist as well. 90% of musicians are weak minded and easily fooled into horrible situations that destroy them mentally and financially. Read up on BMI and ASCAP they will save yur ass. The music industry died years ago but not by the internet as most feel, it was the musicians on local levels (Napster didn't kill music, musicians killed music). Most low to mid end guitars regardless of brand are made in the same factories in Asia then shipped to their respected warehouses. Recording studios are a huge scam, learn a trade and learn to craft yurself, there's great knowledge to be learned on the matter on the web from vids, forums and articles. Most commercial studios run yur work through their generic run of the mill techniques that they use for every project.
Edited December 7, 2011 by mikkenugent
trip 13,556
I can confirm that one.
When I took my job I was told top priority is to stay out of the news papers. I'm sure I'd get into some trouble if I came in here and started spouting off some of our secrets.
Bump.
Please don't do that. If people work in an industry that has secrets and they're confident they won't get caught, I'm sure they'll come here.
3niX 2
Lazy idiot
It all depends on where you end up working...
Ive been in some awful and also in some pretty great companies (mostly to do with electronics and metalworking).
What I have noticed:
*A good number of clients seem to have no clue how parts are produced and hence give you unrealistic or pointlessly tight tolerances, send you unworkable drawings or just generally make your work as difficult as possible.
*Supervisors dont really care how you get your job done, as long as you get it done on time.
*In a company that isnt as smoothly managed as it should be, every single employee (including the CEO) usually complains about other employees. This leads to low morale and lower standards. Stay away from such places!
*Metalworking can be very dirty and very dangerous regardless of the caution you take (I have several scars to prove it).
*Machines break down at the worst possible time.
*There are maintenace guys out there, who have absolutely no clue what they are doing.
*99% of line workers in electronics are women.
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Home Classic Cars Jean Todt’s Lamborghini Miura SV Freshly Restored by Polo Storico
Jean Todt’s Lamborghini Miura SV Freshly Restored by Polo Storico
Jean Todt is a name synonymous with Scuderia Ferrari. He spent 15 years working with the Italian racing team, winning 14 driver and manufacturer world championship’s. More recently he has sat at the top level of motorsport as the president of the FIA. It turns out that Todt has no bias when it comes to road cars though. He recently had his Lamborghini Miura SV restored by Lamborghini’s classic department, Polo Storico!
The restored supercar was on display at the Paris Rétromobile this weekend. The handover ceremony took place last week with the keys handed over by Lamborghini Chairman and Chief Executive Officer, Stefano Domenicali. Domenicali is another name synonymous with the pricing horse.
Lamborghini Miura SV
Todt’s Miura SV is chassis number #3673, which left the Lamborghini factory on 11 November 1972. Interestingly, this particular SV was built upon an existing chassis, that of a 1968 Miura S that had been destroyed in an accident. Lamborghini explained that this was common practice to avoid paying high import taxes on new vehicles in certain countries.
This particular Lamborghini Miura SV was number 751 of 762. It was one of 10 late production models with a split sump and factory installed air conditioning.
Todt’s Miura SV was delivered to its first owner, Mr. Mecin, in South Africa, painted Rosso Corsa (red), with a lower gold band and black leather interior. It came up for auction in 2016 via RM Sotheby’s with a price estimate of $1,900,000 – $2,200,000. It failed to sell at that auction. Todt must have negotiated a private deal to purchase the car.
The Polo Storico restoration restores the car to this specification. It took 13 months to complete, during which time the car was completely dismantled to verify each and every detail. The details were then checked against Lamborghini’s archives and parts were sympathetically replaced where necessary.
Polo Storico is also presenting a 1966 Lamborghini 400 GT at Rétromobile. Chassis #0592, it has also undergone a total restoration at Polo Storico, commissioned by a Canadian collector.
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Lamborghini Sian: Most Powerful Lamborghini Ever Revealed
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Which one is ancient Hinduisam or Dravidiasm [closed]
Closed. This question needs details or clarity. It is not currently accepting answers.
Want to improve this question? Add details and clarify the problem by editing this post.
As per the history Hinduisam is Oldest and ancient on the earth...
As per my research... Hinduthvam is from Aryan Race and their Language was Sanskrit and Pakrit... Dravidians are different Race.. As Per the Records Dravidian language ancient where we can have evidence upto 400BCE ..
And most of the Hinduthva books have wrote in Sanskrit.
My question is Dravidians influenced by aryans ? if So . Dravidains should follow one religion or may be they should worship some .. ?
And Dravidian Race is How ancient is Dravidian race.. Which one is ancient ? If Dravidian Race ancient which religion they followed ?
ancient-history india religion
Rookie007
Rookie007Rookie007
Have you done any preliminary research? – Mark C. Wallace♦ Apr 21 '14 at 8:40
This question is terribly ill-informed. It must be closed in its current state. – Noldorin Apr 23 '14 at 1:59
The premise of the question is incorrect. Hinduism is most certainly and very much prevalent in South India, along with Islam, Christianity, and many other religions. There is no such thing as Dravidianism. If there was such a thing in ancient times, it is a highly debated and contentious issue. Genetics and many other modern tools seem to suggest that these are constructs - just like race. So if the question is with reference to religion- there is no religion called Dravidianism. If it is a racial question- I propose that it is an incorrect premise to construct racial identities.
EDIT: (Addition)
Many of the greatest "revivalists" and thinkers of Hinduism (although the term Hinduism is very broad- i use it here in the conventional sense) have come from South India (South India- again in conventional sense). Three of the most well known scholars/thinkers were Shankaracharya, Ramanuja and Madhavacharya.
Epics such as the Ramayana have been re-interpreted and re-told in South Indian Languages such as Kamban's version of Ramayana. Also, Shaivism and other forms of Hinduism has had rich literary inputs from all languages. To see Tamil literature check this. The other (primary) languages in south India are Kannada, Malayalam, and Telugu. A search will throw up many results, but it is too vast to cover in an SE answer.
RajibRajib
The only thing i know of that has Dravid- as a word stem are Dravidian languages. Usually where there is a language, there is a cultural identity tied to it. Sometimes where there is a cultural identity, there is a people, and where there is a people there might be common genetic traits, or some similar migrational background to arbitrarily group these people together for the purpose of discussion. But this is just conjecture...As i'm not well informed about this, i might just be ignorant of any other stuff "dravidian" might refer to. – Matthaeus Jul 20 '14 at 21:18
As mentioned in Rajib's, the question is not entirely correct. In addition, there are theories that say that the Aryan-Dravidian distinction is not true, and that all are of the same race. But, to answer the question, some of the best songs of Indian classical music were composed in the South Indian language Telugu (by native speakers of course), and all the songs are hymns to some god. The revivals of Hinduism, in the face of opposition from Buddhism and Jainism, was carried by mainly south Indians (Adi Shankaracharya). They also established many "peethams" - so its not like South India didn't influence Hinduism, either. There are translations of Ramayanam, Mahabharatm and Bhagvat Gita in Telugu. Then, again there are the large number of temples in Tamil Nadu. And most importantly, almost since the rule of ChandraGutpa Maurya, the vast bulk of India was under one control. So, to say that "South Indians are not Hindu" is not correct.
tpb261tpb261
It might be worth mentioning that “Hinduism” is an invention of British writers of the 19th century. Before the colonial period people in India defined themselves by caste (Brahmans etc.) or as devotees of a particular god (Shaiva, Vaishnava etc.). There was no concept of “Hindus” as a group in contrast to Buddhists, Jain, Muslims etc.
fdbfdb
I agree to the point that Hinduism is a term coined by British writers. But, I would contradict in terms of your point in about the concept of Hindus. Well before British, the peoples of India followed a way of living known as "Sanathana Dharma". Under this big umbrella there where various sects of peoples with various beliefs and follow different God's. So, I would like to reiterate that Hindu are prevailing for a long time but with a different name. – Karthick Apr 23 '14 at 3:04
@Karthick Can you point to some reference that says "Sanathana Dharma", and that it includes Shaivas, Vaishnavs, and the innumerable other sects? – Rajib Jul 21 '14 at 13:53
@Rajib: Sanathana Dharma is a way of living. Stephan Knapps has written a beautiful artical in his website. Hope this would help you understand the Sanathana dharma and also, the fact that Dharam always refer to God Almighty as universal power and not as Shivites, vaishnavites, ets.. Its we who factorin the dharma into our own practices and name it as Shivites or vaishavites. But, the dharma is universal. Furhter Reading: stephen-knapp.com/sanatana_dharma.htm – Karthick Jul 23 '14 at 1:58
@Karthick A way of living can be defined by anyone. This is not historical fact and has no place in a history discussion unless you can show literature or reference from history that clearly states that such a notion / belief existed. A Post independence attempt to create a pan-Indian credo is politics, not history. – Rajib Jul 23 '14 at 7:36
@Rajib: sanskritweb.net/rigveda/griffith.pdf whis is based on sanathan dharma is ofcouse history. Any written evidence about the past is considered as artifact of history. Tholkappiyam which was dated as 500 BC which says about lord Shiva is history... வட வேங்கடம் தென் குமரி ஆயிடைத் தமிழ் கூறும் நல் உலகத்து வழக்கும் செய்யுளும் ஆயிரு முதலின் எழுத்தும் சொல்லும் பொருளும் நாடிச் 5 செந்தமிழ் இயற்கை சிவணிய நிலத்தொடு முந்து நூல் கண்டு முறைப்பட எண்ணிப் புலம் தொகுத்தோனே போக்கு அறு பனுவல் நிலம் தரு திருவின் பாண்டியன் அவையத்து அறம் கரை நாவின் நான்மறை முற்றிய – Karthick Jul 24 '14 at 2:52
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From Bad to Worse: Immigrant Smearing in a Time of Midterm Cholera
Posted by Seth Hoy | Oct 12, 2010 | Elections, Reform
Well it’s finally here—open season on immigrants. You don’t even have to stare into the headlights of campaign politics to observe how blithely some candidates have taken aim at their opponents and managed to catch immigrants in their crosshairs. Two recent campaign ads portray undocumented immigrants as darkly-clothed thieves—like in one of those overly-dramatized alarm system commercials where just when you turn your back, Hispanic immigrants apparently come sneaking across the border, receive over-sized checks, and steal your children’s college tuition. Right.
Aside from the blatant racial stereotyping, the authors of these ads don’t even get their twisted “facts” straight. But even more troubling is the ubiquity of immigrant-bashing in the run up to midterms. Ever since Arizona’s SB 1070—and some would correctly argue well before—demonizing immigrants has evolved into the latest political strategy in campaign warfare. At least we’d expect this from restrictionsist groups, who by the way, are still hard at work scapegoating immigrants with their usual broken logic, loose facts and ludicrous conclusions. But now it’s going mainstream.
Let’s start with senatorial candidate, Sharron Angle (R-NV), who approved this message:
And this ad was approved by Sen. David Vitter (R-LA), who’s running for re-election:
So in the first video we have tax breaks, Social Security benefits and preferred college tuition rates for undocumented immigrants—and footage of Latino immigrants sneaking across the border. The second video features, footage of immigrants sneaking across the border (with flashlights, mind you), welcoming marching bands, and this is my favorite, undocumented immigrants receiving a Publishers Clearing House-sized check, riding away in a limo, as the band plays and fireworks burst overhead. There may also have been a high five, but you’ll have to check.
Clearly, as America’s Voice references in a blog post, fact-checkers and journalists have dissected these spurious claims and found them to be terribly misleading, if not untrue. But what did we expect? Facts often end up on the cutting room floor, especially when political gains are possible by ignoring them. It is, as Adam Sewer of the American Prospect points out, “a transparent attempt to gain political support by demonizing Latinos.” Which gets us where exactly? Sure, some candidates will likely ride the anti-immigrant wave into office, but what happens when we DO eventually decide to tackle immigration once and for all? It’s not like our broken immigration system is going anywhere and it’s clearly not feasible to deport nearly 11 million undocumented immigrants? Are we really going to begin a serious policy debate with race-baiting and immigrant-bashing?
Practical policy solutions to our immigration problems won’t be found by exploiting and distorting an emotional issue. All politicians need to move out of a framework of “who’s the toughest on immigration” and into “what are the problems and how do we fix them,” or our immigration problems, much like television campaign ads, will only get worse.
Photo by Arenamontanus.
FILED UNDER: Restrictionists, Rhetoric, undocumented immigration, Video
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Entertainment Views
News, Reviews & Interviews
Break A Leg Awards 2017 Winners
Entertainment Views Awards 2018/2019
Tag: Pointless Celebrities
Weekend Watch List ~ 24th & 25th March 2018
Telly at the weekend is a must for all of us at Entertainment Views HQ, we all enjoy a relax in front of the box and last weekend there was plenty to keep us all entertained. Here’s a few of the top picks from our chilled out couple of days as couch potatoes:
Milkshake!
This is usually the start of our weekend, Saturday morning kids television and I love it as much as my little boy does! Milkshake! is a great ‘magazine’ style show which includes an episode of a number of different children’s television favourites. Thomas the Tank Engine, Peppa Pig, Noddy, Shimmer and Shine, they’re all there keeping the smallest member of the family amused. The presenters are all bubbly, energetic whirlwinds, Amy Thompson is the favourite in our house, though.
Pointless Celebrities
Grange Hill week on Pointless Celebrities! I think this should be a monthly thing, it was fantastic to see all the old favourites, including Mr Robson who hasn’t changed one iota. An amazing episode and worthy winners, too.
I have thoroughly enjoyed this series and I have no idea who will win, there’s no front runner in my humble opinion. Some of the judges’ picks for the final have been a surprise, there are three artists in the final line up who may appear too similar to one another and therefore would they stand the best chance? If I were to back a team at this point? Team J Hud!
Robyn (Amanda Henderson) and Glen (Owain Arthur) got married and then tragedy struck! Argh!! I suppose it was always going to head in that direction when the episode kicked off with Glen having a scan due to his worsening condition. At least the pair made it up the aisle without a hitch… almost. It was certainly a lovely moment with Duffy (Cathy Shipton) and Charlie (Derek Thompson) part of the big day. I know there’s been plenty of excitable fan comments about the ‘selfie’ that Duffy insisted on, too!
I’m late to the party with this one, The Durrells has long been a favourite of my husband’s however I’ve really got on board this series. I like the comedy elements and the absurdity. The location is pretty extraordinary too. I now need to binge watch the episodes I’ve missed. See you on the other side! I have a connection to the show because I have visited Jersey Zoo many times as a child so I’m delighted to have ‘discovered’ this.
Weekend Watch List – 10th & 11th March
My weekend television watch list is ever growing and the amount of programmes backed up on the planner is ridiculous (I’m fighting for space on the Sky box! First world problems!!). So here’s my must-see shows from last weekend which made it past the catch-up stage:
Pointless…Picture shows: Alexander Armstrong
I love Pointless because I’m a quiz-a-holic – and Pointless Celebrities always ticks the box for me, not least because some of the contestants they pull out the bag have often been missing form our screens for a while. Although one of the finalists last week included recent Strictly Come Dancing revelation, the lovely Debbie McGee. I’ve not yet found myself a pointless answer, but the time will come!
The final week of battles and it was a tense week. The fact there were no steals left throughout most of the episode was quite a feat to face for the contestants. I agreed with each of the judges’ choices though and thought Will.i.am had a fantastic steal. I can’t wait for the knock outs now, I have no idea who might win it. J Hud does seem to have one of the best teams though.
The mystery blogger has been at the hub of recent goings on in Holby and Jac (Rosie Marcel) was soon on the warpath on behalf of Serena (Catherine Russell), kicking Ethan (George Rainsford) up the backside to try and get a result. Alicia (Chelsea Halfpenny) is rather like a rabbit in the headlights when Ethan asks her outright, although she denies it. However, it’s not long before she’s confessing and Ethan is unimpressed. I foresee more trouble ahead!
Torvill and Dean back on the ice together? Glorious! Max Evans not making it to the final? disappointing (he had all my votes). Brooke Vincent in the final? A remarkable journey for that girl and she deserved to be there. Jake Quickenden winning? Amazing! The right choice and he really has had an incredible journey. I’ve loved Dancing on Ice!
I’ve enjoyed this, more so for the supporting characters though – and of course the mighty Alison Steadman. Although I feel the central storyline is flimsy and whimsical, it’s Queenie (Anne Reid) and Roger (Jason Watkins) that are holding my attention. It’s an easy-viewing comedy though and definitely belongs on a Sunday evening.
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Reinhard Diestel Graph Theory Electronic Edition 2000 c Springer-Verlag New York 1997, 2000 ° This is an electronic ve...
Author: Reinhard Diestel
10 downloads 251 Views 2MB Size Report
Reinhard Diestel
Graph Theory Electronic Edition 2000 c Springer-Verlag New York 1997, 2000 °
This is an electronic version of the second (2000) edition of the above Springer book, from their series Graduate Texts in Mathematics, vol. 173. The cross-references in the text and in the margins are active links: click on them to be taken to the appropriate page. The printed edition of this book can be ordered from your bookseller, or electronically from Springer through the Web sites referred to below. Softcover $34.95, ISBN 0-387-98976-5 Hardcover $69.95, ISBN 0-387-95014-1 Further information (reviews, errata, free copies for lecturers etc.) and electronic order forms can be found on http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/ http://www.springer-ny.com/supplements/diestel/
Almost two decades have passed since the appearance of those graph theory texts that still set the agenda for most introductory courses taught today. The canon created by those books has helped to identify some main fields of study and research, and will doubtless continue to influence the development of the discipline for some time to come. Yet much has happened in those 20 years, in graph theory no less than elsewhere: deep new theorems have been found, seemingly disparate methods and results have become interrelated, entire new branches have arisen. To name just a few such developments, one may think of how the new notion of list colouring has bridged the gulf between invariants such as average degree and chromatic number, how probabilistic methods and the regularity lemma have pervaded extremal graph theory and Ramsey theory, or how the entirely new field of graph minors and tree-decompositions has brought standard methods of surface topology to bear on long-standing algorithmic graph problems. Clearly, then, the time has come for a reappraisal: what are, today, the essential areas, methods and results that should form the centre of an introductory graph theory course aiming to equip its audience for the most likely developments ahead? I have tried in this book to offer material for such a course. In view of the increasing complexity and maturity of the subject, I have broken with the tradition of attempting to cover both theory and applications: this book offers an introduction to the theory of graphs as part of (pure) mathematics; it contains neither explicit algorithms nor ‘real world’ applications. My hope is that the potential for depth gained by this restriction in scope will serve students of computer science as much as their peers in mathematics: assuming that they prefer algorithms but will benefit from an encounter with pure mathematics of some kind, it seems an ideal opportunity to look for this close to where their heart lies! In the selection and presentation of material, I have tried to accommodate two conflicting goals. On the one hand, I believe that an
introductory text should be lean and concentrate on the essential, so as to offer guidance to those new to the field. As a graduate text, moreover, it should get to the heart of the matter quickly: after all, the idea is to convey at least an impression of the depth and methods of the subject. On the other hand, it has been my particular concern to write with sufficient detail to make the text enjoyable and easy to read: guiding questions and ideas will be discussed explicitly, and all proofs presented will be rigorous and complete. A typical chapter, therefore, begins with a brief discussion of what are the guiding questions in the area it covers, continues with a succinct account of its classic results (often with simplified proofs), and then presents one or two deeper theorems that bring out the full flavour of that area. The proofs of these latter results are typically preceded by (or interspersed with) an informal account of their main ideas, but are then presented formally at the same level of detail as their simpler counterparts. I soon noticed that, as a consequence, some of those proofs came out rather longer in print than seemed fair to their often beautifully simple conception. I would hope, however, that even for the professional reader the relatively detailed account of those proofs will at least help to minimize reading time. . . If desired, this text can be used for a lecture course with little or no further preparation. The simplest way to do this would be to follow the order of presentation, chapter by chapter: apart from two clearly marked exceptions, any results used in the proof of others precede them in the text. Alternatively, a lecturer may wish to divide the material into an easy basic course for one semester, and a more challenging follow-up course for another. To help with the preparation of courses deviating from the order of presentation, I have listed in the margin next to each proof the reference numbers of those results that are used in that proof. These references are given in round brackets: for example, a reference (4.1.2) in the margin next to the proof of Theorem 4.3.2 indicates that Lemma 4.1.2 will be used in this proof. Correspondingly, in the margin next to Lemma 4.1.2 there is a reference [ 4.3.2 ] (in square brackets) informing the reader that this lemma will be used in the proof of Theorem 4.3.2. Note that this system applies between different sections only (of the same or of different chapters): the sections themselves are written as units and best read in their order of presentation. The mathematical prerequisites for this book, as for most graph theory texts, are minimal: a first grounding in linear algebra is assumed for Chapter 1.9 and once in Chapter 5.5, some basic topological concepts about the Euclidean plane and 3-space are used in Chapter 4, and a previous first encounter with elementary probability will help with Chapter 11. (Even here, all that is assumed formally is the knowledge of basic definitions: the few probabilistic tools used are developed in the
text.) There are two areas of graph theory which I find both fascinating and important, especially from the perspective of pure mathematics adopted here, but which are not covered in this book: these are algebraic graph theory and infinite graphs. At the end of each chapter, there is a section with exercises and another with bibliographical and historical notes. Many of the exercises were chosen to complement the main narrative of the text: they illustrate new concepts, show how a new invariant relates to earlier ones, or indicate ways in which a result stated in the text is best possible. Particularly easy exercises are identified by the superscript − , the more challenging ones carry a + . The notes are intended to guide the reader on to further reading, in particular to any monographs or survey articles on the theme of that chapter. They also offer some historical and other remarks on the material presented in the text. Ends of proofs are marked by the symbol ¤. Where this symbol is found directly below a formal assertion, it means that the proof should be clear after what has been said—a claim waiting to be verified! There are also some deeper theorems which are stated, without proof, as background information: these can be identified by the absence of both proof and ¤. Almost every book contains errors, and this one will hardly be an exception. I shall try to post on the Web any corrections that become necessary. The relevant site may change in time, but will always be accessible via the following two addresses: http://www.springer-ny.com/supplements/diestel/ http://www.springer.de/catalog/html-files/deutsch/math/3540609180.html
Please let me know about any errors you find. Little in a textbook is truly original: even the style of writing and of presentation will invariably be influenced by examples. The book that no doubt influenced me most is the classic GTM graph theory text by Bollob´ as: it was in the course recorded by this text that I learnt my first graph theory as a student. Anyone who knows this book well will feel its influence here, despite all differences in contents and presentation. I should like to thank all who gave so generously of their time, knowledge and advice in connection with this book. I have benefited particularly from the help of N. Alon, G. Brightwell, R. Gillett, R. Halin, M. Hintz, A. Huck, I. Leader, T. L Ã uczak, W. Mader, V. R¨odl, A.D. Scott, ˇ P.D. Seymour, G. Simonyi, M. Skoviera, R. Thomas, C. Thomassen and P. Valtr. I am particularly grateful also to Tommy R. Jensen, who taught me much about colouring and all I know about k-flows, and who invested immense amounts of diligence and energy in his proofreading of the preliminary German version of this book. March 1997
About the second edition Naturally, I am delighted at having to write this addendum so soon after this book came out in the summer of 1997. It is particularly gratifying to hear that people are gradually adopting it not only for their personal use but more and more also as a course text; this, after all, was my aim when I wrote it, and my excuse for agonizing more over presentation than I might otherwise have done. There are two major changes. The last chapter on graph minors now gives a complete proof of one of the major results of the RobertsonSeymour theory, their theorem that excluding a graph as a minor bounds the tree-width if and only if that graph is planar. This short proof did not exist when I wrote the first edition, which is why I then included a short proof of the next best thing, the analogous result for path-width. That theorem has now been dropped from Chapter 12. Another addition in this chapter is that the tree-width duality theorem, Theorem 12.3.9, now comes with a (short) proof too. The second major change is the addition of a complete set of hints for the exercises. These are largely Tommy Jensen’s work, and I am grateful for the time he donated to this project. The aim of these hints is to help those who use the book to study graph theory on their own, but not to spoil the fun. The exercises, including hints, continue to be intended for classroom use. Apart from these two changes, there are a few additions. The most noticable of these are the formal introduction of depth-first search trees in Section 1.5 (which has led to some simplifications in later proofs) and an ingenious new proof of Menger’s theorem due to B¨ohme, G¨oring and Harant (which has not otherwise been published). Finally, there is a host of small simplifications and clarifications of arguments that I noticed as I taught from the book, or which were pointed out to me by others. To all these I offer my special thanks. The Web site for the book has followed me to http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/
I expect this address to be stable for some time. Once more, my thanks go to all who contributed to this second edition by commenting on the first—and I look forward to further comments! December 1999
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1. The Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1. Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2. The degree of a vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3. Paths and cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4. Connectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5. Trees and forests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6. Bipartite graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.7. Contraction and minors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.8. Euler tours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.9. Some linear algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.10. Other notions of graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.1. Matching in bipartite graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2. Matching in general graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3. Path covers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3. Connectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.1. 3.2. 3.3. 3.4. 3.5. 3.6.
2-Connected graphs and subgraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The structure of 3-connected graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . Menger’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mader’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Edge-disjoint spanning trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Paths between given pairs of vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4. Planar Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.1. 4.2. 4.3. 4.4. 4.5. 4.6.
Topological prerequisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plane graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Planar graphs: Kuratowski’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . Algebraic planarity criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plane duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5. Colouring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.1. 5.2. 5.3. 5.4. 5.5.
Colouring maps and planar graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Colouring vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Colouring edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List colouring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Perfect graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96 98 103 105 110 117 120
6. Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.1. 6.2. 6.3. 6.4. 6.5. 6.6.
Circulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flows in networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Group-valued flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . k-Flows for small k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow-colouring duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tutte’s flow conjectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7. Substructures in Dense Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 7.1. Subgraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 7.2. Szemer´edi’s regularity lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 7.3. Applying the regularity lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
8. Substructures in Sparse Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 8.1. Topological minors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 8.2. Minors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 8.3. Hadwiger’s conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
9. Ramsey Theory for Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 9.1. Ramsey’s original theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 9.2. Ramsey numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 9.3. Induced Ramsey theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 9.4. Ramsey properties and connectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
10. Hamilton Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 10.1. Simple sufficient conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 10.2. Hamilton cycles and degree sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 10.3. Hamilton cycles in the square of a graph . . . . . . . . . . . . . . . . . . . . . . . . 218 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
11. Random Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 11.1. The notion of a random graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 11.2. The probabilistic method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 11.3. Properties of almost all graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 11.4. Threshold functions and second moments . . . . . . . . . . . . . . . . . . . . . . . 242 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
12. Minors, Trees, and WQO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 12.1. Well-quasi-ordering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 12.2. The graph minor theorem for trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 12.3. Tree-decompositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 12.4. Tree-width and forbidden minors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 12.5. The graph minor theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
Hints for all the exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Symbol index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
This chapter gives a gentle yet concise introduction to most of the terminology used later in the book. Fortunately, much of standard graph theoretic terminology is so intuitive that it is easy to remember; the few terms better understood in their proper setting will be introduced later, when their time has come. Section 1.1 offers a brief but self-contained summary of the most basic definitions in graph theory, those centred round the notion of a graph. Most readers will have met these definitions before, or will have them explained to them as they begin to read this book. For this reason, Section 1.1 does not dwell on these definitions more than clarity requires: its main purpose is to collect the most basic terms in one place, for easy reference later. From Section 1.2 onwards, all new definitions will be brought to life almost immediately by a number of simple yet fundamental propositions. Often, these will relate the newly defined terms to one another: the question of how the value of one invariant influences that of another underlies much of graph theory, and it will be good to become familiar with this line of thinking early. By N we denote the set of natural numbers, including zero. The set Z/nZ of integers modulo n is denoted by Zn ; its elements are written as i := i + nZ. For a real number x we denote by bxc the greatest integer 6 x, and by dxe the least integer > x. Logarithms written as ‘log’ are taken at base 2; the natural logarithm will be denoted by ‘ln’. A set A =S { A1 , . . . , Ak } of disjoint subsets of a set A is a partition of A if k A = i=1 Ai and Ai 6= ∅ for every i. Another partition { A01 , . . . , A0` } of A refines the partition A if each A0i is contained in some Aj . By [A]k we denote the set of all k-element subsets of A. Sets with k elements will be called k-sets; subsets with k elements are k-subsets.
Zn bxc, dxe log, ln partition [A]k k-set
1. The Basics
1.1 Graphs graph
vertex edge
A graph is a pair G = (V, E) of sets satisfying E ⊆ [V ]2 ; thus, the elements of E are 2-element subsets of V . To avoid notational ambiguities, we shall always assume tacitly that V ∩ E = ∅. The elements of V are the vertices (or nodes, or points) of the graph G, the elements of E are its edges (or lines). The usual way to picture a graph is by drawing a dot for each vertex and joining two of these dots by a line if the corresponding two vertices form an edge. Just how these dots and lines are drawn is considered irrelevant: all that matters is the information which pairs of vertices form an edge and which do not. 3
Fig. 1.1.1. The graph on V = { 1, . . . , 7 } with edge set E = {{ 1, 2 }, { 1, 5 }, { 2, 5 }, { 3, 4 }, { 5, 7 }} on V (G), E(G)
order |G|, kGk
∅ trivial graph
incident ends
E(X, Y ) E(v)
A graph with vertex set V is said to be a graph on V . The vertex set of a graph G is referred to as V (G), its edge set as E(G). These conventions are independent of any actual names of these two sets: the vertex set W of a graph H = (W, F ) is still referred to as V (H), not as W (H). We shall not always distinguish strictly between a graph and its vertex or edge set. For example, we may speak of a vertex v ∈ G (rather than v ∈ V (G)), an edge e ∈ G, and so on. The number of vertices of a graph G is its order , written as |G|; its number of edges is denoted by kGk. Graphs are finite or infinite according to their order; unless otherwise stated, the graphs we consider are all finite. For the empty graph (∅, ∅) we simply write ∅. A graph of order 0 or 1 is called trivial . Sometimes, e.g. to start an induction, trivial graphs can be useful; at other times they form silly counterexamples and become a nuisance. To avoid cluttering the text with non-triviality conditions, we shall mostly treat the trivial graphs, and particularly the empty graph ∅, with generous disregard. A vertex v is incident with an edge e if v ∈ e; then e is an edge at v. The two vertices incident with an edge are its endvertices or ends, and an edge joins its ends. An edge { x, y } is usually written as xy (or yx). If x ∈ X and y ∈ Y , then xy is an X–Y edge. The set of all X–Y edges in a set E is denoted by E(X, Y ); instead of E({ x }, Y ) and E(X, { y }) we simply write E(x, Y ) and E(X, y). The set of all the edges in E at a vertex v is denoted by E(v).
1.1 Graphs
Two vertices x, y of G are adjacent, or neighbours, if xy is an edge of G. Two edges e 6= f are adjacent if they have an end in common. If all the vertices of G are pairwise adjacent, then G is complete. A complete graph on n vertices is a K n ; a K 3 is called a triangle. Pairwise non-adjacent vertices or edges are called independent. More formally, a set of vertices or of edges is independent (or stable) if no two of its elements are adjacent. Let G = (V, E) and G0 = (V 0 , E 0 ) be two graphs. We call G and 0 G isomorphic, and write G ' G0 , if there exists a bijection ϕ: V → V 0 with xy ∈ E ⇔ ϕ(x)ϕ(y) ∈ E 0 for all x, y ∈ V . Such a map ϕ is called an isomorphism; if G = G0 , it is called an automorphism. We do not normally distinguish between isomorphic graphs. Thus, we usually write G = G0 rather than G ' G0 , speak of the complete graph on 17 vertices, and so on. A map taking graphs as arguments is called a graph invariant if it assigns equal values to isomorphic graphs. The number of vertices and the number of edges of a graph are two simple graph invariants; the greatest number of pairwise adjacent vertices is another.
adjacent neighbour complete Kn independent
' isomorphism
G ∪ G0
2 G − G0
G ∩ G0
Fig. 1.1.2. Union, difference and intersection; the vertices 2,3,4 induce (or span) a triangle in G ∪ G0 but not in G
We set G ∪ G0 := (V ∪ V 0 , E ∪ E 0 ) and G ∩ G0 := (V ∩ V 0 , E ∩ E 0 ). If G ∩ G0 = ∅, then G and G0 are disjoint. If V 0 ⊆ V and E 0 ⊆ E, then G0 is a subgraph of G (and G a supergraph of G0 ), written as G0 ⊆ G. Less formally, we say that G contains G0 . If G0 ⊆ G and G0 contains all the edges xy ∈ E with x, y ∈ V 0 , then 0 G is an induced subgraph of G; we say that V 0 induces or spans G0 in G, and write G0 =: G [ V 0 ]. Thus if U ⊆ V is any set of vertices, then G [ U ] denotes the graph on U whose edges are precisely the edges of G with both ends in U . If H is a subgraph of G, not necessarily induced, we abbreviate G [ V (H) ] to G [ H ]. Finally, G0 ⊆ G is a spanning subgraph of G if V 0 spans all of G, i.e. if V 0 = V .
G ∩ G0 subgraph G0 ⊆ G
induced subgraph G[U ]
Fig. 1.1.3. A graph G with subgraphs G0 and G00 : G0 is an induced subgraph of G, but G00 is not −
+ edgemaximal
minimal maximal
G ∗ G0 complement G line graph L(G)
If U is any set of vertices (usually of G), we write G − U for G [ V r U ]. In other words, G − U is obtained from G by deleting all the vertices in U ∩ V and their incident edges. If U = { v } is a singleton, we write G − v rather than G − { v }. Instead of G − V (G0 ) we simply write G − G0 . For a subset F of [V ]2 we write G − F := (V, E r F ) and G + F := (V, E ∪ F ); as above, G − { e } and G + { e } are abbreviated to G − e and G + e. We call G edge-maximal with a given graph property if G itself has the property but no graph G + xy does, for non-adjacent vertices x, y ∈ G. More generally, when we call a graph minimal or maximal with some property but have not specified any particular ordering, we are referring to the subgraph relation. When we speak of minimal or maximal sets of vertices or edges, the reference is simply to set inclusion. If G and G0 are disjoint, we denote by G ∗ G0 the graph obtained from G ∪ G0 by joining all the vertices of G to all the vertices of G0 . For example, K 2 ∗ K 3 = K 5 . The complement G of G is the graph on V with edge set [V ]2 r E. The line graph L(G) of G is the graph on E in which x, y ∈ E are adjacent as vertices if and only if they are adjacent as edges in G.
Fig. 1.1.4. A graph isomorphic to its complement
1.2 The degree of a vertex N (v)
Let G = (V, E) be a (non-empty) graph. The set of neighbours of a vertex v in G is denoted by NG (v), or briefly by N (v).1 More generally 1 Here, as elsewhere, we drop the index referring to the underlying graph if the reference is clear.
1.2 The degree of a vertex
for U ⊆ V , the neighbours in V r U of vertices in U are called neighbours of U ; their set is denoted by N (U ). The degree (or valency) dG (v) = d(v) of a vertex v is the number |E(v)| of edges at v; by our definition of a graph,2 this is equal to the number of neighbours of v. A vertex of degree 0 is isolated . The number δ(G) := min { d(v) | v ∈ V } is the minimum degree of G, the number ∆(G) := max { d(v) | v ∈ V } its maximum degree. If all the vertices of G have the same degree k, then G is k-regular , or simply regular . A 3-regular graph is called cubic. The number 1 X d(v) d(G) := |V | ∈ v V
is the average degree of G. Clearly,
degree d(v) isolated δ(G) ∆(G) regular cubic
d(G) average degree
δ(G) 6 d(G) 6 ∆(G) . The average degree quantifies globally what is measured locally by the vertex degrees: the number of edges of G per vertex. Sometimes it will be convenient to express this ratio directly, as ε(G) := |E|/|V |. The quantities d and ε are, of course, intimately related. Indeed, if we sum up all the vertex degrees in G, we count every edge exactly twice: once from each of its ends. Thus X d(v) = 12 d(G) · |V | , |E| = 12
ε(G)
v ∈V
and therefore ε(G) = 12 d(G) . Proposition 1.2.1. The number of vertices of odd degree in a graph is always even. P P d(v) is an even Proof . A graph on V has 12 v ∈ V d(v) edges, so number. ¤ If a graph has large minimum degree, i.e. everywhere, locally, many edges per vertex, it also has many edges per vertex globally: ε(G) = 1 1 2 d(G) > 2 δ(G). Conversely, of course, its average degree may be large even when its minimum degree is small. However, the vertices of large degree cannot be scattered completely among vertices of small degree: as the next proposition shows, every graph G has a subgraph whose average degree is no less than the average degree of G, and whose minimum degree is more than half its average degree: 2
but not for multigraphs; see Section 1.10
[ 10.3.3 ]
6 [ 3.6.1 ]
Proposition 1.2.2. Every graph G with at least one edge has a subgraph H with δ(H) > ε(H) > ε(G). Proof . To construct H from G, let us try to delete vertices of small degree one by one, until only vertices of large degree remain. Up to which degree d(v) can we afford to delete a vertex v, without lowering ε? Clearly, up to d(v) = ε : then the number of vertices decreases by 1 and the number of edges by at most ε, so the overall ratio ε of edges to vertices will not decrease. Formally, we construct a sequence G = G0 ⊇ G1 ⊇ . . . of induced subgraphs of G as follows. If Gi has a vertex vi of degree d(vi ) 6 ε(Gi ), we let Gi+1 := Gi − vi ; if not, we terminate our sequence and set H := Gi . By the choices of vi we have ε(Gi+1 ) > ε(Gi ) for all i, and hence ε(H) > ε(G). What else can we say about the graph H? Since ε(K 1 ) = 0 < ε(G), none of the graphs in our sequence is trivial, so in particular H 6= ∅. The fact that H has no vertex suitable for deletion thus implies δ(H) > ε(H), as claimed. ¤
1.3 Paths and cycles path
A path is a non-empty graph P = (V, E) of the form V = { x0 , x1 , . . . , xk }
length Pk
E = { x0 x1 , x1 x2 , . . . , xk−1 xk } ,
where the xi are all distinct. The vertices x0 and xk are linked by P and are called its ends; the vertices x1 , . . . , xk−1 are the inner vertices of P . The number of edges of a path is its length, and the path of length k is denoted by P k . Note that k is allowed to be zero; thus, P 0 = K 1 .
P Fig. 1.3.1. A path P = P 6 in G
We often refer to a path by the natural sequence of its vertices,3 writing, say, P = x0 x1 . . . xk and calling P a path from x0 to xk (as well as between x0 and xk ). 3 More precisely, by one of the two natural sequences: x0 . . . xk and xk . . . x0 denote the same path. Still, it often helps to fix one of these two orderings of V (P ) notationally: we may then speak of things like the ‘first’ vertex on P with a certain property, etc.
1.3 Paths and cycles
For 0 6 i 6 j 6 k we write
˚ xP y, P
P xi := x0 . . . xi xi P := xi . . . xk xi P xj := xi . . . xj and ˚ := P P˚ xi := ˚ xi P := ˚ xi P˚ xj :=
x1 . . . xk−1 x0 . . . xi−1 xi+1 . . . xk xi+1 . . . xj−1
for the appropriate subpaths of P . We use similar intuitive notation for the concatenation of paths; for example, if the union P x ∪ xQy ∪ yR of three paths is again a path, we may simply denote it by P xQyR.
P xQyR
P y y x
z Q
xP yQz
Fig. 1.3.2. Paths P , Q and xP yQz
Given sets A, B of vertices, we call P = x0 . . . xk an A–B path if V (P ) ∩ A = { x0 } and V (P ) ∩ B = { xk }. As before, we write a–B path rather than { a }–B path, etc. Two or more paths are independent if none of them contains an inner vertex of another. Two a–b paths, for instance, are independent if and only if a and b are their only common vertices. Given a graph H, we call P an H-path if P is non-trivial and meets H exactly in its ends. In particular, the edge of any H-path of length 1 is never an edge of H. If P = x0 . . . xk−1 is a path and k > 3, then the graph C := P + xk−1 x0 is called a cycle. As with paths, we often denote a cycle by its (cyclic) sequence of vertices; the above cycle C might be written as x0 . . . xk−1 x0 . The length of a cycle is its number of edges (or vertices); the cycle of length k is called a k-cycle and denoted by C k . The minimum length of a cycle (contained) in a graph G is the girth g(G) of G; the maximum length of a cycle in G is its circumference. (If G does not contain a cycle, we set the former to ∞, the latter to zero.) An edge which joins two vertices of a cycle but is not itself an edge of the cycle is a chord of that cycle. Thus, an induced cycle in G, a cycle in G forming an induced subgraph, is one that has no chords (Fig. 1.3.3).
A–B path independent
H-path
cycle length Ck girth g(G) circumference chord induced cycle
y Fig. 1.3.3. A cycle C 8 with chord xy, and induced cycles C 6 , C 4
If a graph has large minimum degree, it contains long paths and cycles: [ 3.6.1 ]
Proposition 1.3.1. Every graph G contains a path of length δ(G) and a cycle of length at least δ(G) + 1 (provided that δ(G) > 2). Proof . Let x0 . . . xk be a longest path in G. Then all the neighbours of xk lie on this path (Fig. 1.3.4). Hence k > d(xk ) > δ(G). If i < k is minimal with xi xk ∈ E(G), then xi . . . xk xi is a cycle of length at least δ(G) + 1. ¤
Fig. 1.3.4. A longest path x0 . . . xk , and the neighbours of xk
distance dG (x, y) diameter diam(G)
Minimum degree and girth, on the other hand, are not related (unless we fix the number of vertices): as we shall see in Chapter 11, there are graphs combining arbitrarily large minimum degree with arbitrarily large girth. The distance dG (x, y) in G of two vertices x, y is the length of a shortest x–y path in G; if no such path exists, we set d(x, y) := ∞. The greatest distance between any two vertices in G is the diameter of G, denoted by diam(G). Diameter and girth are, of course, related: Proposition 1.3.2. Every graph G containing a cycle satisfies g(G) 6 2 diam(G) + 1. Proof . Let C be a shortest cycle in G. If g(G) > 2 diam(G) + 2, then C has two vertices whose distance in C is at least diam(G) + 1. In G, these vertices have a lesser distance; any shortest path P between them is therefore not a subgraph of C. Thus, P contains a C-path xP y. Together with the shorter of the two x–y paths in C, this path xP y forms a shorter cycle than C, a contradiction. ¤
A vertex is central in G if its greatest distance from any other vertex is as small as possible. This distance is the radius of G, denoted by rad(G). Thus, formally, rad(G) = minx ∈ V (G) maxy ∈ V (G) dG (x, y). As one easily checks (exercise), we have
central radius rad(G)
rad(G) 6 diam(G) 6 2 rad(G) . Diameter and radius are not directly related to the minimum or average degree: a graph can combine large minimum degree with large diameter, or small average degree with small diameter (examples?). The maximum degree behaves differently here: a graph of large order can only have small radius and diameter if its maximum degree is large. This connection is quantified very roughly in the following proposition: Proposition 1.3.3. A graph G of radius at most k and maximum degree at most d has no more than 1 + kdk vertices.
[ 9.4.1 ] [ 9.4.2 ]
Proof . Let z be a central vertex in G, and letSDi denote the set of k vertices of G at distance i from z. Then V (G) = i=0 Di , and |D0 | = 1. Since ∆(G) 6 d, we have |Di | 6 d |Di−1 | for i = 1, . . . , k, and thus |Di | 6 di by induction. Adding up these inequalities we obtain |G| 6 1 +
k X i=1
di 6 1 + kdk . ¤
A walk (of length k) in a graph G is a non-empty alternating sequence v0 e0 v1 e1 . . . ek−1 vk of vertices and edges in G such that ei = { vi , vi+1 } for all i < k. If v0 = vk , the walk is closed . If the vertices in a walk are all distinct, it defines an obvious path in G. In general, every walk between two vertices contains4 a path between these vertices (proof?).
1.4 Connectivity A non-empty graph G is called connected if any two of its vertices are linked by a path in G. If U ⊆ V (G) and G [ U ] is connected, we also call U itself connected (in G).
Proposition 1.4.1. The vertices of a connected graph G can always be enumerated, say as v1 , . . . , vn , so that Gi := G [ v1 , . . . , vi ] is connected for every i.
[ 1.5.2 ]
4 We shall often use terms defined for graphs also for walks, as long as their meaning is obvious.
Proof . Pick any vertex as v1 , and assume inductively that v1 , . . . , vi have been chosen for some i < |G|. Now pick a vertex v ∈ G − Gi . As G is connected, it contains a v–v1 path P . Choose as vi+1 the last vertex of P in G − Gi ; then vi+1 has a neighbour in Gi . The connectedness of every Gi follows by induction on i. ¤
Let G = (V, E) be a graph. A maximal connected subgraph of G is called a component of G. Note that a component, being connected, is always non-empty; the empty graph, therefore, has no components.
Fig. 1.4.1. A graph with three components, and a minimal spanning connected subgraph in each component
cutvertex bridge
If A, B ⊆ V and X ⊆ V ∪ E are such that every A–B path in G contains a vertex or an edge from X, we say that X separates the sets A and B in G. This implies in particular that A ∩ B ⊆ X. More generally we say that X separates G, and call X a separating set in G, if X separates two vertices of G − X in G. A vertex which separates two other vertices of the same component is a cutvertex , and an edge separating its ends is a bridge. Thus, the bridges in a graph are precisely those edges that do not lie on any cycle.
Fig. 1.4.2. A graph with cutvertices v, x, y, w and bridge e = xy k-connected
connectivity κ(G) `-edgeconnected
G is called k-connected (for k ∈ N) if |G| > k and G − X is connected for every set X ⊆ V with |X| < k. In other words, no two vertices of G are separated by fewer than k other vertices. Every (non-empty) graph is 0-connected, and the 1-connected graphs are precisely the non-trivial connected graphs. The greatest integer k such that G is k-connected is the connectivity κ(G) of G. Thus, κ(G) = 0 if and only if G is disconnected or a K 1 , and κ(K n ) = n − 1 for all n > 1. If |G| > 1 and G − F is connected for every set F ⊆ E of fewer than ` edges, then G is called `-edge-connected. The greatest integer `
Fig. 1.4.3. The octahedron G (left) with κ(G) = λ(G) = 4, and a graph H with κ(H) = 2 but λ(H) = 4
such that G is `-edge-connected is the edge-connectivity λ(G) of G. In particular, we have λ(G) = 0 if G is disconnected. For every non-trivial graph G we have
edgeconnectivity λ(G)
κ(G) 6 λ(G) 6 δ(G) (exercise), so in particular high connectivity requires a large minimum degree. Conversely, large minimum degree does not ensure high connectivity, not even high edge-connectivity (examples?). It does, however, imply the existence of a highly connected subgraph: Theorem 1.4.2. (Mader 1972) Every graph of average degree at least 4k has a k-connected subgraph. Proof . For k ∈ { 0, 1 } the assertion is trivial; we consider k > 2 and a graph G = (V, E) with |V | =: n and |E| =: m. For inductive reasons it will be easier to prove the stronger assertion that G has a k-connected subgraph whenever (i) n > 2k − 1
(ii) m > (2k − 3)(n − k + 1) + 1. (This assertion is indeed stronger, i.e. (i) and (ii) follow from our assumption of d(G) > 4k: (i) holds since n > ∆(G) > d(G) > 4k, while (ii) follows from m = 12 d(G)n > 2kn.) We apply induction on n. If n = 2k − 1, then k = 12 (n + 1), and hence m > 12 n(n − 1) by (ii). Thus G = K n ⊇ K k+1 , proving our claim. We now assume that n > 2k. If v is a vertex with d(v) 6 2k − 3, we can apply the induction hypothesis to G − v and are done. So we assume that δ(G) > 2k − 2. If G is k-connected, there is nothing to show. We may therefore assume that G has the form G = G1 ∪ G2 with |G1 ∩ G2 | < k and |G1 |, |G2 | < n. As every edge of G lies in G1 or in G2 , G has no edge between G1 − G2 and G2 − G1 . Since each vertex in these subgraphs has at least δ(G) > 2k − 2 neighbours, we have |G1 |, |G2 | > 2k − 1. But then at least one of the graphs G1 , G2 must satisfy the induction hypothesis
[ 8.1.1 ] [ 11.2.3 ]
(completing the proof): if neither does, we have kGi k 6 (2k − 3)(|Gi | − k + 1) for i = 1, 2, and hence m 6 kG1 k + kG2 k ¢ ¡ 6 (2k − 3) |G1 | + |G2 | − 2k + 2 6 (2k − 3)(n − k + 1)
(by |G1 ∩ G2 | 6 k − 1) ¤
contradicting (ii).
1.5 Trees and forests forest tree leaf
An acyclic graph, one not containing any cycles, is called a forest. A connected forest is called a tree. (Thus, a forest is a graph whose components are trees.) The vertices of degree 1 in a tree are its leaves. Every nontrivial tree has at least two leaves—take, for example, the ends of a longest path. This little fact often comes in handy, especially in induction proofs about trees: if we remove a leaf from a tree, what remains is still a tree.
Fig. 1.5.1. A tree [ 1.6.1 ] [ 1.9.6 ] [ 4.2.7 ]
Theorem 1.5.1. The following assertions are equivalent for a graph T : (i) T is a tree; (ii) any two vertices of T are linked by a unique path in T ; (iii) T is minimally connected, i.e. T is connected but T − e is disconnected for every edge e ∈ T ; (iv) T is maximally acyclic, i.e. T contains no cycle but T + xy does, for any two non-adjacent vertices x, y ∈ T . ¤
1.5 Trees and forests
The proof of Theorem 1.5.1 is straightforward, and a good exercise for anyone not yet familiar with all the notions it relates. Extending our notation for paths from Section 1.3, we write xT y for the unique path in a tree T between two vertices x, y (see (ii) above). A frequently used application of Theorem 1.5.1 is that every connected graph contains a spanning tree: by the equivalence of (i) and (iii), any minimal connected spanning subgraph will be a tree. Figure 1.4.1 shows a spanning tree in each of the three components of the graph depicted.
xT y
Corollary 1.5.2. The vertices of a tree can always be enumerated, say as v1 , . . . , vn , so that every vi with i > 2 has a unique neighbour in { v1 , . . . , vi−1 }. ¤
Corollary 1.5.3. A connected graph with n vertices is a tree if and only if it has n − 1 edges.
[ 1.9.6 ] [ 3.5.1 ] [ 3.5.4 ] [ 4.2.7 ] [ 8.2.2 ]
Proof . Use the enumeration from Proposition 1.4.1.
Proof . Induction on i shows that the subgraph spanned by the first i vertices in Corollary 1.5.2 has i − 1 edges; for i = n this proves the forward implication. Conversely, let G be any connected graph with n vertices and n − 1 edges. Let G0 be a spanning tree in G. Since G0 has ¤ n − 1 edges by the first implication, it follows that G = G0 . Corollary 1.5.4. If T is a tree and G is any graph with δ(G) > |T | − 1, then T ⊆ G, i.e. G has a subgraph isomorphic to T .
Proof . Find a copy of T in G inductively along its vertex enumeration from Corollary 1.5.2. ¤ Sometimes it is convenient to consider one vertex of a tree as special; such a vertex is then called the root of this tree. A tree with a fixed root is a rooted tree. Choosing a root r in a tree T imposes a partial ordering on V (T ) by letting x 6 y if x ∈ rT y. This is the tree-order on V (T ) associated with T and r. Note that r is the least element in this partial order, every leaf x 6= r of T is a maximal element, the ends of any edge of T are comparable, and every set of the form { x | x 6 y } (where y is any fixed vertex) is a chain, a set of pairwise comparable elements. (Proofs?) A rooted tree T contained in a graph G is called normal in G if the ends of every T -path in G are comparable in the tree-order of T . If T spans G, this amounts to requiring that two vertices of T must be comparable whenever they are adjacent in G; see Figure 1.5.2. Normal spanning trees are also called depth-first search trees, because of the way they arise in computer searches on graphs (Exercise 17).
root tree-order
chain normal tree
T r Fig. 1.5.2. A depth-first search tree with root r
Normal spanning trees provide a simple but powerful structural tool in graph theory. And they always exist: [ 6.5.3 ]
Proposition 1.5.5. Every connected graph contains a normal spanning tree, with any specified vertex as its root. Proof . Let G be a connected graph and r ∈ G any specified vertex. Let T be a maximal normal tree with root r in G; we show that V (T ) = V (G). Suppose not, and let C be a component of G − T . As T is normal, N (C) is a chain in T . Let x be its greatest element, and let y ∈ C be adjacent to x. Let T 0 be the tree obtained from T by joining y to x; the tree-order of T 0 then extends that of T . We shall derive a contradiction by showing that T 0 is also normal in G. Let P be a T 0 -path in G. If the ends of P both lie in T , then they are comparable in the tree-order of T (and hence in that of T 0 ), because then P is also a T -path and T is normal in G by assumption. If not, then y is one end of P , so P lies in C except for its other end z, which lies in N (C). Then z 6 x, by the choice of x. For our proof that y and z are comparable it thus suffices to show that x < y, i.e. that x ∈ rT 0 y. This, however, is clear since y is a leaf of T 0 with neighbour x. ¤
1.6 Bipartite graphs r-partite
bipartite complete r-partite
Let r > 2 be an integer. A graph G = (V, E) is called r-partite if V admits a partition into r classes such that every edge has its ends in different classes: vertices in the same partition class must not be adjacent. Instead of ‘2-partite’ one usually says bipartite. An r-partite graph in which every two vertices from different partition classes are adjacent is called complete; the complete r-partite graphs for all r together are the complete multipartite graphs. The
1.6 Bipartite graphs
K2,2,2 = K23 Fig. 1.6.1. Two 3-partite graphs
complete r-partite graph K n1 ∗ . . . ∗ K nr is denoted by Kn1 ,...,nr ; if n1 = . . . = nr =: s, we abbreviate this to Ksr . Thus, Ksr is the complete r-partite graph in which every partition class contains exactly s vertices.5 (Figure 1.6.1 shows the example of the octahedron K23 ; compare its drawing with that in Figure 1.4.3.) Graphs of the form K1,n are called stars.
Kn1 ,...,nr Ksr
Fig. 1.6.2. Three drawings of the bipartite graph K3,3 = K32
Clearly, a bipartite graph cannot contain an odd cycle, a cycle of odd length. In fact, the bipartite graphs are characterized by this property:
odd cycle
Proposition 1.6.1. A graph is bipartite if and only if it contains no odd cycle.
Proof . Let G = (V, E) be a graph without odd cycles; we show that G is bipartite. Clearly a graph is bipartite if all its components are bipartite or trivial, so we may assume that G is connected. Let T be a spanning tree in G, pick a root r ∈ T , and denote the associated tree-order on V by 6T . For each v ∈ V , the unique path rT v has odd or even length. This defines a bipartition of V ; we show that G is bipartite with this partition. Let e = xy be an edge of G. If e ∈ T , with x
x e Ce
r Fig. 1.6.3. The cycle Ce in T + e
1.7 Contraction and minors
G/e contraction
In Section 1.1 we saw two fundamental containment relations between graphs: the subgraph relation, and the ‘induced subgraph’ relation. In this section we meet another: the minor relation. Let e = xy be an edge of a graph G = (V, E). By G/e we denote the graph obtained from G by contracting the edge e into a new vertex ve , which becomes adjacent to all the former neighbours of x and of y. Formally, G/e is a graph (V 0 , E 0 ) with vertex set V 0 := (V r { x, y }) ∪ { ve } (where ve is the ‘new’ vertex, i.e. ve ∈/ V ∪ E) and edge set n o E 0 := vw ∈ E | { v, w } ∩ { x, y } = ∅ o n ∪ ve w | xw ∈ E r { e } or yw ∈ E r { e } .
x ve
e y
G/e
Fig. 1.7.1. Contracting the edge e = xy
MX branch sets
More generally, if X is another graph and { Vx | x ∈ V (X) } is a partition of V into connected subsets such that, for any two vertices x, y ∈ X, there is a Vx –Vy edge in G if and only if xy ∈ E(X), we call G an M X and write6 G = M X (Fig. 1.7.2). The sets Vx are the branch sets of this M X. Intuitively, we obtain X from G by contracting every 6
Thus formally, the expression M X—where M stands for ‘minor’; see below— refers to a whole class of graphs, and G = M X means (with slight abuse of notation) that G belongs to this class.
Vx G Fig. 1.7.2. Y ⊇ G = M X, so X is a minor of Y
branch set to a single vertex and deleting any ‘parallel edges’ or ‘loops’ that may arise. If Vx = U ⊆ V is one of the branch sets above and every other branch set consists just of a single vertex, we also write G/U for the graph X and vU for the vertex x ∈ X to which U contracts, and think of the rest of X as an induced subgraph of G. The contraction of a single edge uu0 defined earlier can then be viewed as the special case of U = { u, u0 }.
G/U vU
Proposition 1.7.1. G is an M X if and only if X can be obtained from G by a series of edge contractions, i.e. if and only if there are graphs G0 , . . . , Gn and edges ei ∈ Gi such that G0 = G, Gn ' X, and Gi+1 = Gi /ei for all i < n. Proof . Induction on |G| − |X|.
If G = M X is a subgraph of another graph Y , we call X a minor of Y and write X 4 Y . Note that every subgraph of a graph is also its minor; in particular, every graph is its own minor. By Proposition 1.7.1, any minor of a graph can be obtained from it by first deleting some vertices and edges, and then contracting some further edges. Conversely, any graph obtained from another by repeated deletions and contractions (in any order) is its minor: this is clear for one deletion or contraction, and follows for several from the transitivity of the minor relation (Proposition 1.7.3). If we replace the edges of X with independent paths between their ends (so that none of these paths has an inner vertex on another path or in X), we call the graph G obtained a subdivision of X and write G = T X.7 If G = T X is the subgraph of another graph Y , then X is a topological minor of Y (Fig. 1.7.3). 7 So again T X denotes an entire class of graphs: all those which, viewed as a topological space in the obvious way, are homeomorphic to X. The T in T X stands for ‘topological’.
minor; 4
subdivision TX topological minor
Y Fig. 1.7.3. Y ⊇ G = T X, so X is a topological minor of Y
branch vertices
If G = T X, we view V (X) as a subset of V (G) and call these vertices the branch vertices of G; the other vertices of G are its subdividing vertices. Thus, all subdividing vertices have degree 2, while the branch vertices retain their degree from X. Proposition 1.7.2. (i) Every T X is also an M X (Fig. 1.7.4); thus, every topological minor of a graph is also its (ordinary) minor. (ii) If ∆(X) 6 3, then every M X contains a T X; thus, every minor with maximum degree at most 3 of a graph is also its topological minor. ¤
Fig. 1.7.4. A subdivision of K 4 viewed as an M K 4 [ 12.4.1 ]
Proposition 1.7.3. The minor relation 4 and the topological-minor relation are partial orderings on the class of finite graphs, i.e. they are reflexive, antisymmetric and transitive. ¤
1.8 Euler tours Any mathematician who happens to find himself in the East Prussian city of K¨ onigsberg (and in the 18th century) will lose no time to follow the great Leonhard Euler’s example and inquire about a round trip through
1.8 Euler tours
Fig. 1.8.1. The bridges of K¨ onigsberg (anno 1736)
the old city that traverses each of the bridges shown in Figure 1.8.1 exactly once. Thus inspired,8 let us call a closed walk in a graph an Euler tour if it traverses every edge of the graph exactly once. A graph is Eulerian if it admits an Euler tour.
Eulerian
Fig. 1.8.2. A graph formalizing the bridge problem
Theorem 1.8.1. (Euler 1736) A connected graph is Eulerian if and only if every vertex has even degree. Proof . The degree condition is clearly necessary: a vertex appearing k times in an Euler tour (or k + 1 times, if it is the starting and finishing vertex and as such counted twice) must have degree 2k. 8 Anyone to whom such inspiration seems far-fetched, even after contemplating Figure 1.8.2, may seek consolation in the multigraph of Figure 1.10.1.
Conversely, let G be a connected graph with all degrees even, and let W = v0 e0 . . . e`−1 v` be a longest walk in G using no edge more than once. Since W cannot be extended, it already contains all the edges at v` . By assumption, the number of such edges is even. Hence v` = v0 , so W is a closed walk. Suppose W is not an Euler tour. Then G has an edge e outside W but incident with a vertex of W , say e = uvi . (Here we use the connectedness of G, as in the proof of Proposition 1.4.1.) Then the walk uevi ei . . . e`−1 v` e0 . . . ei−1 vi ¤
is longer than W , a contradiction.
1.9 Some linear algebra vertex space V(G)
edge space E(G) standard basis
hF, F 0 i
Let G = (V, E) be a graph with n vertices and m edges, say V = { v1 , . . . , vn } and E = { e1 , . . . , em }. The vertex space V(G) of G is the vector space over the 2-element field F2 = { 0, 1 } of all functions V → F2 . Every element of V(G) corresponds naturally to a subset of V , the set of those vertices to which it assigns a 1, and every subset of V is uniquely represented in V(G) by its indicator function. We may thus think of V(G) as the power set of V made into a vector space: the sum U + U 0 of two vertex sets U, U 0 ⊆ V is their symmetric difference (why?), and U = −U for all U ⊆ V . The zero in V(G), viewed in this way, is the empty (vertex) set ∅. Since { { v1 }, . . . , { vn } } is a basis of V(G), its standard basis, we have dim V(G) = n. In the same way as above, the functions E → F2 form the edge space E(G) of G: its elements are the subsets of E, vector addition amounts to symmetric difference, ∅ ⊆ E is the zero, and F = −F for all F ⊆ E. As before, { { e1 }, . . . , { em } } is the standard basis of E(G), and dim E(G) = m. Since the edges of a graph carry its essential structure, we shall mostly be concerned with the edge space. Given two edge sets F, F 0 ∈ E(G) and their coefficients λ1 , . . . , λm and λ01 , . . . , λ0m with respect to the standard basis, we write hF, F 0 i := λ1 λ01 + . . . + λm λ0m
Note that hF, F 0 i = 0 may hold even when F = F 0 6= ∅: indeed, hF, F 0 i = 0 if and only if F and F 0 have an even number of edges
1.9 Some linear algebra
in common. Given a subspace F of E(G), we write © F ⊥ := D
E(G) | hF, Di = 0 for all F
ª F .
F⊥
This is again a subspace of E(G) (the space of all vectors solving a certain set of linear equations—which?), and we have dim F + dim F ⊥ = m . The cycle space C = C(G) is the subspace of E(G) spanned by all the cycles in G—more precisely, by their edge sets.9 The dimension of C(G) is the cyclomatic number of G.
cycle space C(G)
Proposition 1.9.1. The induced cycles in G generate its entire cycle space.
Proof . By definition of C(G) it suffices to show that the induced cycles in G generate every cycle C ⊆ G with a chord e. This follows at once by induction on |C|: the two cycles in C + e with e but no other edge in common are shorter than C, and their symmetric difference is precisely C. ¤ Proposition 1.9.2. An edge set F ⊆ E lies in C(G) if and only if every vertex of (V, F ) has even degree.
Proof . The forward implication holds by induction on the number of cycles needed to generate F , the backward implication by induction on the number of cycles in (V, F ). ¤ If { V1 , V2 } is a partition of V , the set E(V1 , V2 ) of all the edges of G crossing this partition is called a cut. Recall that for V1 = { v } this cut is denoted by E(v). Proposition 1.9.3. Together with ∅, the cuts in G form a subspace C ∗ of E(G). This space is generated by cuts of the form E(v). Proof . Let C ∗ denote the set of all cuts in G, together with ∅. To prove that C ∗ is a subspace, we show that for all D, D0 ∈ C ∗ also D + D0 (= D − D0 ) lies in C ∗ . Since D + D = ∅ ∈ C ∗ and D + ∅ = D ∈ C ∗ , we may assume that D and D0 are distinct and non-empty. Let { V1 , V2 } and { V10 , V20 } be the corresponding partitions of V . Then D + D0 consists of all the edges that cross one of these partitions but not the other (Fig. 1.9.1). But these are precisely the edges between (V1 ∩ V10 ) ∪ (V2 ∩ V20 ) and (V1 ∩ V20 ) ∪ (V2 ∩ V10 ), and by D 6= D0 these two 9 For simplicity, we shall not normally distinguish between cycles and their edge sets in connection with the cycle space.
D Fig. 1.9.1. Cut edges in D + D0
sets form another partition of V . Hence D + D0 ∈ C ∗ , and C ∗ is indeed a subspace of E(G). Our second assertion, that the cuts E(v) generate all of C ∗ , follows from the fact that every edge xy ∈ G lies in exactly two such cuts (in E(x) and in E(y)); thus every partition { V1 , V2 } of V satisfies E(V1 , V2 ) = P ¤ v ∈ V1 E(v). cut space C ∗ (G)
The subspace C ∗ =: C ∗ (G) of E(G) from Proposition 1.9.3 will be called the cut space of G. It is not difficult to find among the cuts E(v) an explicit basis for C ∗ (G), and thus to determine its dimension (exercise); together with Theorem 1.9.5 this yields an independent proof of Theorem 1.9.6. The following lemma will be useful when we study the duality of plane graphs in Chapter 4.6: Lemma 1.9.4. The minimal cuts in a connected graph generate its entire cut space. Proof . Note first that a cut in a connected graph G = (V, E) is minimal if and only if both sets in the corresponding partition of V are connected in G. Now consider any connected subgraph C ⊆ G. If D is a component of G − C, then also G − D is connected (Fig. 1.9.2); the edges between D
D G−D C
Fig. 1.9.2. G − D is connected, and E(C, D) a minimal cut
and G − D thus form a minimal cut. By choice of D, this cut is precisely the set E(C, D) of all C–D edges in G. To prove the lemma, let a partition { V1 , V2 } of V be given, and consider a component C of G [ V1 ]. Then E(C, V2 ) = E(C, G − C) is the disjoint union of the edge sets E(C, D) over all components D of G − C, and is thus the disjoint union of minimal cuts (see above). Now the disjoint union of all these edge sets E(C, V2 ), taken over all the components C of G [ V1 ], is precisely our cut E(V1 , V2 ). So this cut is generated by minimal cuts, as claimed. ¤ Theorem 1.9.5. The cycle space C and the cut space C ∗ of any graph satisfy C = C ∗⊥ and C ∗ = C ⊥ . Proof . Let us consider a graph G = (V, E). Clearly, any cycle in G has an even number of edges in each cut. This implies C ⊆ C ∗⊥ . Conversely, recall from Proposition 1.9.2 that for every edge set F ∈/ C there exists a vertex v incident with an odd number of edges in F . Then hE(v), F i = 1, so E(v) ∈ C ∗ implies F ∈/ C ∗⊥ . This completes the proof of C = C ∗⊥ . To prove C ∗ = C ⊥ , it now suffices to show C ∗ = (C ∗⊥ )⊥ . Here C ∗ ⊆ (C ∗⊥ )⊥ follows directly from the definition of ⊥. But since dim C ∗ + dim C ∗⊥ = m = dim C ∗⊥ + dim (C ∗⊥ )⊥ , C ∗ has the same dimension as (C ∗⊥ )⊥ , so C ∗ = (C ∗⊥ )⊥ as claimed.
Theorem 1.9.6. Every connected graph G with n vertices and m edges satisfies dim C(G) = m − n + 1 and
dim C ∗ (G) = n − 1 .
Proof . Let G = (V, E). As dim C + dim C ∗ = m by Theorem 1.9.5, it suffices to find m − n + 1 linearly independent vectors in C and n − 1 linearly independent vectors in C ∗ : since these numbers add up to m, neither the dimension of C nor that of C ∗ can then be strictly greater. Let T be a spanning tree in G. By Corollary 1.5.3, T has n − 1 edges, so m − n + 1 edges of G lie outside T . For each of these m − n + 1 edges e ∈ E r E(T ), the graph T + e contains a cycle Ce (see Fig. 1.6.3 and Theorem 1.5.1 (iv)). Since none of the edges e lies on Ce0 for e0 6= e, these m − n + 1 cycles are linearly independent. For each of the n − 1 edges e ∈ T , the graph T − e has exactly two components (Theorem 1.5.1 (iii)), and the set De of edges in G between these components form a cut (Fig.1.9.3). Since none of the edges e ∈ T ¤ lies in De0 for e0 6= e, these n − 1 cuts are linearly independent.
(1.5.1) (1.5.3)
Fig. 1.9.3. The cut De incidence matrix
The incidence matrix B = (bij )n×m of a graph G = (V, E) with V = { v1 , . . . , vn } and E = { e1 , . . . , em } is defined over F2 by n bij :=
1 if vi ∈ ej 0 otherwise.
As usual, let B t denote the transpose of B. Then B and B t define linear maps B: E(G) → V(G) and B t : V(G) → E(G) with respect to the standard bases. Proposition 1.9.7. (i) The kernel of B is C(G). (ii) The image of B t is C ∗ (G). adjacency matrix
The adjacency matrix A = (aij )n×n of G is defined by n aij :=
1 if vi vj ∈ E 0 otherwise.
Our last proposition establishes a simple connection between A and B (now viewed as real matrices). Let D denote the real diagonal matrix (dij )n×n with dii = d(vi ) and dij = 0 otherwise. Proposition 1.9.8. BB t = A + D.
1.10 Other notions of graphs
1.10 Other notions of graphs For completeness, we now mention a few other notions of graphs which feature less frequently or not at all in this book. A hypergraph is a pair (V, E) of disjoint sets, where the elements of E are non-empty subsets (of any cardinality) of V . Thus, graphs are special hypergraphs. A directed graph (or digraph) is a pair (V, E) of disjoint sets (of vertices and edges) together with two maps init: E → V and ter: E → V assigning to every edge e an initial vertex init(e) and a terminal vertex ter(e). The edge e is said to be directed from init(e) to ter(e). Note that a directed graph may have several edges between the same two vertices x, y. Such edges are called multiple edges; if they have the same direction (say from x to y), they are parallel . If init(e) = ter(e), the edge e is called a loop. A directed graph D is an orientation of an (undirected) graph G if V (D) = V (G) and E(D) = E(G), and if { init(e), ter(e) } = { x, y } for every edge e = xy. Intuitively, such an oriented graph arises from an undirected graph simply by directing every edge from one of its ends to the other. Put differently, oriented graphs are directed graphs without loops or multiple edges. A multigraph is a pair (V, E) of disjoint sets (of vertices and edges) together with a map E → V ∪ [V ]2 assigning to every edge either one or two vertices, its ends. Thus, multigraphs too can have loops and multiple edges: we may think of a multigraph as a directed graph whose edge directions have been ‘forgotten’. To express that x and y are the ends of an edge e we still write e = xy, though this no longer determines e uniquely. A graph is thus essentially the same as a multigraph without loops or multiple edges. Somewhat surprisingly, proving a graph theorem more generally for multigraphs may, on occasion, simplify the proof. Moreover, there are areas in graph theory (such as plane duality; see Chapters 4.6 and 6.5) where multigraphs arise more naturally than graphs, and where any restriction to the latter would seem artificial and be technically complicated. We shall therefore consider multigraphs in these cases, but without much technical ado: terminology introduced earlier for graphs will be used correspondingly. Two differences, however, should be pointed out. First, a multigraph may have cycles of length 1 or 2: loops, and pairs of multiple edges (or double edges). Second, the notion of edge contraction is simpler in multigraphs than in graphs. If we contract an edge e = xy in a multigraph G = (V, E) to a new vertex ve , there is no longer a need to delete any edges other than e itself: edges parallel to e become loops at ve , while edges xv and yv become parallel edges between ve and v (Fig. 1.10.1). Thus, formally, E(G/e) = E r { e }, and only the incidence
hypergraph
directed graph init(e) ter(e)
loop orientation oriented graph
multigraph
map e0 7→ { init(e0 ), ter(e0 ) } of G has to be adjusted to the new vertex set in G/e. The notion of a minor adapts to multigraphs accordingly.
ve e G
Fig. 1.10.1. Contracting the edge e in the multigraph corresponding to Fig. 1.8.1
Finally, it should be pointed out that authors who usually work with multigraphs tend to call them graphs; in their terminology, our graphs would be called simple graphs.
Exercises 1.− What is the number of edges in a K n ? 2.
Let d ∈ N and V := { 0, 1 }d ; thus, V is the set of all 0–1 sequences of length d. The graph on V in which two such sequences form an edge if and only if they differ in exactly one position is called the d-dimensional cube. Determine the average degree, number of edges, diameter, girth and circumference of this graph. (Hint for circumference. Induction on d.)
Let G be a graph containing a cycle C, and assume that G contains a path of length at least k between √ two vertices of C. Show that G contains a cycle of length at least k. Is this best possible?
4.− Is the bound in Proposition 1.3.2 best possible? 5. +
Show that rad(G) 6 diam(G) 6 2 rad(G) for every graph G. Assuming that d > 2 and k > 3, improve the bound in Proposition 1.3.3 to dk .
7.− Show that the components of a graph partition its vertex set. (In other words, show that every vertex belongs to exactly one component.) 8.− Show that every 2-connected graph contains a cycle. 9.
(i)− Determine κ(G) and λ(G) for G = P k , C k , K k , Km,n (k, m, n > 3). (ii)+ Determine the connectivity of the n-dimensional cube (defined in Exercise 2). (Hint for (ii). Induction on n.)
Show that κ(G) 6 λ(G) 6 δ(G) for every non-trivial graph G.
11.− Is there a function f : N → N such that, for all k minimum degree at least f (k) is k-connected? 12.
N, every graph of
Let α, β be two graph invariants with positive integer values. Formalize the two statements below, and show that each implies the other: (i) α is bounded above by a function of β; (ii) β can be forced up by making α large enough. Show that the statement (iii) β is bounded below by a function of α is not equivalent to (i) and (ii). Which small change would make it so?
13.+ What is the deeper reason behind the fact that the proof of Theorem 1.4.2 is based on an assumption of the form m > cn − b rather than just on a lower bound for the average degree? 14.
Prove Theorem 1.5.1.
Show that any tree T has at least ∆(T ) leaves.
Show that the ‘tree-order’ associated with a rooted tree T is indeed a partial order on V (T ), and verify the claims made about this partial order in the text.
Let G be a connected graph, and let r ∈ G be a vertex. Starting from r, move along the edges of G, going whenever possible to a vertex not visited so far. If there is no such vertex, go back along the edge by which the current vertex was first reached (unless the current vertex is r; then stop). Show that the edges traversed form a normal spanning tree in G with root r. (This procedure has earned those trees the name of depth-first search trees.)
Let T be a set of subtrees of a tree T . Assume that the trees in T have pairwise non-empty intersection. Show that their overall intersection T T is non-empty.
Show that every automorphism of a tree fixes a vertex or an edge.
Are the partition classes of a regular bipartite graph always of the same size?
Show that a graph is bipartite if and only if every induced cycle has even length.
Find a function f : N → N such that, for all k ∈ N, every graph of average degree at least f (k) has a bipartite subgraph of minimum degree at least k.
Show that the minor relation 4 defines a partial ordering on any set of (finite) graphs. Is the same true for infinite graphs?
24.− Show that the elements of the cycle space of a graph G are precisely the unions of the edges sets of edge-disjoint cycles in G.
Given a graph G, find among all cuts of the form E(v) a basis for the cut space of G.
Prove that the cycles and the cuts in a graph together generate its entire edge space, or find a counterexample.
Give a direct proof of the fact that the cycles Ce defined in the proof of Theorem 1.9.6 generate the cycle space.
Give a direct proof of the fact that the cuts De defined in the proof of Theorem 1.9.6 generate the cut space.
What are the dimensions of the cycle and the cut space of a graph with k components?
Notes The terminology used in this book is mostly standard. Alternatives do exist, of course, and some of these are stated when a concept is first defined. There is one small point where our notation deviates slightly from standard usage. Whereas complete graphs, paths, cycles etc. of given order are mostly denoted by Kn , Pk , C` and so on, we use superscripts instead of subscripts. This has the advantage of leaving the variables K, P , C etc. free for ad-hoc use: we may now enumerate components as C1 , C2 , . . ., speak of paths P1 , . . . , Pk , and so on—without any danger of confusion. Theorem10 1.4.2 is due to W. Mader, Existenz n-fach zusammenh¨ angender Teilgraphen in Graphen gen¨ ugend großer Kantendichte, Abh. Math. Sem. Univ. Hamburg 37 (1972) 86–97. Theorem 1.8.1 is from L. Euler, Solutio problematis ad geometriam situs pertinentis, Comment. Acad. Sci. I. Petropolitanae 8 (1736), 128–140. Of the large subject of algebraic methods in graph theory, Section 1.9 does not claim to convey an adequate impression. The standard monograph here is N.L. Biggs, Algebraic Graph Theory (2nd edn.), Cambridge University Press 1993. Another comprehensive account is given by C.D. Godsil & G.F. Royle, Algebraic Graph Theory, in preparation. Surveys on the use of algebraic methods can also be found in the Handbook of Combinatorics (R.L. Graham, M. Gr¨ otschel & L. Lov´ asz, eds.), North-Holland 1995.
In the interest of readability, the end-of-chapter notes in this book give references only for Theorems, and only in cases where these references cannot be found in a monograph or survey cited for that chapter.
Suppose we are given a graph and are asked to find in it as many independent edges as possible. How should we go about this? Will we be able to pair up all its vertices in this way? If not, how can we be sure that this is indeed impossible? Somewhat surprisingly, this basic problem does not only lie at the heart of numerous applications, it also gives rise to some rather interesting graph theory. A set M of independent edges in a graph G = (V, E) is called a matching. M is a matching of U ⊆ V if every vertex in U is incident with an edge in M . The vertices in U are then called matched (by M ); vertices not incident with any edge of M are unmatched . A k-regular spanning subgraph is called a k-factor . Thus, a subgraph H ⊆ G is a 1-factor of G if and only if E(H) is a matching of V . The problem of how to characterize the graphs that have a 1-factor, i.e. a matching of their entire vertex set, will be our main theme in this chapter.
matching matched factor
2.1 Matching in bipartite graphs For this whole section, we let G = (V, E) be a fixed bipartite graph with bipartition { A, B }. Vertices denoted as a, a0 etc. will be assumed to lie in A, vertices denoted as b etc. will lie in B. How can we find a matching in G with as many edges as possible? Let us start by considering an arbitrary matching M in G. A path in G which starts in A at an unmatched vertex and then contains, alternately, edges from E r M and from M , is an alternating path with respect to M . An alternating path P that ends in an unmatched vertex of B is called an augmenting path (Fig. 2.1.1), because we can use it to turn M into a larger matching: the symmetric difference of M with E(P ) is again a
G = (V, E) A, B a, b etc.
alternating path augmenting path
2. Matching
Fig. 2.1.1. Augmenting the matching M by the alternating path P
matching (consider the edges at a given vertex), and the set of matched vertices is increased by two, the ends of P . Alternating paths play an important role in the practical search for large matchings. In fact, if we start with any matching and keep applying augmenting paths until no further such improvement is possible, the matching obtained will always be an optimal one, a matching with the largest possible number of edges (Exercise 1). The algorithmic problem of finding such matchings thus reduces to that of finding augmenting paths—which is an interesting and accessible algorithmic problem.
vertex cover
Our first theorem characterizes the maximal cardinality of a matching in G by a kind of duality condition. Let us call a set U ⊆ V a cover of E (or a vertex cover of G) if every edge of G is incident with a vertex in U . Theorem 2.1.1. (K¨ onig 1931) The maximum cardinality of a matching in G is equal to the minimum cardinality of a vertex cover.
Proof . Let M be a matching in G of maximum cardinality. From every edge in M let us choose one of its ends: its end in B if some alternating path ends in that vertex, and its end in A otherwise (Fig. 2.1.2). We shall prove that the set U of these |M | vertices covers G; since any vertex cover of G must cover M , there can be none with fewer than |M | vertices, and so the theorem will follow.
U ∩B
U ∩A
Fig. 2.1.2. The vertex cover U
2.1 Matching in bipartite graphs
Let ab ∈ E be an edge; we show that either a or b lies in U . If ab ∈ M , this holds by definition of U , so we assume that ab ∈/ M . Since M is a maximal matching, it contains an edge a0 b0 with a = a0 or b = b0 . In fact, we may assume that a = a0 : for if a is unmatched (and b = b0 ), then ab is an alternating path, and so the end of a0 b0 ∈ M chosen for U was the vertex b0 = b. Now if a0 = a is not in U , then b0 ∈ U , and some alternating path P ends in b0 . But then there is also an alternating path P 0 ending in b: either P 0 := P b (if b ∈ P ) or P 0 := P b0 a0 b. By the maximality of M , however, P 0 is not an augmenting path. So b must be matched, and was chosen for U from the edge of M containing it. ¤ Let us return to our main problem, the search for some necessary and sufficient conditions for the existence of a 1-factor. In our present case of a bipartite graph, we may as well ask more generally when G contains a matching of A; this will define a 1-factor of G if |A| = |B|, a condition that has to hold anyhow if G is to have a 1-factor. A condition clearly necessary for the existence of a matching of A is that every subset of A has enough neighbours in B, i.e. that |N (S)| > |S|
for all S ⊆ A.
marriage condition
The following marriage theorem says that this obvious necessary condition is in fact sufficient: marriage theorem
Theorem 2.1.2. (Hall 1935) G contains a matching of A if and only if |N (S)| > |S| for all S ⊆ A. We give three proofs for the non-trivial implication of this theorem, i.e. that the ‘marriage condition’ implies the existence of a matching of A. The first of these is based on K¨ onig’s theorem; the second is a direct constructive proof by augmenting paths; the third will be an independent proof from first principles. First proof. If G contains no matching of A, then by Theorem 2.1.1 it has a cover U consisting of fewer than |A| vertices, say U = A0 ∪ B 0 with A0 ⊆ A and B 0 ⊆ B. Then |A0 | + |B 0 | = |U | < |A| , and hence |B 0 | < |A| − |A0 | = |A r A0 | (Fig. 2.1.3). By definition of U , however, G has no edges between A r A0 and B r B 0 , so |N (A r A0 )| 6 |B 0 | < |A r A0 | and the marriage condition fails for S := A r A0 .
Fig. 2.1.3. A cover by fewer than |A| vertices M
Second proof. Consider a matching M of G that leaves a vertex of A unmatched; we shall construct an augmenting path with respect to M . Let a0 , b1 , a1 , b2 , a2 , . . . be a maximal sequence of distinct vertices ai ∈ A and bi ∈ B satisfying the following conditions for all i > 1 (Fig. 2.1.4): (i) a0 is unmatched;
f (i)
(ii) bi is adjacent to some vertex af (i) (iii) ai bi
{ a0 , . . . , ai−1 };
By the marriage condition, our sequence cannot end in a vertex of A: the i vertices a0 , . . . , ai−1 together have at least i neighbours in B, so we can always find a new vertex bi 6= b1 , . . . , bi−1 that satisfies (ii). Let bk ∈ B be the last vertex of the sequence. By (i)–(iii),
P := bk af (k) bf (k) af 2 (k) bf 2 (k) af 3 (k) . . . af r (k) with f r (k) = 0 is an alternating path. a2
Fig. 2.1.4. Proving the marriage theorem by alternating paths
What is it that prevents us from extending our sequence further? If bk is matched, say to a, we can indeed extend it by setting ak := a, unless a = ai with 0 < i < k, in which case (iii) would imply bk = bi with a contradiction. So bk is unmatched, and hence P is an augmenting path between a0 and bk . ¤
Third proof. We apply induction on |A|. For |A| = 1 the assertion is true. Now let |A| > 2, and assume that the marriage condition is sufficient for the existence of a matching of A when |A| is smaller. If |N (S)| > |S| + 1 for every non-empty set S $ A, we pick an edge ab ∈ G and consider the graph G0 := G − { a, b }. Then every non-empty set S ⊆ A r { a } satisfies |NG0 (S)| > |NG (S)| − 1 > |S| , so by the induction hypothesis G0 contains a matching of A r { a }. Together with the edge ab, this yields a matching of A in G. Suppose now that A has a non-empty proper subset A0 with |B 0 | = 0 |A | for B 0 := N (A0 ). By the induction hypothesis, G0 := G [ A0 ∪ B 0 ] contains a matching of A0 . But G − G0 satisfies the marriage condition too: for any set S ⊆ A r A0 with |NG−G0 (S)| < |S| we would have |NG (S ∪ A0 )| < |S ∪ A0 |, contrary to our assumption. Again by induction, G − G0 contains a matching of A r A0 . Putting the two matchings together, we obtain a matching of A in G. ¤ Corollary 2.1.3. If |N (S)| > |S| − d for every set S ⊆ A and some fixed d ∈ N, then G contains a matching of cardinality |A| − d. Proof . We add d new vertices to B, joining each of them to all the vertices in A. By the marriage theorem the new graph contains a matching of A, and at least |A| − d edges in this matching must be edges of G. ¤ Corollary 2.1.4. If G is k-regular with k > 1, then G has a 1-factor. Proof . If G is k-regular, then clearly |A| = |B|; it thus suffices to show by Theorem 2.1.2 that G contains a matching of A. Now every set S ⊆ A is joined to N (S) by a total of k |S| edges, and these are among the k |N (S)| edges of G incident with N (S). Therefore k |S| 6 k |N (S)|, so G does indeed satisfy the marriage condition. ¤ Despite its seemingly narrow formulation, the marriage theorem counts among the most frequently applied graph theorems, both outside graph theory and within. Often, however, recasting a problem in the setting of bipartite matching requires some clever adaptation. As a simple example, we now use the marriage theorem to derive one of the earliest results of graph theory, a result whose original proof is not all that simple, and certainly not short: Corollary 2.1.5. (Petersen 1891) Every regular graph of positive even degree has a 2-factor.
A0 , B 0 G0
34 (1.8.1)
Proof . Let G be any 2k-regular graph (k > 1), without loss of generality connected. By Theorem 1.8.1, G contains an Euler tour v0 e0 . . . e`−1 v` , with v` = v0 . We replace every vertex v by a pair (v − , v + ), and every − (Fig. 2.1.5). The resulting bipartite edge ei = vi vi+1 by the edge vi+ vi+1 0 graph G is k-regular, so by Corollary 2.1.4 it has a 1-factor. Collapsing every vertex pair (v − , v + ) back into a single vertex v, we turn this 1¤ factor of G0 into a 2-factor of G.
v− v v+
Fig. 2.1.5. Splitting vertices in the proof of Corollary 2.1.5
2.2 Matching in general graphs CG q(G) Tutte’s condition
Given a graph G, let us denote by CG the set of its components, and by q(G) the number of its odd components, those of odd order. If G has a 1-factor, then clearly q(G − S) 6 |S|
for all S ⊆ V (G),
since every odd component of G − S will send a factor edge to S.
Fig. 2.2.1. Tutte’s condition q(G − S) 6 |S| for q = 3, and the contracted graph HS from Theorem 2.2.3.
Again, this obvious necessary condition for the existence of a 1-factor is also sufficient:
2.2 Matching in general graphs
Theorem 2.2.1. (Tutte 1947) A graph G has a 1-factor if and only if q(G − S) 6 |S| for all S ⊆ V (G). Proof . Let G = (V, E) be a graph without a 1-factor. Our task is to find a bad set S ⊆ V , one that violates Tutte’s condition. We may assume that G is edge-maximal without a 1-factor. Indeed, if G0 is obtained from G by adding edges and S ⊆ V is bad for G0 , then S is also bad for G: any odd component of G0 − S is the union of components of G − S, and one of these must again be odd. What does G look like? Clearly, if G contains a bad set S then, by its edge-maximality and the trivial forward implication of the theorem, all the components of G − S are complete and every vertex s ∈ S is adjacent to all the vertices of G − s.
V, E bad set
(∗)
But also conversely, if a set S ⊆ V satisfies (∗) then either S or the empty set must be bad: if S is not bad we can join the odd components of G − S disjointly to S and pair up all the remaining vertices—unless |G| is odd, in which case ∅ is bad. So it suffices to prove that G has a set S of vertices satisfying (∗). Let S be the set of vertices that are adjacent to every other vertex. If this set S does not satisfy (∗), then some component of G − S has nonadjacent vertices a, a0 . Let a, b, c be the first three vertices on a shortest a–a0 path in this component; then ab, bc ∈ E but ac ∈/ E. Since b ∈/ S, there is a vertex d ∈ V such that bd ∈/ E. By the maximality of G, there is a matching M1 of V in G + ac, and a matching M2 of V in G + bd.
S a, b, c d M1 , M 2
a d 1
Fig. 2.2.2. Deriving a contradiction if S does not satisfy (∗)
Let P = d . . . v be a maximal path in G starting at d with an edge from M1 and containing alternately edges from M1 and M2 (Fig. 2.2.2). If the last edge of P lies in M1 , then v = b, since otherwise we could continue P . Let us then set C := P + bd. If the last edge of P lies in M2 , then by the maximality of P the M1 -edge at v must be ac, so v ∈ { a, c }; then let C be the cycle dP vbd. In each case, C is an even cycle with every other edge in M2 , and whose only edge not in E is bd. Replacing in M2 its edges on C with the edges of C − M2 , we obtain a matching of V contained in E, a contradiction. ¤
Corollary 2.2.2. (Petersen 1891) Every bridgeless cubic graph has a 1-factor. Proof . We show that any bridgeless cubic graph G satisfies Tutte’s condition. Let S ⊆ V (G) be given, and consider an odd component C of G − S. Since G is cubic, the degrees (in G) of the vertices in C sum to an odd number, but only an even part of this sum arises from edges of C. So G has an odd number of S–C edges, and therefore has at least 3 such edges (since G has no bridge). The total number of edges between S and G − S thus is at least 3q(G − S). But it is also at most 3|S|, because G is cubic. Hence q(G − S) 6 |S|, as required. ¤
factorcritical matchable
In order to shed a little more light on the techniques used in matching theory, we now give a second proof of Tutte’s theorem. In fact, we shall prove a slightly stronger result, a result that places a structure interesting from the matching point of view on an arbitrary graph. If the graph happens to satisfy the condition of Tutte’s theorem, this structure will at once yield a 1-factor. A graph G = (V, E) is called factor-critical if G 6= ∅ and G − v has a 1-factor for every vertex v ∈ G. Then G itself has no 1-factor, because it has odd order. We call a vertex set S ⊆ V matchable to G − S if the (bipartite1 ) graph HS , which arises from G by contracting the components C ∈ CG−S to single vertices and deleting all the edges inside S, contains a matching of S. (Formally, HS is the graph with vertex set S ∪ CG−S and edge set { sC | ∃ c ∈ C : sc ∈ E }; see Fig. 2.2.1.) Theorem 2.2.3. Every graph G = (V, E) contains a vertex set S with the following two properties: (i) S is matchable to G − S; (ii) every component of G − S is factor-critical. Given any such set S, the graph G contains a 1-factor if and only if |S| = |CG−S |. For any given G, the assertion of Tutte’s theorem follows easily from this result. Indeed, by (i) and (ii) we have |S| 6 |CG−S | = q(G − S) (since factor-critical graphs have odd order); thus Tutte’s condition of q(G − S) 6 |S| implies |S| = |CG−S |, and the existence of a 1-factor follows from the last statement of Theorem 2.2.3.
Proof of Theorem 2.2.3. Note first that the last assertion of the theorem follows at once from the assertions (i) and (ii): if G has a 1-factor, we have q(G − S) 6 |S| and hence |S| = |CG−S | as above; 1
except for the—permitted—case that S or CG−S is empty
conversely if |S| = |CG−S |, then the existence of a 1-factor follows straight from (i) and (ii). We now prove the existence of a set S satisfying (i) and (ii). We apply induction on |G|. For |G| = 0 we may take S = ∅. Now let G be given with |G| > 0, and assume the assertion holds for graphs with fewer vertices. Let d be the least non-negative integer such that q(G − T ) 6 |T | + d
for every T ⊆ V .
Then there exists a set T for which equality holds in (∗): this follows from the minimality of d if d > 0, and from q(G − ∅) > |∅| + 0 if d = 0. Let S be such a set T of maximum cardinality, and let C := CG−S . We first show that every component C ∈ C is odd. If |C| is even, pick a vertex c ∈ C, and let S 0 := S ∪ { c } and C 0 := C − c. Then C 0 has odd order, and thus has at least one odd component. Hence, q(G − S 0 ) > q(G − S) + 1. Since T := S satisfies (∗) with equality, we obtain q(G − S 0 ) > q(G − S) + 1 = |S| + d + 1 = |S 0 | + d > q(G − S 0 ) (∗)
with equality, which contradicts the maximality of S. Next we prove the assertion (ii), that every C ∈ C is factor-critical. Suppose there exist C ∈ C and c ∈ C such that C 0 := C − c has no 1-factor. By the induction hypothesis (and the fact that, as shown earlier, for fixed G our theorem implies Tutte’s theorem) there exists a set T 0 ⊆ V (C 0 ) with q(C 0 − T 0 ) > |T 0 | . Since |C| is odd and hence |C 0 | is even, the numbers q(C 0 − T 0 ) and |T 0 | are either both even or both odd, so they cannot differ by exactly 1. We may therefore sharpen the above inequality to q(C 0 − T 0 ) > |T 0 | + 2 . For T := S ∪ { c } ∪ T 0 we thus obtain q(G − T ) = q(G − S) − 1 + q(C 0 − T 0 ) > |S| + d − 1 + |T 0 | + 2 = |T | + d > q(G − T )
with equality, again contradicting the maximality of S. It remains to show that S is matchable to G − S. If S = ∅, this is trivial, so we assume that S 6= ∅. Since T := S satisfies (∗) with
S, C
equality, this implies that C too is non-empty. We now apply Corollary 2.1.3 to H := HS , but ‘backwards’, i.e. with A := C. Given C 0 ⊆ C, set S 0 := NH (C 0 ) ⊆ S. Since every C ∈ C 0 is an odd component also of G − S 0 , we have |NH (C 0 )| = |S 0 | > q(G − S 0 ) − d > |C 0 | − d . (∗)
By Corollary 2.1.3, then, H contains a matching of cardinality |C| − d = q(G − S) − d = |S| , which is therefore a matching of S. S C kS , k C
Let us consider once more the set S from Theorem 2.2.3, together with any matching M in G. As before, we write C := CG−S . Let us denote by kS the number of edges in M with at least one end in S, and by kC the number of edges in M with both ends in G − S. Since each C ∈ C is odd, at least one of its vertices is not incident with an edge of the second type. Therefore every matching M satisfies ³ ´ kS 6 |S| and kC 6 12 |V | − |S| − |C| . (1) Moreover, G contains a matching S M0 with equality in both cases: first choose |S| edges between S and ¡ ¢ C according to (i), and then use (ii) to find a suitable set of 12 |C| − 1 edges in every component C ∈ C. This matching M0 thus has exactly ³ ´ |M0 | = |S| + 12 |V | − |S| − |C| (2) edges. Now (1) and (2) together imply that every matching M of maximum cardinality satisfies both parts¡ of (1) with equality: by |M | > |M0 | ¢ and (2), M has at least |S| + 12 |V | − |S| − |C| edges, which implies by (1) that neither of the inequalities in (1) can be strict. But equality in (1), in turn, implies that M has the structure described above: by kS = |S|, every ¡vertex s ∈ S is ¢the end of an edge ¢st ∈ M with t ∈ G − S, and by kC = 12 |V | − |S| − |C| exactly 12 (|C| − 1 edges of M lie in C, for every C ∈ C. Finally, since these latter edges miss only one vertex in each C, the ends t of the edges st above lie in different components C for different s. The seemingly technical Theorem 2.2.3 thus hides a wealth of structural information: it contains the essence of a detailed description of all maximum-cardinality matchings in all graphs.2 2 A reference to the full statement of this structural result, known as the GallaiEdmonds matching theorem, is given in the notes at the end of this chapter.
2.3 Path covers
2.3 Path covers Let us return for a moment to K¨ onig’s duality theorem for bipartite graphs, Theorem 2.1.1. If we orient every edge of G from A to B, the theorem tells us how many disjoint directed paths we need in order to cover all the vertices of G: every directed path has length 0 or 1, and clearly the number of paths in such a ‘path cover’ is smallest when it contains as many paths of length 1 as possible—in other words, when it contains a maximum-cardinality matching. In this section we put the above question more generally: how many paths in a given directed graph will suffice to cover its entire vertex set? Of course, this could be asked just as well for undirected graphs. As it turns out, however, the result we shall prove is rather more trivial in the undirected case (exercise), and the directed case will also have an interesting corollary. A directed path is a directed graph P 6= ∅ with distinct vertices x0 , . . . , xk and edges e0 , . . . , ek−1 such that ei is an edge directed from xi to xi+1 , for all i < k. We denote the last vertex xk of P by ter(P ). In this section, path will always mean ‘directed path’. A path cover of a directed graph G is a set of disjoint paths in G which together contain all the vertices of G. Let us denote the maximum cardinality of an independent set of vertices in G by α(G).
ter(P ) path path cover α(G)
Theorem 2.3.1. (Gallai & Milgram 1960) Every directed graph G has a path cover by at most α(G) paths. Proof . Given two path covers P1 , P2 of a graph, we write P1 < P2 if { ter(P ) | P ∈ P1 } ⊆ { ter(P ) | P ∈ P2 } and |P1 | < |P2 |. We shall prove the following: If P is a <-minimal path cover of G, then G contains an independent set { vP | P ∈ P } of vertices with vP ∈ P for every P ∈ P.
P1 < P 2
Clearly, (∗) implies the assertion of the theorem. We prove (∗) by induction on |G|. Let P = { P1 , . . . , Pm } be given as in (∗), and let vi := ter(Pi ) for every i. If { vi | 1 6 i 6 m } is independent, there is nothing more to show; we may therefore assume that G has an edge from v2 to v1 . Since P2 v2 v1 is again a path, the minimality of P implies that v1 is not the only vertex of P1 ; let v be the vertex preceding v1 on P1 . Then P 0 := { P1 v, P2 , . . . , Pm } is a path cover of G0 := G − v1 (Fig. 2.3.1). We first show that P 0 is <-minimal with this property. Suppose that P 00 < P 0 is another path cover of G0 . If a path P ∈ P 00 ends in v, we may replace P in P 00 by P vv1 to obtain a smaller path cover of G than P, a contradiction to the minimality of P. If a path
P, Pi , m vi
v P0 G0
v1 v
... P1
Fig. 2.3.1. The path cover P 0 of G0
P ∈ P 00 ends in v2 (but none in v), we replace P in P 00 by P v2 v1 , again contradicting the minimality of P. Hence { ter(P ) | P ∈ P 00 } ⊆ { v3 , . . . , vm }, and in particular |P 00 | 6 |P| − 2. But now P 00 and the trivial path { v1 } together form a path cover of G that contradicts the minimality of P. Hence P 0 is minimal, as claimed. By the induction hypothesis, { V (P ) | P ∈ P 0 } has an independent set of representatives. But this is also a set of representatives for P, and (∗) is proved. ¤
chain antichain
As a corollary to Theorem 2.3.1 we now deduce a classic result from the theory of partial orders. Recall that a subset of a partially ordered set (P, 6) is a chain in P if its elements are pairwise comparable; it is an antichain if they are pairwise incomparable. Corollary 2.3.2. (Dilworth 1950) In every finite partially ordered set (P, 6), the minimum number of chains covering P is equal to the maximum cardinality of an antichain in P . Proof . If A is an antichain in P of maximum cardinality, then clearly P cannot be covered by fewer than |A| chains. The fact that |A| chains will suffice follows from Theorem 2.3.1 applied to the directed graph on P with the edge set { (x, y) | x < y }. ¤
Exercises 1.
Let M be a matching in a bipartite graph G. Show that if M is suboptimal, i.e. contains fewer edges than some other matching in G, then G contains an augmenting path with respect to M . Does this fact generalize to matchings in non-bipartite graphs? (Hint. Symmetric difference.)
Describe an algorithm that finds, as efficiently as possible, a matching of maximum cardinality in any bipartite graph.
Find an infinite counterexample to the statement of the marriage theorem.
Let k be an integer. Show that any two partitions of a finite set into k-sets admit a common choice of representatives.
Let A be a finite set with subsets A1 , . . . , An , and let d1 , . . . , dn ∈ N. Show that there are disjoint subsets Dk ⊆ Ak , with |Dk | = dk for all k 6 n, if and only if
¯[ ¯ X ¯ ¯ Ai ¯ > di ¯ i∈I
i∈I
for all I ⊆ { 1, . . . , n }. 6.+ Prove Sperner’s lemma: in an n-set X there are never more than subsets such that none of these contains another. (Hint. Construct
n bn/2c
chains covering the power set lattice of X.)
Find a set S for Theorem 2.2.3 when G is a forest.
Using (only) Theorem 2.2.3, show that a k-connected graph with at least 2k vertices contains a matching of size k. Is this best possible?
A graph G is called (vertex-) transitive if, for any two vertices v, w ∈ G, there is an automorphism of G mapping v to w. Using the observations following the proof of Theorem 2.2.3, show that every transitive connected graph is either factor-critical or contains a 1-factor. (Hint. Consider the cases of S = ∅ and S 6= ∅ separately.)
Show that a graph G contains k independent edges if and only if q(G − S) 6 |S| + |G| − 2k for all sets S ⊆ V (G). (Hint. For the ‘if’ direction, suppose that G has no k independent edges, and apply Tutte’s 1-factor theorem to the graph G ∗ K |G|−2k . Alternatively, use Theorem 2.2.3.)
11.− Find a cubic graph without a 1-factor. 12.
Derive the marriage theorem from Tutte’s theorem.
13.− Prove the undirected version of the theorem of Gallai & Milgram (without using the directed version). 14. −
Derive the marriage theorem from the theorem of Gallai & Milgram.
Show that a partially ordered set of at least rs + 1 elements contains either a chain of size r + 1 or an antichain of size s + 1.
Prove the following dual version of Dilworth’s theorem: in every finite partially ordered set (P, 6), the minimum number of antichains covering P is equal to the maximum cardinality of a chain in P .
Derive K¨ onig’s theorem from Dilworth’s theorem.
18.+ Find a partially ordered set that has no infinite antichain but cannot be covered by finitely many chains. (Hint. N × N.)
Notes There is a very readable and comprehensive monograph about matching in finite graphs: L. Lov´ asz & M.D. Plummer, Matching Theory, Annals of Discrete Math. 29, North Holland 1986. All the references for the results in this chapter can be found there. As we shall see in Chapter 3, K¨ onig’s Theorem of 1931 is no more than the bipartite case of a more general theorem due to Menger, of 1929. At the time, neither of these results was nearly as well known as Hall’s marriage theorem, which was proved even later, in 1935. To this day, Hall’s theorem remains one of the most applied graph-theoretic results. Its special case that both partition sets have the same size was proved implicitly already by Frobenius (1917) in a paper on determinants. Our proof of Tutte’s 1-factor theorem is based on a proof by Lov´ asz (1975). Our extension of Tutte’s theorem, Theorem 2.2.3 (including the informal discussion following it) is a lean version of a comprehensive structure theorem for matchings, due to Gallai (1964) and Edmonds (1965). See Lov´ asz & Plummer for a detailed statement and discussion of this theorem. Theorem 2.3.1 is due to T. Gallai & A.N. Milgram, Verallgemeinerung eines graphentheoretischen Satzes von R´edei, Acta Sci. Math. (Szeged) 21 (1960), 181–186.
Our definition of k-connectedness, given in Chapter 1.4, is somewhat unintuitive. It does not tell us much about ‘connections’ in a k-connected graph: all it says is that we need at least k vertices to disconnect it. The following definition—which, incidentally, implies the one above—might have been more descriptive: ‘a graph is k-connected if any two of its vertices can be joined by k independent paths’. It is one of the classic results of graph theory that these two definitions are in fact equivalent, are dual aspects of the same property. We shall study this theorem of Menger (1927) in some depth in Section 3.3. In Sections 3.1 and 3.2, we investigate the structure of the 2-connected and the 3-connected graphs. For these small values of k it is still possible to give a simple general description of how these graphs can be constructed. In the remaining sections of this chapter we look at other concepts of connectedness, more recent than the standard one but no less important: the number of H-paths in a graph for a given subgraph H; the number of edge-disjoint spanning trees; and the existence of disjoint paths linking up several given pairs of vertices.
3.1 2-Connected graphs and subgraphs A maximal connected subgraph without a cutvertex is called a block . Thus, every block of a graph G is either a maximal 2-connected subgraph, or a bridge (with its ends), or an isolated vertex. Conversely, every such subgraph is a block. By their maximality, different blocks of G overlap in at most one vertex, which is then a cutvertex of G. Hence, every edge of G lies in a unique block, and G is the union of its blocks. In a sense, blocks are the 2-connected analogues of components, the maximal connected subgraphs of a graph. While the structure of G is
block graph
3. Connectivity
determined fully by that of its components, however, it is not captured completely by the structure of its blocks: since the blocks need not be disjoint, the way they intersect defines another structure, giving a coarse picture of G as if viewed from a distance. The following proposition describes this coarse structure of G as formed by its blocks. Let A denote the set of cutvertices of G, and B the set of its blocks. We then have a natural bipartite graph on A ∪ B formed by the edges aB with a ∈ B. This block graph of G is shown in Figure 3.1.1.
Fig. 3.1.1. A graph and its block graph
Proposition 3.1.1. The block graph of a connected graph is a tree. ¤ Proposition 3.1.1 reduces the structure of a given graph to that of its blocks. So what can we say about the blocks themselves? The following proposition gives a simple method by which, in principle, a list of all 2-connected graphs could be compiled: [ 4.2.5 ]
Proposition 3.1.2. A graph is 2-connected if and only if it can be constructed from a cycle by successively adding H-paths to graphs H already constructed (Fig. 3.1.2).
Fig. 3.1.2. The construction of 2-connected graphs
3.1 2-Connected graphs and subgraphs
Proof . Clearly, every graph constructed as described is 2-connected. Conversely, let a 2-connected graph G be given. Then G contains a cycle, and hence has a maximal subgraph H constructible as above. Since any edge xy ∈ E(G) r E(H) with x, y ∈ H would define an Hpath, H is an induced subgraph of G. Thus if H 6= G, then by the connectedness of G there is an edge vw with v ∈ G − H and w ∈ H. As G is 2-connected, G − w contains a v–H path P . Then wvP is an H-path in G, and H ∪ wvP is a constructible subgraph of G larger than H. This contradicts the maximality of H. ¤
3.2 The structure of 3-connected graphs We start this section with the analogue of Proposition 3.1.2 for 3connectedness: our first theorem describes how every 3-connected graph can be obtained from a K 4 by a succession of elementary operations preserving 3-connectedness. We then prove a deep result of Tutte about the algebraic structure of the cycle space of 3-connected graphs; this will play an important role again in Chapter 4.5. Lemma 3.2.1. If G is 3-connected and |G| > 4, then G has an edge e such that G/e is again 3-connected.
Proof . Suppose there is no such edge e. Then, for every edge xy ∈ G, the graph G/xy contains a separating set S of at most 2 vertices. Since κ(G) > 3, the contracted vertex vxy of G/xy (see Chapter 1.7) lies in S and |S| = 2, i.e. G has a vertex z ∈/ { x, y } such that { vxy , z } separates G/xy. Then any two vertices separated by { vxy , z } in G/xy are separated in G by T := { x, y, z }. Since no proper subset of T separates G, every vertex in T has a neighbour in every component C of G − T . We choose the edge xy, the vertex z, and the component C so that |C| is as small as possible, and pick a neighbour v of z in C (Fig. 3.2.1).
Fig. 3.2.1. Separating vertices in the proof of Lemma 3.2.1
By assumption, G/zv is again not 3-connected, so again there is a vertex w such that { z, v, w } separates G, and as before every vertex in { z, v, w } has a neighbour in every component of G − { z, v, w }. As x and y are adjacent, G − { z, v, w } has a component D such that D ∩ { x, y } = ∅. Then every neighbour of v in D lies in C (since v ∈ C), so D ∩ C 6= ∅ and hence D $ C by the choice of D. This contradicts the choice of xy, z and C. ¤ Theorem 3.2.2. (Tutte 1961) A graph G is 3-connected if and only if there exists a sequence G0 , . . . , Gn of graphs with the following properties: (i) G0 = K 4 and Gn = G; (ii) Gi+1 has an edge xy with d(x), d(y) > 3 and Gi = Gi+1 /xy, for every i < n.
xy S C1 , C 2
Proof . If G is 3-connected, a sequence as in the theorem exists by Lemma 3.2.1. Note that all the graphs in this sequence are 3-connected. Conversely, let G0 , . . . , Gn be a sequence of graphs as stated; we show that if Gi = Gi+1 /xy is 3-connected then so is Gi+1 , for every i < n. Suppose not, let S be a separating set of at most 2 vertices in Gi+1 , and let C1 , C2 be two components of Gi+1 − S. As x and y are adjacent, we may assume that { x, y } ∩ V (C1 ) = ∅ (Fig. 3.2.2). Then C2 contains neiy
C1 Fig. 3.2.2. The position of xy rem 3.2.2
Gi+1 in the proof of Theo-
ther both vertices x, y nor a vertex v ∈/ { x, y }: otherwise vxy or v would be separated from C1 in Gi by at most two vertices, a contradiction. But now C2 contains only one vertex: either x or y. This contradicts our assumption of d(x), d(y) > 3. ¤ Theorem 3.2.2 is the essential core of a result of Tutte known as his wheel theorem.1 Like Proposition 3.1.2 for 2-connected graphs, it enables us to construct all 3-connected graphs by a simple inductive process depending only on local information: starting with K 4 , we pick a vertex v in a graph constructed already, split it into two adjacent vertices v 0 , v 00 , and join these to the former neighbours of v as we please—provided only that v 0 and v 00 each acquire at least 3 incident edges, and that every former neighbour of v becomes adjacent to at least one of v 0 , v 00 . wheel
Graphs of the form C n ∗ K 1 are called wheels; thus, K 4 is the smallest wheel.
3.2 The structure of 3-connected graphs
Theorem 3.2.3. (Tutte 1963) The cycle space of a 3-connected graph is generated by its non-separating induced cycles. Proof . We apply induction on the order of the graph G considered. In K 4 , every cycle is a triangle or (in terms of edges) the symmetric difference of triangles. As these are both induced and non-separating, the assertion holds for |G| = 4. For the induction step, let e = xy be an edge of G for which G0 := G/e is again 3-connected; cf. Lemma 3.2.1. Then every edge e0 ∈ E(G0 ) r E(G) is of the form e0 = uve , where at least one of the two edges ux and uy lies in G. We pick one that does (either ux or uy), and identify it notationally with the edge e0 ; thus e0 now denotes both the edge uve of G0 and one of the two edges ux, uy. In this way we may regard E(G0 ) as a subset of E(G), and E(G0 ) as a subspace of E(G); thus all vector operations will take place unambiguously in E(G). Let us consider an induced cycle C ⊆ G. If e ∈ C and C = C 3 , we call C a fundamental triangle; then C/e = K 2 . If e ∈ C but C 6= C 3 , then C/e is a cycle in G0 . Finally if e ∈/ C, then at most one of x, y lies on C (otherwise e would be a chord), so the vertices of C in order also form a cycle in G0 if we replace x or y by ve ; this cycle, too, will be denoted by C/e. Thus, as long as C is not a fundamental triangle, C/e will always denote a unique cycle in G0 . Note, however, that in the case of e ∈/ C the edge set of C/e when viewed as a subset of E(G) need not coincide with E(C), or even be a cycle at all; an example is shown in Figure 3.2.3. x u
w y C
e0 ve
x w
e = xy G0
fundamental triangle
e00 w
e0 y E(C/e) ⊆ G
Fig. 3.2.3. One of the four possibilities for E(C/e) when e ∈/ C
Let us refer to the non-separating induced cycles in G or G0 as basic cycles. An element of C(G) will be called good if it is a linear combination of basic cycles in G; we thus want to show that every element of C(G) is good. The basic idea of our proof is to contract a given cycle C ∈ C(G) to C/e, generate C/e in C(G0 ) by induction, and try to lift the generators back to basic cycles in G that generate C. We start by proving three auxiliary facts. Every fundamental triangle is a basic cycle in G.
basic cycles good
A fundamental triangle, wxyw say, is clearly induced in G. If it separated G, then { ve , w } would separate G0 , which contradicts the choice of e. This proves (1). If C ⊆ G is an induced cycle but not a fundamental triangle, then C + C/e + D ∈ { ∅, {e} } for some good D ∈ C(G).
The gist of (2) is that, in terms of ‘generatability’, C and C/e differ only a little: after the addition of a permissible error term D, at most in the edge e. In which other edges, then, can C and C/e differ? Clearly at most in the two edges eu = uve and ew = ve w incident with ve in C/e; cf. Fig. 3.2.3. But these differences between the edge sets of C/e and C are levelled out precisely by adding the corresponding fundamental triangles uxy and xyw (which are basic by (1)). Indeed, let Du denote the triangle uxy if eu ∈/ C and ∅ otherwise, and let Dw denote xyw if ew ∈/ C and ∅ otherwise. Then D := Du + Dw satisfies (2) as desired. Next, we show how to lift basic cycles of G0 back to G: For every basic cycle C 0 ⊆ G0 there exists a basic cycle C = C(C 0 ) ⊆ G with C/e = C 0 .
u, w P
If ve ∈/ C 0 , then (3) is satisfied with C := C 0 . So we assume that ve ∈ C 0 . Let u and w be the two neighbours of ve on C 0 , and let P be the u–w path in C 0 avoiding ve (Fig. 3.2.4). Then P ⊆ G. x u
w y P
Fig. 3.2.4. The search for a basic cycle C with C/e = C 0
Cx , C y
We first assume that { ux, uy, wx, wy } ⊆ E(G), and consider (as candidates for C) the cycles Cx := uP wxu and Cy := uP wyu. Both are induced cycles in G (because C 0 is induced in G0 ), and clearly Cx /e = Cy /e = C 0 . Moreover, neither of these cycles separates two vertices of G − (V (P ) ∪ { x, y }) in G, since C 0 does not separate such vertices in G0 . Thus, if Cx (say) is a separating cycle in G, then one of the components of G − Cx consists just of y. Likewise, if Cy separates G then one of the arising components contains only x. However, this cannot happen for both Cx and Cy at once: otherwise NG ({ x, y }) ⊆ V (P ) and hence NG ({ x, y }) = { u, w } (since C 0 has no chord), which contradicts κ(G) > 3. Hence, at least one of Cx , Cy is a basic cycle in G.
It remains to consider the case that { ux, uy, wx, wy } 6⊆ E(G), say ux ∈/ E(G). Then, as above, either uP wyu or uP wxyu is a basic cycle in G, according as wy is an edge of G or not. This completes the proof of (3). We now come to the main part of our proof, the proof that every C ∈ C(G) is good. By Proposition 1.9.1 we may assume that C is an induced cycle in G. By (1) we may further assume that C is not a fundamental triangle; so C/e is a cycle. Our aim is to argue as follows. By (2), C differs from C/e at most by some good error term D (and possibly in e); by (3), the basic cycles Ci0 of G0 that sum to C/e by induction can be contracted from basic cycles of G, which likewise differ from the Ci0 only by a good error term Di (and possibly in e); hence these basic cycles of G and all the error terms together sum to C—except that the edge e will need some special attention. By the induction hypothesis, C/e has a representation C/e = C10 + . . . + Ck0
C10 , . . . , Ck0
in C(G0 ), where every Ci0 is a basic cycle in G0 . For each i, we obtain from (3) a basic cycle C(Ci0 ) ⊆ G with C(Ci0 )/e = Ci0 (in particular, C(Ci0 ) is not a fundamental triangle), and from (2) some good Di ∈ C(G) such that C(Ci0 ) + Ci0 + Di
{ ∅, {e} } .
We let Ci := C(Ci0 ) + Di ;
C1 , . . . , C k
then Ci is good, and by (4) it differs from Ci0 at most in e. Again by (2), we have C + C/e + D
{ ∅, {e} }
for some good D ∈ C(G), i.e. C + D differs from C/e at most in e. But then C + D + C1 + . . . + Ck differs from C/e + C10 + . . . + Ck0 = ∅ at most in e, that is, C + D + C1 + . . . + Ck Since C + D + C1 + . . . + Ck fact
C(G) but {e} ∈/ C(G), this means that in
C + D + C 1 + . . . + Ck = ∅ , so C = D + C1 + . . . + Ck is good.
3.3 Menger’s theorem The following theorem is one of the cornerstones of graph theory. [ 3.6.2 ] [ 8.1.2 ] [ 12.3.9 ] [ 12.4.4 ] [ 12.4.5 ]
Theorem 3.3.1. (Menger 1927) Let G = (V, E) be a graph and A, B ⊆ V . Then the minimum number of vertices separating A from B in G is equal to the maximum number of disjoint A–B paths in G. We offer three proofs. Whenever G, A, B are given as in the theorem, we denote by k = k (G, A, B) the minimum number of vertices separating A from B in G. Clearly, G cannot contain more than k disjoint A–B paths; our task will be to show that k such paths exist. First proof. We prove the following stronger statement: If P is any set of fewer than k disjoint A–B paths in G then there is a set Q of |P| + 1 disjoint A–B paths whose set of ends includes the set of ends of the paths in P. Keeping G and A fixed, we let B vary and apply induction on |G − B|. Let R be an A–B path that avoids the (fewer than k) vertices of B that lie on a path in P. If R avoids all the paths in P, then Q := P ∪ { R } is as desired. (This will happen for |G − B| = 0 when all A–B paths are trivial.) If not, let x be the last vertex of R that ¡lies on some ¢ P ∈ P (Fig. 3.3.1). Put B 0 := B ∪ V (xP ∪ xR) and P 0 := P r { P } ∪ { P x }. Then |P 0 | = |P| and k(G, A, B 0 ) > k(G, A, B), so by the induction hypothesis there is a set Q0 of |P| + 1 disjoint A–B 0 paths whose ends include those of the paths in P 0 . Then Q0 contains a path Q ending in x, and a unique path Q0 whose last vertex y is not among the last vertices of the paths in P 0 . If y ∈/ xP , we let Q be obtained from Q0 by adding xP , and we let xP to Q, and adding yR to Q0 if y ∈/ B. Otherwise y ∈ ˚ ¤ Q be obtained from Q0 by adding xR to Q and adding yP to Q0 . R P
Fig. 3.3.1. Paths in the first proof of Menger’s theorem
3.3 Menger’s theorem
Second proof. We show by induction on |G| + kGk that G contains k disjoint A–B paths. For all G, A, B with k ∈ { 0, 1 } this is true. For the induction step let G, A, B with k > 2 be given, and assume that the assertion holds for graphs with fewer vertices or edges. If there is a vertex x ∈ A ∩ B, then G − x contains k − 1 disjoint A–B paths by the induction hypothesis. (Why?) Together with the trivial path { x }, these form the desired paths in G. We shall therefore assume that A∩B = ∅. (1) We first construct the desired paths for the case that A and B are separated by a set X ⊆ V with |X| = k and X 6= A, B. Let CA be the union of all the components of G − X meeting A; note that CA 6= ∅, since |A| > k = |X| but A 6= X. The subgraph CB defined likewise is not empty either, and CA ∩ CB = ∅. Let us write GA := G [ V (CA ) ∪ X ] and GB := G [ V (CB ) ∪ X ]. Since every A–B path in G contains an A–X path in GA , we cannot separate A from X in GA by fewer than k vertices. Thus, by the induction hypothesis, GA contains k disjoint A–X paths (Fig. 3.3.2). In the same way, there are k disjoint X–B paths in GB . As |X| = k, we can put these paths together to form k disjoint A–B paths.
X CA , C B GA , GB
X Fig. 3.3.2. Disjoint A–X paths in GA
For the general case, let P be any A–B path in G. By (1), P has an edge ab with a ∈/ B and b ∈/ A. Let Y be a set of as few vertices as possible separating A from B in G − ab (Fig. 3.3.3). Then Ya := Y ∪ { a } and Yb := Y ∪ { b } both separate A from B in G, and by definition of k we have |Ya |, |Yb | > k . If equality holds here, we may assume by the case already treated that { Ya , Yb } ⊆ { A, B }, so { Ya , Yb } = { A, B } since a ∈/ B and b ∈/ A. Thus, Y = A ∩ B. Since |Y | > k − 1 > 1, this contradicts (1). We therefore have either |Ya | > k or |Yb | > k, and hence |Y | > k. By the induction hypothesis, then, there are k disjoint A–B paths even in G − ab ⊆ G. ¤
ab Y Ya , Yb
b P
Fig. 3.3.3. Separating A from B in G − ab
Applied to a bipartite graph, Menger’s theorem specializes to the assertion of K¨ onig’s theorem (2.1.1). For our third proof, we now adapt the alternating path proof of K¨ onig’s theorem to the more general setup of Theorem 3.3.1. Let again G, A, B be given, and let P be a set of disjoint A–B paths in G. We write V [ P ] :=
{ V (P ) | P [ E [ P ] := { E(P ) | P
alternating walk
P}
P }.
A walk W = x0 e0 x1 e1 . . . en−1 xn in G with ei 6= ej for i 6= j is said to be alternating with respect to P if the following three conditions are satisfied for all i < n (Fig. 3.3.4): (i) if ei = e ∈ E [ P ], then W traverses the edge e backwards, i.e. xi+1 ∈ P˚ xi for some P ∈ P; (ii) if xi = xj with i 6= j, then xi (iii) if xi
V [ P ];
V [ P ], then { ei−1 , ei } ∩ E [ P ] 6= ∅.2
xn P
B A Fig. 3.3.4. An alternating walk from A to B
For i = 0 we let { ei−1 , ei } := { e0 }.
Let us consider a walk W = x0 e0 x1 e1 . . . en−1 xn from A r V [ P ] to B r V [ P ], alternating with respect to P. By (ii), any vertex outside V [ P ] occurs at most once on W . Since the edges ei of W are all distinct, (iii) implies that any vertex in V [ P ] occurs at most twice on W . This can happen in two ways: if xi = xj with 0 < i < j < n, say, then either ei−1 , ej
E [ P ] and ei , ej−1 ∈/ E [ P ]
or ei , ej−1
E [ P ] and ei−1 , ej ∈/ E [ P ] .
W, xi , ei
Lemma 3.3.2. If such a walk W exists, then G contains |P| + 1 disjoint A–B paths. Proof . Let H be the graph on V [ P ] ∪ { x0 , . . . , xn } whose edge set is the symmetric difference of E [ P ] with { e0 , . . . , en−1 }. In H, the ends of the paths in P and of W have degree 1 (or 0, if the path or W is trivial), and all other vertices have degree 0 or 2. For each of the |P| + 1 vertices a ∈ (A ∩ V [ P ]) ∪ { x0 }, therefore, the component of H containing a is a path, P = v0 . . . vk say, which starts in a and ends in A or B. Using conditions (i) and (iii), one easily shows by induction on i = 0, . . . , k − 1 that P traverses each of its edges e = vi vi+1 in the forward direction with respect to P or W . (Formally: if e ∈ P 0 with P 0 ∈ P, then vi ∈ P 0˚ vi+1 ; if e = ej ∈ W , then vi = xj and vi+1 = xj+1 .) Hence, P ends in B. As we have |P| + 1 disjoint such paths P , this completes the proof. ¤ Third proof of Menger’s theorem. Let P be a set of as many disjoint A–B paths in G as possible. Unless otherwise stated, all alternating walks considered are alternating with respect to P. We set
A1 := A ∩ V [ P ]
and A2 := A r A1 ,
A1 , A2
B1 := B ∩ V [ P ]
and B2 := B r B1 .
B1 , B 2
For every path P ∈ P, let xP be the last vertex of P that lies on some alternating walk starting in A2 ; if no such vertex exists, let xP be the first vertex of P . Clearly, the set X := { xP | P
has cardinality |P|; it thus suffices to show that X separates A from B. Let Q be any A–B path in G; we show that Q meets X. Suppose not. By the maximality of P, the path Q meets V [ P ]. Since the A– V [ P ] path in Q is trivially an alternating walk, Q also meets the vertex set V [ P 0 ] of P 0 := { P xP | P
P };
54 y, P x, W
let y be the last vertex of Q in V [ P 0 ], let P be the path in P containing y, and let x := xP . Finally, let W be an alternating walk from A2 to x, as in the definition of xP . By assumption, Q avoids X and hence x, so y ∈ P˚ x, and W ∪ xP yQ is a walk from A2 to B (Fig. 3.3.5). If this walk is alternating and ends in B2 , we are home: then G contains |P| + 1 disjoint A–B paths by Lemma 3.3.2, contrary to the maximality of P.
P y
W Fig. 3.3.5. Alternating walks in the third proof of Menger’s theorem
x0 , W 0
How could W ∪ xP yQ fail to be an alternating walk? For a start, W might already use an edge of xP y. But if x0 is the first vertex of W on xP˚ y , then W 0 := W x0 P y is an alternating walk from A2 to y. (By 0 W x we mean the initial segment of W ending at the first occurrence of x0 on W ; from there onwards, W 0 follows P back to y.) Even our new walk W 0 yQ need not yet be alternating: W 0 might still meet ˚ y Q. By definition of P 0 and W , however, and the choice of y on Q, we have V (W 0 ) ∩ V [ P ] ⊆ V [ P 0 ]
z W 00
and V (˚ y Q) ∩ V [ P 0 ] = ∅ .
Thus, W 0 and ˚ y Q can meet only outside P. y Q, let z be the first vertex of W 0 on ˚ y Q. As If W 0 does indeed meet ˚ z lies outside V [ P ], it occurs only once on W 0 (condition (ii)), and we let W 00 := W 0 zQ. On the other hand if W 0 ∩˚ y Q = ∅, we set W 00 := W 0 ∪ yQ. 00 In both cases, W is alternating with respect to P 0 , because W 0 is and ˚ yQ avoids V [ P 0 ]. (Note that W 00 satisfies condition (iii) at y in the second case, while in the first case (iii) is not applicable to z.) By definition of P 0 , therefore, W 00 avoids V [ P ] r V [ P 0 ]; in particular, V (˚ y Q) ∩ V [ P ] = ∅. Thus W 00 is also alternating with respect to P, and it ends in B2 . (Note that y cannot be the last vertex of W 00 , since y ∈ P˚ x and hence y ∈/ B.) Furthermore, W 00 starts in A2 , because W does. We may therefore use W 00 with Lemma 3.3.2 to obtain the desired contradiction to the maximality of P. ¤
A set of a–B paths is called an a–B fan if any two of the paths have only a in common.
Corollary 3.3.3. For B ⊆ V and a ∈ V r B, the minimum number of vertices 6= a separating a from B in G is equal to the maximum number of paths forming an a–B fan in G.
Proof . Apply Theorem 3.3.1 with A := N (a).
Corollary 3.3.4. Let a and b be two distinct vertices of G. (i) If ab ∈/ E, then the minimum number of vertices 6= a, b separating a from b in G is equal to the maximum number of independent a–b paths in G. (ii) The minimum number of edges separating a from b in G is equal to the maximum number of edge-disjoint a–b paths in G. Proof . (i) Apply Theorem 3.3.1 with A := N (a) and B := N (b). (ii) Apply Theorem 3.3.1 to the line graph of G, with A := E(a) and B := E(b). ¤ Theorem 3.3.5. (Global Version of Menger’s Theorem) (i) A graph is k-connected if and only if it contains k independent paths between any two vertices.
[ 4.2.10 ] [ 6.6.1 ] [ 9.4.2 ]
(ii) A graph is k-edge-connected if and only if it contains k edgedisjoint paths between any two vertices. Proof . (i) If a graph G contains k independent paths between any two vertices, then |G| > k and G cannot be separated by fewer than k vertices; thus, G is k-connected. Conversely, suppose that G is k-connected (and, in particular, has more than k vertices) but contains vertices a, b not linked by k independent paths. By Corollary 3.3.4 (i), a and b are adjacent; let G0 := G − ab. Then G0 contains at most k − 2 independent a–b paths. By Corollary 3.3.4 (i), we can separate a and b in G0 by a set X of at most k − 2 vertices. As |G| > k, there is at least one further vertex v ∈/ X ∪ { a, b } in G. Now X separates v in G0 from either a or b—say, from a. But then X ∪ { b } is a set of at most k − 1 vertices separating v from a in G, contradicting the k-connectedness of G. (ii) follows straight from Corollary 3.3.4 (ii). ¤
a, b G0 X v
3.4 Mader’s theorem
X F
CF ∂C
In analogy to Menger’s theorem we may consider the following question: given a graph G with an induced subgraph H, up to how many independent H-paths can we find in G? In this section, we present without proof a deep theorem of Mader, which solves the above problem in a fashion similar to Menger’s theorem. Again, the theorem says that an upper bound on the number of such paths that arises naturally from the size of certain separators is indeed attained by some suitable set of paths. What could such an upper bound look like? Clearly, if X ⊆ V (G − H) and F ⊆ E(G − H) are such that every H-path in G has a vertex or an edge in X ∪ F , then G cannot contain more than |X ∪ F | independent H-paths. Hence, the least cardinality of such a set X ∪ F is a natural upper bound for the maximum number of independent H-paths. (Note that every H-path meets G − H, because H is induced in G and edges of H do not count as H-paths.) In contrast to Menger’s theorem, this bound can still be improved. Clearly, we may assume that no edge in F has an end in X: otherwise this edge would not be needed in the separator. Let Y := V (G − H) r X, and denote by CF the set of components of the graph (Y, F ). Since every H-path avoiding X contains an edge from F , it has at least two vertices in ∂C for some C ∈ CF , where ∂C denotes the set of vertices in C with a neighbour in G − X − C (Fig. 3.4.1). The number of independent
C ∂C
Fig. 3.4.1. An H-path in G − X
MG (H)
H-paths in G is therefore bounded above by ³ X ¥ ¦´ 1 MG (H) := min |X| + , 2 |∂C| C ∈ CF
where the minimum is taken over all X and F as described above: X ⊆ V (G − H) and F ⊆ E(G − H − X) such that every H-path in G has a vertex or an edge in X ∪ F .
Now Mader’s theorem says that this upper bound is always attained by some set of independent H-paths: Theorem 3.4.1. (Mader 1978) Given a graph G with an induced subgraph H, there are always MG (H) independent H-paths in G. In order to obtain direct analogues to the vertex and edge version of Menger’s theorem, let us consider the two special cases of the above problem where either F or X is required to be empty. Given an induced subgraph H ⊆ G, we denote by κG (H) the least cardinality of a vertex set X ⊆ V (G − H) that meets every H-path in G. Similarly, we let λG (H) denote the least cardinality of an edge set F ⊆ E(G) that meets every H-path in G.
κG (H) λG (H)
Corollary 3.4.2. Given a graph G with an induced subgraph H, there are at least 12 κG (H) independent H-paths and at least 12 λG (H) edgedisjoint H-paths in G. Proof . To prove the first assertion, let k be the maximum number of independent H-paths in G. By Theorem 3.4.1, there are sets X ⊆ V (G − H) and F ⊆ E(G − H − X) with k = |X| +
X ¥ 1 2
|∂C|
C ∈ CF
such that every H-path in G has a vertex in X or an edge in F . For every C ∈ CF with ∂C 6= ∅, pick a¥ vertex¦ v ∈ ∂C and let YC := ∂C r { v }; if 1 1 ∈ ∂C = ∅, let S YC := ∅. Then 2 |∂C| > 2 |YC | for all C CF . Moreover, for Y := C ∈ CF YC every H-path has a vertex in X ∪ Y . Hence k > |X| +
|YC | >
|X ∪ Y | > 12 κG (H)
as claimed. The second assertion follows from the first by considering the line graph of G (Exercise 16). ¤ It may come as a surprise to see that the bounds in Corollary 3.4.2 are best possible (as general bounds): one can find examples for G and H where G contains no more than 12 κG (H) independent H-paths or no more than 12 λG (H) edge-disjoint H-paths (Exercises 17 and 18).
3.5 Edge-disjoint spanning trees
cross-edges
The edge version of Menger’s theorem tells us when a graph G contains k edge-disjoint paths between any two vertices. The actual routes of these paths within G may depend a lot on the choice of those two vertices: having found the paths for one pair of endvertices, we are not necessarily better placed to find them for another pair. In a situation where quick access to a set of k edge-disjoint paths between any two vertices is desirable, it may be a good idea to ask for more than just k-edge-connectedness. For example, if G has k edgedisjoint spanning trees, there will be k canonical such paths between any two vertices, one in each tree. When do such trees exist? If they do, the graph is clearly k-edgeconnected. The converse is easily seen to be false; indeed, it is not even clear whether any edge-connectivity, however large, will imply the existence of k edge-disjoint spanning trees. Our first aim in this section will be to study conditions under which k edge-disjoint spanning trees exist. As before, it is easy to write down some obvious necessary conditions for the existence of k edge-disjoint spanning trees. With respect to any partition of V (G) into r sets, every spanning tree of G has at least r − 1 cross-edges, edges whose ends lie in different partition sets (why?). Thus if G has k edge-disjoint spanning trees, it has at least k (r − 1) crossedges. Once more, this obvious necessary condition is also sufficient: Theorem 3.5.1. (Tutte 1961; Nash-Williams 1961) A multigraph contains k edge-disjoint spanning trees if and only if for every partition P of its vertex set it has at least k (|P | − 1) cross-edges. Before we prove Theorem 3.5.1, let us note a surprising corollary: to ensure the existence of k edge-disjoint spanning trees, it suffices to raise the edge-connectivity to just 2k:
Corollary 3.5.2. Every 2k-edge-connected multigraph G has k edgedisjoint spanning trees. Proof . Every set in a vertex partition of G is joined to other partition sets by at P least 2k edges. Hence, for any partition into r sets, G has r at least 12 i=1 2k = kr cross-edges. The assertion thus follows from Theorem 3.5.1. ¤
G = (V, E) k, F
For the proof of Theorem 3.5.1, let a multigraph G = (V, E) and k ∈ N be given. Let F be the set of all k-tuples F = (F1 , . . . , Fk ) of edge-disjoint spanning forests in G with the maximum total number of
¯ ¯ edges, i.e. such that kF k := ¯E [ F ]¯ with E [ F ] := E(F1 ) ∪ . . . ∪ E(Fk ) is as large as possible. If F = (F1 , . . . , Fk ) ∈ F and e ∈ E r E [ F ], then every Fi + e contains a cycle (i = 1, . . . , k): otherwise we could replace Fi by Fi + e in F and obtain a contradiction to the maximality of kF k. Let us consider an edge e0 6= e of this cycle, for some fixed i. Putting Fi0 := Fi + e − e0 , and Fj0 := Fj for all j 6= i, we see that F 0 := (F10 , . . . , Fk0 ) is again in F; we say that F 0 has been obtained from F by the replacement of the edge e0 with e. Note that the component of Fi containing e0 keeps its vertex set when it changes into a component of Fi0 . Hence for every path x . . . y ⊆ Fi0 there is a unique path xFi y in Fi ; this will be used later. We now consider a fixed k-tuple F 0 = (F10 , . . . , Fk0 ) ∈ F. The set of all k-tuples in F that can be obtained from F 0 by a series of edge replacements will be denoted by F 0 . Finally, we let [ E 0 := (E r E [ F ]) F
and G0 := (V, E 0 ).
E[F ], kF k
edge replacement
xFi y F0 F0 E0
∈F 0
Lemma 3.5.3. For every e0 ∈ E r E [ F 0 ] there exists a set U ⊆ V that is connected in every Fi0 ( i = 1, . . . , k) and contains the ends of e0 . Proof . As F 0 ∈ F 0 , we have e0 ∈ E 0 ; let C 0 be the component of G0 containing e0 . We shall prove the assertion for U := V (C 0 ). Let i ∈ { 1, . . . , k } be given; we have to show that U is connected in Fi0 . To this end, we first prove the following: Let F = (F1 , . . . , Fk ) ∈ F 0 , and let (F10 , . . . , Fk0 ) have been obtained from F by the replacement of an edge of Fi . If x, y are the ends of a path in Fi0 ∩ C 0 , then also xFi y ⊆ C 0 .
Let e = vw be the new edge in E(Fi0 ) r E [ F ]; this is the only edge of Fi0 not lying in Fi . We assume that e ∈ xFi0 y: otherwise we would have xFi y = xFi0 y and nothing to show. It suffices to show that vFi w ⊆ C 0 : then (xFi0 y − e) ∪ vFi w is a connected subgraph of Fi ∩ C 0 that contains x, y, and hence also xFi y. Let e0 be any edge of vFi w. Since we could replace e0 in F ∈ F 0 by e and obtain an element of F 0 not containing e0 , we have e0 ∈ E 0 . Thus vFi w ⊆ G0 , and hence vFi w ⊆ C 0 since v, w ∈ xFi0 y ⊆ C 0 . This proves (1). In order to prove that U = V (C 0 ) is connected in Fi0 we show that, for every edge xy ∈ C 0 , the path xFi0 y exists and lies in C 0 . As C 0 is connected, the union of all these paths will then be a connected spanning subgraph of Fi0 [ U ]. So let e = xy ∈ C 0 be given. As e ∈ E 0 , there exist an s ∈ N and k-tuples F r = (F1r , . . . , Fkr ) for r = 1, . . . , s such that each F r is obtained from F r−1 by edge replacement and e ∈ E r E [ F s ]. Setting
C0 U i
F := F s in (1), we may think of e as a path of length 1 in Fi0 ∩ C 0 . Successive applications of (1) to F = F s , . . . , F 0 then give xFi0 y ⊆ C 0 as desired. ¤ (1.5.3)
Proof of Theorem 3.5.1. We prove the backward implication by induction on |G|. For |G| = 2 the assertion holds. For the induction step, we now suppose that for every partition P of V there are at least k (|P | − 1) cross-edges, and construct k edge-disjoint spanning trees in G. Pick a k-tuple F 0 = (F10 , . . . , Fk0 ) ∈ F. If every Fi0 is a tree, we are done. If not, we have kF 0 k =
kFi0 k < k (|G| − 1)
i=1
e0 U
graph partition
by Corollary 1.5.3. On the other hand, we have kGk > k (|G| − 1) by assumption: consider the partition of V into single vertices. So there exists an edge e0 ∈ E r E [ F 0 ]. By Lemma 3.5.3, there exists a set U ⊆ V that is connected in every Fi0 and contains the ends of e0 ; in particular, |U | > 2. Since every partition of the contracted multigraph G/U induces a partition of G with the same cross-edges,3 G/U has at least k (|P | − 1) cross-edges with respect to any partition P . By the induction hypothesis, therefore, G/U has k edge-disjoint spanning trees T1 , . . . , Tk . Replacing in each Ti the vertex vU contracted from U by the spanning tree Fi0 ∩ G [ U ] of G [ U ], we obtain k edge-disjoint spanning trees in G. ¤ Let us say that subgraphs G1 , . . . , Gk of a graph G partition G if their edge sets form a partition of E(G). Our spanning tree problem may then be recast as follows: into how many connected spanning subgraphs can we partition a given graph? The excuse for rephrasing our simple tree problem in this more complicated way is that it now has an obvious dual (cf. Theorem 1.5.1): into how few acyclic (spanning) subgraphs can we partition a given graph? Or for given k: which graphs can be partitioned into at most k forests? An obvious necessary condition now is that every set U ⊆ V (G) induces at most k (|U | − 1) edges, no more than |U | − 1 for each forest. Once more, this condition turns out to be sufficient too. And surprisingly, this can be shown with the help of Lemma 3.5.3, which was designed for the proof of our theorem on edge-disjoint spanning trees: Theorem 3.5.4. (Nash-Williams 1964) A multigraph G = (V, E) can be partitioned into at most k forests if and only if kG [ U ]k 6 k (|U | − 1) for every non-empty set U ⊆ V . 3
see Chapter 1.10 on the contraction of multigraphs
Proof . The forward implication was shown above. Conversely, we show that every k-tuple F = (F1 , . . . , Fk ) ∈ F partitions G, i.e. that E [ F ] = E. If not, let e ∈ E r E [ F ]. By Lemma 3.5.3, there exists a set U ⊆ V that is connected in every Fi and contains the ends of e. Then G [ U ] contains |U | − 1 edges from each Fi , and in addition the edge e. Thus kG [ U ]k > k (|U | − 1), contrary to our assumption. ¤ The least number of forests forming a partition of a graph G is called the arboricity of G. By Theorem 3.5.4, the arboricity is a measure for the maximum local density: a graph has small arboricity if and only if it is ‘nowhere dense’, i.e. if and only if it has no subgraph H with ε(H) large.
arboricity
3.6 Paths between given pairs of vertices A graph with at least 2k vertices is said to be k-linked if for every 2k distinct vertices s1 , . . . , sk , t1 , . . . , tk it contains k disjoint paths P1 , . . . , Pk with Pi = si . . . ti for all i. Thus unlike in Menger’s theorem, we are not merely asking for k disjoint paths between two sets of vertices: we insist that each of these paths shall link a specified pair of endvertices. Clearly, every k-linked graph is k-connected. The converse, however, is far from true: being k-linked is generally a much stronger property than k-connectedness. But still, the two properties are related: our aim in this section is to prove the existence of a function f : N → N such that every f (k)-connected graph is k-linked. As a lemma, we need a result that would otherwise belong in Chapter 8:
k-linked
Theorem 3.6.1. (Mader 1967) There is a function h: N → N such that every graph with average degree at least h(r) contains K r as a topological minor, for every r ∈ N. Proof . For r 6 2, the assertion holds with h(r) ¡ ¢ = 1; we now assume that r > 3. We show by induction on m = r, . . . , 2r that every graph G with m average degree d(G) and ¡r¢> 2 has a topological minor X with r vertices r m edges; for m = 2 this implies the assertion with h(r) = 2(2) . If m = r then, by Propositions 1.2.2 and 1.3.1, G contains a cycle of length at least ε(G) + 1 > 2r−1 + 1 > r + 1, and the assertion follows with X = C r . ¡ ¢ Now let r < m 6 2r , and assume the assertion holds for smaller m. Let G with d(G) > 2m be given; thus, ε(G) > 2m−1 . Since G has a component C with ε(C) > ε(G), we may assume that G is connected. Consider a maximal set U ⊆ V (G) such that U is connected in G and
ε(G/U ) > 2m−1 ; such a set U exists, because G itself has the form G/U with |U | = 1. Since G is connected, we have N (U ) 6= ∅. Let H := G [ N (U ) ]. If H has a vertex v of degree dH (v) < 2m−1 , we may add it to U and obtain a contradiction to the maximality of U : when we contract the edge vvU in G/U , we lose one vertex and dH (v) + 1 6 2m−1 edges, so ε will still be at least 2m−1 . Therefore d(H) > δ(H) > 2m−1 . By the induction hypothesis, H contains a T Y with |Y | = r and kY k = m − 1. Let x, y be two branch vertices of this T Y that are non-adjacent in Y . Since x and y lie in N (U ) and U is connected in G, G contains an x–y path whose inner vertices lie in U . Adding this path to the T Y , we obtain the desired T X. ¤ How can Theorem 3.6.1 help with our aim to show that high connectivity will make a graph k-linked? Since high connectivity forces the average degree up (even the minimum degree), we may assume by the theorem that our graph contains a subdivision K of a large complete graph. Our plan now is to use Menger’s theorem to link the given vertices si and ti disjointly to branch vertices of K, and then to join up the correct pairs of those branch vertices inside K. Theorem 3.6.2. (Jung 1970; Larman & Mani 1970) There is a function f : N → N such that every f (k)-connected graph is k-linked, for all k ∈ N.
(3.3.1) G K U si , ti
Pi , Qi P
ui Li vi
Mi wi
Proof . We prove the assertion for f (k) = h(3k) + 2k, where h is a function as in Theorem 3.6.1. Let G be an f (k)-connected graph. Then d(G) > δ(G) > κ(G) > h(3k); choose K = T K 3k ⊆ G as in Theorem 3.6.1, and let U denote its set of branch vertices. For the proof that G is k-linked, let distinct vertices s1 , . . . , sk and t1 , . . . , tk of G be given. By definition of f (k), we have κ(G) > 2k. Hence by Menger’s theorem (3.3.1), G contains disjoint paths P1 , . . . , Pk , Q1 , . . . , Qk , such that each Pi starts in si , each Qi starts in ti , and all these paths end in U but have no inner vertices in U . Let the set P of these paths be chosen so that their total number of edges outside E(K) is as small as possible. Let u1 , . . . , uk be those k vertices in U that are not an end of a path in P. For each i = 1, . . . , k, let Li be the U -path in K (i.e., the subdivided edge of the K 3k ) from ui to the end of Pi in U , and let vi be the first vertex of Li on any path P ∈ P. By definition of P, P has no more edges outside E(K) than P vi Li ui does, so vi P = vi Li and hence P = Pi (Fig. 3.6.1). Similarly, if Mi denotes the U -path in K from ui to the end of Qi in U , and wi denotes the first vertex of Mi on any path in P, then this path is Qi . Then the paths si Pi vi Li ui Mi wi Qi ti are disjoint for different i and show that G is k-linked. ¤
3.6 Paths between given pairs of vertices
ui si
Qi Li
Fig. 3.6.1. Constructing an si –ti path via ui
In our proof of Theorem 3.6.2 we did not try to find any particularly good bound on the connectivity needed to force a graph to be k-linked; the function f we used grows exponentially in k. Not surprisingly, this is far from being best possible. It is still remarkable, though, that f can in fact be chosen linear: as Bollob´ as & Thomason (1996) have shown, every 22k-connected graph is k-linked.
Exercises For the first three exercises, let G be a graph and a, b ∈ V (G). Suppose that X ⊆ V (G) r { a, b } separates a from b in G. We say that X separates a from b minimally if no proper subset of X separates a from b in G. 1.− Show that X separates a from b minimally if and only if every vertex in X has a neighbour in the component Ca of G − X containing a, and another in the component Cb of G − X containing b. 2.
Let X 0 ⊆ V (G) r { a, b } be another set separating a from b, and define Ca0 and Cb0 correspondingly. Show that both and
Ya := (X ∩ Ca0 ) ∪ (X ∩ X 0 ) ∪ (X 0 ∩ Ca ) Yb := (X ∩ Cb0 ) ∪ (X ∩ X 0 ) ∪ (X 0 ∩ Cb )
separate a from b (see figure). X0
Ya X
b X0
Do Ya and Yb separate a from b minimally if X and X 0 do? Are |Ya | and |Yb | minimal for vertex sets separating a from b if |X| and |X 0 | are?
Let X and X 0 be minimal separating vertex sets in G such that X meets at least two components of G − X 0 . Show that X 0 meets all the components of G − X, and that X meets all the components of G − X 0 .
5.− Prove the elementary properties of blocks mentioned at the beginning of Section 3.1. 6.
Show that the block graph of any connected graph is a tree.
Show, without using Menger’s theorem, that any two vertices of a 2connected graph lie on a common cycle.
For edges e, e0 ∈ G write e ∼ e0 if either e = e0 or e and e0 lie on some common cycle in G. Show that ∼ is an equivalence relation on E(G) whose equivalence classes are the edge sets of the non-trivial blocks of G.
Let G be a 2-connected graph but not a triangle, and let e be an edge of G. Show that either G − e or G/e is again 2-connected.
Let G be a 3-connected graph, and let xy be an edge of G. Show that G/xy is 3-connected if and only if G − { x, y } is 2-connected.
(i) Show that every cubic 3-edge-connected graph is 3-connected. (ii) Show that a graph is cubic and 3-connected if and only if it can be constructed from a K 4 by successive applications of the following operation: subdivide two edges by inserting a new vertex on each of them, and join the two new subdividing vertices by an edge.
12.− Show that Menger’s theorem is equivalent to the following statement. For every graph G and vertex sets A, B ⊆ V (G), there exist a set P of disjoint A–B paths in G and a set X ⊆ V (G) separating A from B in G such that X has the form X = { xP | P ∈ P } with xP ∈ P for all P ∈ P. 13.
Work out the details of the proof of Corollary 3.3.4 (ii).
Let k > 2. Show that every k-connected graph of order at least 2k contains a cycle of length at least 2k.
Let k > 2. Show that in a k-connected graph any k vertices lie on a common cycle.
Derive the edge part of Corollary 3.4.2 from the vertex part. (Hint. Consider the H-paths in the graph obtained from the disjoint union of H and the line graph L(G) by adding all the edges he such that h is a vertex of H and e ∈ E(G) r E(H) is an edge at h.)
17.− To the disjoint union of the graph H = K 2m+1 with k copies of K 2m+1 add edges joining H bijectively to each of the K 2m+1 . Show that the resulting graph G contains at most km = 12 κG (H) independent Hpaths. 18.
Find a bipartite graph G, with partition classes A and B say, such that for H := G [ A ] there are at most 12 λG (H) edge-disjoint H-paths in G.
19.+ Derive Tutte’s 1-factor theorem (2.2.1) from Mader’s theorem. (Hint. Extend the given graph G to a graph G0 by adding, for each vertex v ∈ G, a new vertex v 0 and joining v 0 to v. Choose H ⊆ G0 so that the 1-factors in G correspond to the large enough sets of independent H-paths in G0 .) 20.
Find the error in the following short ‘proof’ of Theorem 3.5.1. Call a partition non-trivial if it has at least two classes and at least one of the classes has more than one element. We show by induction on |V | + |E| that G = (V, E) has k edge-disjoint spanning trees if every non-trivial partition of V into r sets (say) has at least k(r − 1) cross-edges. The induction starts trivially with G = K 1 if we allow k copies of K 1 as a family of k edge-disjoint spanning trees of K 1 . We now consider the induction step. If every non-trivial partition of V into r sets (say) has more than k(r − 1) cross-edges, we delete any edge of G and are done by induction. So V has a non-trivial partition { V1 , . . . , Vr } with exactly k(r − 1) cross-edges. Assume that |V1 | > 2. If G0 := G [ V1 ] has k disjoint spanning trees, we may combine these with k disjoint spanning trees that exist in G/V1 by induction. We may thus assume that G0 has no k disjoint spanning trees. Then by induction it has a non-trivial vertex partition { V10 , . . . , Vs0 } with fewer than k(s − 1) cross-edges. Then { V10 , . . . , Vs0 , V2 , . . . , Vr } is a non-trivial vertex partition of G into r + s − 1 sets with fewer than k(r − 1) + k(s − 1) = k((r + s − 1) − 1) cross-edges, a contradiction.
21.− Show that every k-linked graph is (2k − 1)-connected.
Notes Although connectivity theorems are doubtless among the most natural, and also the most applicable, results in graph theory, there is still no comprehensive monograph on this subject. Some areas are covered in B. Bollob´ as, Extremal Graph Theory, Academic Press 1978, in R. Halin, Graphentheorie, Wissenschaftliche Buchgesellschaft 1980, and in A. Frank’s chapter of the Handbook of Combinatorics (R.L. Graham, M. Gr¨ otschel & L. Lov´ asz, eds.), North-Holland 1995. A survey specifically of techniques and results on minimally k-connected graphs (see below) is given by W. Mader, On vertices of degree n in minimally n-connected graphs and digraphs, in (D. Mikl´ os, V.T. S´ os & T. Sz˝ onyi, eds.) Paul Erd˝ os is 80, Vol. 2, Proc. Colloq. Math. Soc. J´ anos Bolyai, Budapest 1996. Our proof of Tutte’s Theorem 3.2.3 is due to C. Thomassen, Planarity and duality of finite and infinite graphs, J. Combin. Theory B 29 (1980), 244–271. This paper also contains Lemma 3.2.1 and its short proof from first principles. (The lemma’s assertion, of course, follows from Tutte’s wheel theorem—its significance lies in its independent proof, which has shortened the proofs of both of Tutte’s theorems considerably.) An approach to the study of connectivity not touched upon in this chapter is the investigation of minimal k-connected graphs, those that lose their k-connectedness as soon as we delete an edge. Like all k-connected graphs, these have minimum degree at least k, and by a fundamental result of Halin
(1969), their minimum degree is exactly k. The existence of a vertex of small degree can be particularly useful in induction proofs about k-connected graphs. Halin’s theorem was the starting point for a series of more and more sophisticated studies of minimal k-connected graphs; see the books of Bollob´ as and Halin cited above, and in particular Mader’s survey. Our first proof of Menger’s theorem is due to T. B¨ ohme, F. G¨ oring and J. Harant (manuscript 1999); the second to J.S. Pym, A proof of Menger’s theorem, Monatshefte Math. 73 (1969), 81–88; the third to T. Gr¨ unwald (later Gallai), Ein neuer Beweis eines Mengerschen Satzes, J. London Math. Soc. 13 (1938), 188–192. The global version of Menger’s theorem (Theorem 3.3.5) was first stated and proved by Whitney (1932). ¨ Mader’s Theorem 3.4.1 is taken from W. Mader, Uber die Maximalzahl kreuzungsfreier H -Wege, Arch. Math. 31 (1978), 387–402. The theorem may be viewed as a common generalization of Menger’s theorem and Tutte’s 1factor theorem (Exercise 19). Theorem 3.5.1 was proved independently by Nash-Williams and by Tutte; both papers are contained in J. London Math. Soc. 36 (1961). Theorem 3.5.4 is due to C.St.J.A. Nash-Williams, Decompositions of finite graphs into forests, J. London Math. Soc. 39 (1964), 12. Our proofs follow an account by Mader (personal communication). Both results can be elegantly expressed and proved in the setting of matroids; see § 18 in B. Bollob´ as, Combinatorics, Cambridge University Press 1986. In Chapter 8.1 we shall prove that, in order to force a topological K r mir nor in a graph G, we do not need an average degree of G as high as h(r) = 2(2) (as used in our proof of Theorem 3.6.1): the average degree required can be bounded above by a function quadratic in r (Theorem 8.1.1). The improvement of Theorem 3.6.2 mentioned in the text is due to B. Bollob´ as & A.G. Thomason, Highly linked graphs, Combinatorica 16 (1996), 313–320. N. Robertson & P.D. Seymour, Graph Minors XIII: The disjoint paths problem, J. Combin. Theory B 63 (1995), 65-110, showed that, for every fixed k, there is an O(n3 ) algorithm that decides whether a given graph of order n is k-linked. If k is taken as part of the input, the problem becomes NP-hard.
Planar Graphs
When we draw a graph on a piece of paper, we naturally try to do this as transparently as possible. One obvious way to limit the mess created by all the lines is to avoid intersections. For example, we may ask if we can draw the graph in such a way that no two edges meet in a point other than a common end. Graphs drawn in this way are called plane graphs; abstract graphs that can be drawn in this way are called planar . In this chapter we study both plane and planar graphs—as well as the relationship between the two: the question of how an abstract graph might be drawn in fundamentally different ways. After collecting together in Section 4.1 the few basic topological facts that will enable us later to prove all results rigorously without too much technical ado, we begin in Section 4.2 by studying the structural properties of plane graphs. In Section 4.3, we investigate how two drawings of the same graph can differ. The main result of that section is that 3-connected planar graphs have essentially only one drawing, in some very strong and natural topological sense. The next two sections are devoted to the proofs of all the classical planarity criteria, conditions telling us when an abstract graph is planar. We complete the chapter with a section on plane duality, a notion with fascinating links to algebraic, colouring, and flow properties of graphs (Chapters 1.9 and 6.5). The traditional notion of a graph drawing is that its vertices are represented by points in the Euclidean plane, its edges are represented by curves between these points, and different curves meet only in common endpoints. To avoid unnecessary topological complication, however, we shall only consider curves that are piecewise linear; it is not difficult to show that any drawing can be straightened out in this way, so the two notions come to the same thing.
4. Planar Graphs
4.1 Topological prerequisites
region separate frontier
[ 4.2.1 ] [ 4.2.4 ] [ 4.2.5 ] [ 4.2.10 ] [ 4.3.1 ] [ 4.5.1 ] [ 4.6.1 ] [ 5.1.2 ]
In this section we briefly review some basic topological definitions and facts needed later. All these facts have (by now) easy and well-known proofs; see the notes for sources. Since those proofs contain no graph theory, we do not repeat them here: indeed our aim is to collect precisely those topological facts that we need but do not want to prove. Later, all proofs will follow strictly from the definitions and facts stated here (and be guided by but not rely on geometric intuition), so the material presented now will help to keep elementary topological arguments in those proofs to a minimum. A straight line segment in the Euclidean plane is a subset of R2 that has the form { p + λ(q − p) | 0 6 λ 6 1 } for distinct points p, q ∈ R2 . A polygon is a subset of R2 which is the union of finitely many straight line segments and is homeomorphic to the unit circle. Here, as later, any subset of a topological space is assumed to carry the subspace topology. A polygonal arc is a subset of R2 which is the union of finitely many straight line segments and is homeomorphic to the closed unit interval [ 0, 1 ]. The images of 0 and of 1 under such a homeomorphism are the endpoints of this polygonal arc, which links them and runs between them. Instead of ‘polygonal arc’ we shall simply say arc. If P is an arc between ˚. x and y, we denote the point set P r { x, y }, the interior of P , by P 2 Let O ⊆ R be an open set. Being linked by an arc in O defines an equivalence relation on O. The corresponding equivalence classes are again open; they are the regions of O. A closed set X ⊆ R2 is said to separate O if O r X has more than one region. The frontier of a set X ⊆ R2 is the set Y of all points y ∈ R2 such that every neighbourhood of y meets both X and R2 r X. Note that if X is open then its frontier lies in R2 r X. The frontier of a region O of R2 r X, where X is a finite union of points and arcs, has two important properties. The first is accessibility: if x ∈ X lies on the frontier of O, then x can be linked to some point in O by a straight line segment whose interior lies wholly inside O. As a consequence, any two points on the frontier of O can be linked by an arc whose interior lies in O (why?). The second notable property of the frontier of O is that it separates O from the rest of R2 . Indeed, if ϕ: [ 0, 1 ] → P ⊆ R2 is continuous, with ϕ(0) ∈ O and ϕ(1) ∈/ O, then P meets the frontier of O at least in the point ϕ(y) for y := inf { x | ϕ(x) ∈/ O }, the first point of P in R2 r O. Theorem 4.1.1. (Jordan Curve Theorem for Polygons) For every polygon P ⊆ R2 , the set R2 r P has exactly two regions, of which exactly one is bounded. Each of the two regions has the entire polygon P as its frontier.
With the help of Theorem 4.1.1, it is not difficult to prove the following lemma. Lemma 4.1.2. Let P1 , P2 , P3 be three arcs, between the same two endpoint but otherwise disjoint. (i) R2 r (P1 ∪ P2 ∪ P3 ) has exactly three regions, with frontiers P1 ∪ P2 , P2 ∪ P3 and P1 ∪ P3 . ˚1 and a point in P ˚3 whose (ii) If P is an arc between a point in P ˚2 , then interior lies in the region of R2 r (P1 ∪ P3 ) that contains P ˚∩ P ˚2 6= ∅. P
[ 4.2.5 ] [ 4.2.6 ] [ 4.2.10 ]
P P2 P1
Fig. 4.1.1. The arcs in Lemma 4.1.2 (ii)
Our next lemma complements the Jordan curve theorem by saying that an arc does not separate the plane. For easier application later, we phrase this a little more generally: Lemma 4.1.3. Let X1 , X2 ⊆ R2 be disjoint sets, each the union of finitely many points and arcs, and let P be an arc between a point in ˚ lies in a region O of R2 r (X1 ∪ X2 ). X1 and one in X2 whose interior P 2 ˚ Then O r P is a region of R r (X1 ∪ P ∪ X2 ).
P X1
Fig. 4.1.2. P does not separate the region O of R2 r (X1 ∪ X2 )
It remains to introduce a few terms and facts that will be used only once, when we consider notions of equivalence for graph drawings in Chapter 4.3. As usual, we denote by S n the n-dimensional sphere, the set of points in Rn+1 at distance 1 from the origin. The 2-sphere minus its ‘north pole’ (0, 0, 1) is homeomorphic to the plane; let us choose a fixed such homeomorphism π: S 2 r { (0, 0, 1) } → R2 (for example, stereographic projection). If P ⊆ R2 is a polygon and O is the bounded region of
R2 r P , let us call C := π −1 (P ) a circle on S 2 , and the sets π −1 (O) and S 2 r π −1 (P ∪ O) the regions of C. Our last tool is the theorem of Jordan and Schoenflies, again adapted slightly for our purposes: [ 4.3.1 ]
Theorem 4.1.4. Let ϕ: C1 → C2 be a homeomorphism between two circles on S 2 , let O1 be a region of C1 , and let O2 be a region of C2 . Then ϕ can be extended to a homeomorphism C1 ∪ O1 → C2 ∪ O2 .
4.2 Plane graphs plane graph
A plane graph is a pair (V, E) of finite sets with the following properties (the elements of V are again called vertices, those of E edges): (i) (ii) (iii) (iv)
F (G)
V ⊆ R2 ; every edge is an arc between two vertices; different edges have different sets of endpoints; the interior of an edge contains no vertex and no point of any other edge.
A plane graph (V, E) defines a graph G on V in a natural way. As long as no confusion can arise, we shall use the name G of this abstract graph S also for the plane graph (V, E), or for the point set V ∪ E; similar notational conventions will be used for abstract versus plane edges, for subgraphs, and so on.1 For every plane graph G, the set R2 r G is open; its regions are the faces of G. Since G is bounded—i.e., lies inside some sufficiently large disc D—exactly one of its faces is unbounded: the face that contains R2 r D. This face is the outer face of G; the other faces are its inner faces. We denote the set of faces of G by F (G). Note that if H ⊆ G then every face of G is contained in a face of H. In order to lay the foundations for the (easy but) rigorous introduction to plane graphs that this section aims to provide, let us descend once now into the realm of truly elementary topology of the plane, and prove what seems entirely obvious:2 that the frontier of a face of a plane graph G is always a subgraph of G—not, say, half an edge. The following lemma states this formally, together with two similarly ‘obvious’ properties of plane graphs: 1
However, we shall continue to use r for differences of point sets and − for graph differences—which may help a little to keep the two apart. 2 Note that even the best intuition can only ever be ‘accurate’, i.e., coincide with what the technical definitions imply, inasmuch as those definitions do indeed formalize what is intuitively intended. Given the complexity of definitions in elementary topology, this can hardly be taken for granted.
4.2 Plane graphs
Lemma 4.2.1. Let G be a plane graph and e an edge of G.
(i) If X is the frontier of a face of G, then either e ⊆ X or X ∩˚ e = ∅. (ii) If e lies on a cycle C ⊆ G, then e lies on the frontier of exactly two faces of G, and these are contained in distinct faces of C. (iii) If e lies on no cycle, then e lies on the frontier of exactly one face of G. Proof . We prove all three assertions together. Let us start by considering one point x0 ∈ ˚ e. We show that x0 lies on the frontier of either exactly two faces or exactly one, according as e lies on a cycle in G or not. We then show that every other point in ˚ e lies on the frontier of exactly the same faces as x0 . Then the endpoints of e will also lie on the frontier of these faces—simply because every neighbourhood of an endpoint of e is also the neighbourhood of an inner point of e. G is the union of finitely many straight line segments; we may assume that any two of these intersect in at most one point. Around every point x ∈ ˚ e we can find an open disc Dx , with centre x, which meets only those (one or two) straight line segments that contain x. Let us pick an inner point x0 from a straight line segment S ⊆ e. Then Dx0 ∩ G = Dx0 ∩ S, so Dx0 r G is the union of two open half-discs. Since these half-discs do not meet G, they each lie in a face of G. Let us denote these faces by f1 and f2 ; they are the only faces of G with x0 on their frontier, and they may coincide (Fig. 4.2.1).
Dx x0 , S
f1 , f 2
x0 f2
Fig. 4.2.1. Faces f1 , f2 of G in the proof of Lemma 4.2.1
If e lies on a cycle C ⊆ G, then Dx0 meets both faces of C (Theorem 4.1.1). The faces f1 , f2 of G are therefore contained in distinct faces of C—since C ⊆ G, every face of G is a subset of a face of C—and in particular f1 6= f2 . If e does not lie on any cycle, then e is a bridge and thus links two disjoint point sets X1 , X2 with X1 ∪ X2 = G r˚ e. Clearly, f1 ∪˚ e ∪ f2 is the subset of a face f of G − e. (Why?) By Lemma 4.1.3, f r˚ e is a face of G. But f r˚ e contains f1 and f2 by definition of f , so f1 = f r˚ e = f2 since f1 , f2 and f are all faces of G. e. Let P be the arc from x0 to Now consider any other point x1 ∈ ˚ x1 contained in e. Since P is compact, finitely many of the discs Dx with x ∈ P cover P . Let us enumerate these discs as D0 , . . . , Dn in the natural order of their centres along P ; adding Dx0 or Dx1 as necessary, we may assume that D0 = Dx0 and Dn = Dx1 . By induction on n, one easily proves that every point y ∈ Dn r e can be linked by an arc inside
x1 P D0 , . . . , Dn
(D0 ∪ . . . ∪ Dn ) r e to a point z ∈ D0 r e (Fig. 4.2.2); then y and z are equivalent in R2 r G. Hence, every point of Dn r e lies in f1 or in f2 , so x1 cannot lie on the frontier of any other face of G. Since both half-discs of D0 r e can be linked to Dn r e in this way (swap the roles of D0 and Dn ), we find that x1 lies on the frontier of both f1 and f2 . ¤ e x0 D0
Fig. 4.2.2. An arc from y to D0 , close to P
Corollary 4.2.2. The frontier of a face is always the point set of a subgraph. ¤
boundary G[f ]
The subgraph of G whose point set is the frontier of a face f is said to bound f and is called its boundary; we denote it by G [ f ]. A face is said to be incident with the vertices and edges of its boundary. Note that if H ⊆ G then every face f of G is contained in a face f 0 of H. If G [ f ] ⊆ H then f = f 0 (why?); in particular, f is always also a face of its own boundary G [ f ]. These basic facts will be used frequently in the proofs to come.
Proposition 4.2.3. A plane forest has exactly one face.
Proof . Use induction on the number of edges and Lemma 4.1.3.
With just one exception, different faces of a plane graph have different boundaries: [ 4.3.1 ]
Lemma 4.2.4. If a plane graph has different faces with the same boundary, then the graph is a cycle.
Proof . Let G be a plane graph, and let H ⊆ G be the boundary of distinct faces f1 , f2 of G. Since f1 and f2 are also faces of H, Proposition 4.2.3 implies that H contains a cycle C. By Lemma 4.2.1 (ii), f1 and f2 are contained in different faces of C. Since f1 and f2 both have all of H as boundary, this implies that H = C: any further vertex or edge of H would lie in one of the faces of C and hence not on the boundary of the other. Thus, f1 and f2 are distinct faces of C. As C has only two faces, it follows that f1 ∪ C ∪ f2 = R2 and hence G = C. ¤
[ 4.3.1 ] [ 4.4.3 ] [ 4.5.1 ] [ 4.5.2 ]
Proposition 4.2.5. In a 2-connected plane graph, every face is bounded by a cycle.
Proof . Let f be a face in a 2-connected plane graph G. We show by induction on |G| that G [ f ] is a cycle. If G is itself a cycle, this holds by Theorem 4.1.1; we therefore assume that G is not a cycle. By Proposition 3.1.2, there exist a 2-connected plane graph H ⊆ G and a plane H-path P such that G = H ∪ P . The interior of P lies in a face f 0 of H, which by the induction hypothesis is bounded by a cycle C. If f is also a face of H, we are home by the induction hypothesis. If not, then the frontier of f meets P r H, so f ⊆ f 0 . Therefore f is a face of C ∪ P , and is hence bounded by a cycle (Lemma 4.1.2 (i)). ¤
(3.1.2) (4.1.1) (4.1.2)
A plane graph G is called maximally plane, or just maximal , if we cannot add a new edge to form a plane graph G0 % G with V (G0 ) = V (G). We call G a plane triangulation if every face of G (including the outer face) is bounded by a triangle.
maximal plane graph
H P f 0, C
plane triangulation
Proposition 4.2.6. A plane graph of order at least 3 is maximally plane if and only if it is a plane triangulation.
Proof . Let G be a plane graph of order at least 3. It is easy to see that if every face of G is bounded by a triangle, then G is maximally plane. Indeed, any additional edge e would have its interior inside a face of G and its ends on the boundary of that face. Hence these ends are already adjacent in G, so G ∪ e cannot satisfy condition (iii) in the definition of a plane graph. Conversely, assume that G is maximally plane and let f ∈ F (G) be a face; let us write H := G [ f ]. Since G is maximal as a plane graph, G [ H ] is complete: any two vertices of H that are not already adjacent in G could be linked by an arc through f , extending G to a larger plane graph. Thus G [ H ] = K n for some n—but we do not know yet which edges of G [ H ] lie in H. Let us show first that H contains a cycle. If not, then G r H 6= ∅: by G ⊇ K n if n > 3, or else by |G| > 3. On the other hand we have f ∪ H = R2 by Proposition 4.2.3 and hence G = H, a contradiction. Since H contains a cycle, it suffices to show that n 6 3: then H = K 3 as claimed. Suppose n > 4, and let C = v1 v2 v3 v4 v1 be a cycle in G [ H ] (= K n ). By C ⊆ G, our face f is contained in a face fC of C; let fC0 be the other face of C. Since the vertices v1 and v3 lie on the boundary of f , they can be linked by an arc whose interior lies in fC and avoids G.
fC ⊇ f
v2 C
Fig. 4.2.3. The edge v2 v4 of G runs through the face fC0
f H
C, vi 0 fC , f C
Hence by Lemma 4.1.2 (ii), the plane edge v2 v4 of G [ H ] runs through fC0 rather than fC (Fig. 4.2.3). Analogously, since v2 , v4 ∈ G [ f ], the edge v1 v3 runs through fC0 . But the edges v1 v3 and v2 v4 are disjoint, so this contradicts Lemma 4.1.2 (ii). ¤ The following classic result of Euler (1752)—here stated in its simplest form, for the plane—marks one of the common origins of graph theory and topology. The theorem relates the number of vertices, edges and faces in a plane graph: taken with the correct signs, these numbers always add up to 2. The general form of Euler’s theorem asserts the same for graphs suitably embedded in other surfaces, too: the sum obtained is always a fixed number depending only on the surface, not on the graph, and this number differs for distinct (orientable closed) surfaces. Hence, any two such surfaces can be distinguished by a simple arithmetic invariant of the graphs embedded in them!3 Let us then prove Euler’s theorem in its simplest form: Theorem 4.2.7. (Euler’s Formula) Let G be a connected plane graph with n vertices, m edges, and ` faces. Then n−m+` = 2. (1.5.1) (1.5.3) e, G0 f1 , f 2 f1,2
Proof . We fix n and apply induction on m. For m 6 n − 1, G is a tree and m = n − 1 (why?), so the assertion follows from Proposition 4.2.3. Now let m > n. Then G has an edge e lying on a cycle; let G0 := G − e. By Lemma 4.2.1 (ii), e lies on the boundary of exactly two faces f1 , f2 of G; we put f1,2 := f1 ∪˚ e ∪ f2 . We shall prove that F (G) r { f1 , f2 } = F (G0 ) r { f1,2 } , ψ
f0 0 f1,2
e must lie in some without assuming that f1,2 ∈ F (G0 ). However, since ˚ face of G0 and this will not be a face of G, by (∗) it can only be f1,2 . Thus again by (∗), G0 has one face less than G. As G0 also has one edge less than G, the assertion then follows from the induction hypothesis for G0 . For our proof of (∗) we first consider any f ∈ F (G) r { f1 , f2 }. By Lemma 4.2.1 (i), we have G [ f ] ⊆ G r˚ e = G0 . So f is also a face of G0 (but obviously not equal to f1,2 ) and hence lies in F (G0 ) r { f1,2 }. Conversely, let a face f 0 6= f1,2 of G0 be given. Since e lies on the boundary of both f1 and f2 , we can link any two points of f1,2 by an 0 arc in R2 r G0 , so f1,2 lies inside a face f1,2 of G0 . Our assumption 0 0 0 of f 6= f1,2 therefore implies f 6⊆ f1,2 (as otherwise f 0 ⊆ f1,2 ⊆ f1,2 3 This fundamental connection between graphs and surfaces lies at the heart of the proof of the famous Robertson-Seymour graph minor theorem; see Chapter 12.5.
0 ); let x be a point in f 0 r f1,2 . Then x lies and hence f 0 = f1,2 = f1,2 in some face f 6= f1 , f2 of G. As shown above, f is also a face of G0 . Hence x ∈ f ∩ f 0 implies f = f 0 , and we have f 0 ∈ F (G) r { f1 , f2 } as desired. ¤
Corollary 4.2.8. A plane graph with n > 3 vertices has at most 3n − 6 edges. Every plane triangulation with n vertices has 3n − 6 edges.
[ 4.4.1 ] [ 5.1.2 ] [ 8.3.5 ]
Proof . By Proposition 4.2.6 it suffices to prove the second assertion. In a plane triangulation G, every face boundary contains exactly three edges, and every edge lies on the boundary of exactly two faces (Lemma 4.2.1). The bipartite graph on E(G) ∪ F (G) with edge set { ef | e ⊆ G [ f ] } thus has exactly 2 |E(G)| = 3 |F (G)| edges. According to this identity we may replace ` with 2m/3 in Euler’s formula, and obtain m = 3n − 6. ¤ Euler’s formula can be useful for showing that certain graphs cannot occur as plane graphs. The graph K 5 , for example, has 10 > 3 · 5 − 6 edges, more than allowed by Corollary 4.2.8. Similarly, K3,3 cannot be a plane graph. For since K3,3 is 2-connected but contains no triangle, every face of a plane K3,3 would be bounded by a cycle of length > 4 (Proposition 4.2.5). As in the proof of Corollary 4.2.8 this implies 2m > 4`, which yields m 6 2n − 4 when substituted in Euler’s formula. But K3,3 has 9 > 2 · 6 − 4 edges. Clearly, along with K 5 and K3,3 themselves, their subdivisions cannot occur as plane graphs either: Corollary 4.2.9. A plane graph contains neither K 5 nor K3,3 as a topological minor. ¤
Surprisingly, it turns out that this simple property of plane graphs identifies them among all other graphs: as Section 4.4 will show, an arbitrary graph can be drawn in the plane if and only if it has no (topological) K 5 or K3,3 minor. As we have seen, every face boundary in a 2-connected plane graph is a cycle. In a 3-connected graph, these cycles can be identified combinatorially: Proposition 4.2.10. The face boundaries in a 3-connected plane graph are precisely its non-separating induced cycles. Proof . Let G be a 3-connected plane graph, and let C ⊆ G. If C is a non-separating induced cycle, then by the Jordan curve theorem its two faces cannot both contain points of G r C. Therefore it bounds a face of G. Conversely, suppose that C bounds a face f . By Proposition 4.2.5, C is a cycle. If C has a chord e = xy, then the components of C − { x, y }
[ 4.3.2 ] [ 4.5.2 ] (3.3.5) (4.1.1) (4.1.2)
C, f
are linked by a C-path in G, because G is 3-connected. This path and e both run through the other face of C (not f ) but do not intersect, a contradiction to Lemma 4.1.2 (ii). It remains to show that C does not separate any two vertices x, y ∈ G − C. By Menger’s theorem (3.3.5), x and y are linked in G by three independent paths. Clearly, f lies inside a face of their union, and by Lemma 4.1.2 (i) this face is bounded by only two of the paths. The third therefore avoids f and its boundary C. ¤
4.3 Drawings planar embedding drawing
G; V, E, F G0 ; V ,0 E ,0 F 0 σ
π topological isomorphism
An embedding in the plane, or planar embedding, of an (abstract) graph ˜ The latter will G is an isomorphism between G and a plane graph G. be called a drawing of G. We shall not always distinguish notationally ˜ between the vertices and edges of G and of G. In this section we investigate how two planar embeddings of a graph can differ. For this to make sense, we first have to agree when two embeddings are to be considered the same: for example, if we compose one embedding with a simple rotation of the plane, the resulting embedding will hardly count as a genuinely different way of drawing that graph. To prepare the ground, let us first consider three possible notions of equivalence for plane graphs (refining abstract isomorphism), and see how they are related. Let G = (V, E) and G0 = (V 0 , E 0 ) be two plane graphs, with face sets F (G) =: F and F (G0 ) =: F 0 . Assume that G and G0 are isomorphic as abstract graphs, and let σ: V → V 0 be an isomorphism. Setting xy 7→ σ(x)σ(y), we may extend σ in a natural way to a bijection V ∪ E → V 0 ∪ E 0 which maps V to V 0 and E to E 0 , and which preserves incidence (and non-incidence) between vertices and edges. Our first notion of equivalence between plane graphs is perhaps the most natural one. Intuitively, we would like to call our isomorphism σ ‘topological’ if it is induced by a homeomorphism from the plane R2 to itself. To avoid having to grant the outer faces of G and G0 a special status, however, we take a detour via the homeomorphism π: S 2 r { (0, 0, 1) } → R2 chosen in Section 4.1: we call σ a topological isomorphism between the plane graphs G and G0 if there exists a homeomorphism ϕ: S 2 → S 2 such that ψ := π ◦ ϕ ◦ π −1 induces σ on V ∪ E. (More formally: we ask that ψ agree with σ on V , and that it map every plane edge e ∈ G onto the plane edge σ(e) ∈ G0 . Unless ϕ fixes the point (0, 0, 1), the map ψ will be undefined at π(ϕ−1 (0, 0, 1)).) It can be shown that, up to topological isomorphism, inner and outer faces are indeed no longer different: if we choose as ϕ a rotation of S 2 mapping the π −1 -image of a point of some inner face of G to the north pole (0, 0, 1) of S 2 , then ψ maps the rest of this face to the outer
4.3 Drawings
Fig. 4.3.1. Two drawings of a graph that are not topologically isomorphic—why not?
face of ψ(G). (To ensure that the edges of ψ(G) are again piecewise linear, however, one may have to adjust ϕ a little.) If σ is a topological isomorphism as above, then—except possibly for a pair of missing points where ψ or ψ −1 is undefined—ψ maps the faces of G onto those of G0 (proof?). In this way, σ extends naturally to a bijection σ: V ∪ E ∪ F → V 0 ∪ E 0 ∪ F 0 which preserves incidence of vertices, edges and faces. Let us single out this last property of a topological isomorphism as the defining property for our second notion of equivalence for plane graphs: let us call our given isomorphism σ between the abstract graphs G and G0 a combinatorial isomorphism of the plane graphs G and G0 if it can be extended to a bijection σ: V ∪ E ∪ F → V 0 ∪ E 0 ∪ F 0 that preserves incidence not only of vertices with edges but also of vertices and edges with faces. (Formally: we require that a vertex or edge x ∈ G shall lie on the boundary of a face f ∈ F if and only if σ(x) lies on the boundary of the face σ(f ).)
combinatorial isomorphism
Fig. 4.3.2. Two drawings of a graph that are combinatorially isomorphic but not topologically—why not?
If σ is a combinatorial isomorphism of the plane graphs G and G0 , it maps the face boundaries of G to those of G0 . Let us raise this property to our third definition of equivalence for plane graphs: we call our isomorphism σ of the abstract graphs G and G0 a graph-theoretical isomorphism of the plane graphs G and G0 if © ª © ª σ(G [ f ]) : f ∈ F = G0 [ f 0 ] : f 0 ∈ F 0 . Thus, we no longer keep track of which face is bounded by a given subgraph: the only information we keep is whether a subgraph bounds
graphtheoretical isomorphism
some face or not, and we require that σ map the subgraphs that do onto each other. At first glance, this third notion of equivalence may appear a little less natural than the previous two. However, it has the practical advantage of being formally weaker and hence easier to verify, and moreover, it will turn out to be equivalent to the other two notions in most cases. As we have seen, every topological isomorphism between two plane graphs is also combinatorial, and every combinatorial isomorphism is also graph-theoretical. The following theorem shows that, for most graphs, the converse is true as well:
(4.1.1) (4.1.4) (4.2.4) (4.2.5)
σ ˜ ˜ G ˜0 G,
Theorem 4.3.1. (i) Every graph-theoretical isomorphism between two plane graphs is combinatorial. Its extension to a face bijection is unique if and only if the graph is not a cycle. (ii) Every combinatorial isomorphism between two 2-connected plane graphs is topological. Proof . Let G = (V, E) and G0 = (V 0 , E 0 ) be two plane graphs, put F (G) =: F and F (G0 ) =: F 0 , and let σ: V ∪ E → V 0 ∪ E 0 be an isomorphism between the underlying abstract graphs. (i) If G is a cycle, the assertion follows from the Jordan curve theorem. We now assume that G is not a cycle. Let H and H0 be the sets of all face boundaries in G and G0 , respectively. If σ is a graph-theoretical isomorphism, then the map H 7→ σ(H) is a bijection between H and H0 . By Lemma 4.2.4, the map f 7→ G [ f ] is a bijection between F and H, and likewise for F 0 and H0 . The composition of these three bijections is a bijection between F and F 0 , which we choose as σ: F → F 0 . By construction, this extension of σ to V ∪ E ∪ F preserves incidences (and is unique with this property), so σ is indeed a combinatorial isomorphism. (ii) Let us assume that G is 2-connected, and that σ is a combinatorial isomorphism. We have to construct a homeomorphism ϕ: S 2 → S 2 which, for every vertex or plane edge x ∈ G, maps π −1 (x) to π −1 (σ(x)). Since σ is a combinatorial isomorphism, σ ˜ : π −1 ◦ σ ◦ π is an incidence ˜ := π −1 (G) preserving bijection from the vertices, edges and faces4 of G 0 −1 0 ˜ := π (G ). to the vertices, edges and faces of G We construct ϕ in three steps. Let us first define ϕ on the vertex ˜ setting ϕ(x) := σ ˜ set of G, ˜ (x) for all x ∈ V (G). This is trivially a ˜ and V (G ˜ 0 ). homeomorphism between V (G) As the second step, we now extend ϕ to a homeomorphism between ˜ ∪ E(G). ˜ We may do this edge by ˜ and G ˜ 0 that induces σ ˜ on V (G) G 4 ˜ and G ˜ 0 we mean the images under π −1 By the ‘vertices, edges and faces’ of G of the vertices, edges and faces of G and G0 (plus (0, 0, 1) in the case of the outer ˜ E(G), ˜ F (G) ˜ and V (G ˜ 0 ), E(G ˜ 0 ), F (G ˜ 0 ), face). Their sets will be denoted by V (G), and incidence is defined as inherited from G and G0 .
σ ˜
y
˜ S2 ⊇ G
π y
π y R2 ⊇ G
˜0 ⊇ S 2 G
G0 ⊇ R2
Fig. 4.3.3. Defining σ ˜ via σ
˜ is homeomorphic to the edge edge, as follows. Every edge xy of G 0 ˜ σ ˜ (xy) = ϕ(x)ϕ(y) of G , by a homeomorphism mapping x to ϕ(x) and y to ϕ(y). Then the union of all these homeomorphisms, one for every ˜ is indeed a homeomorphism between G ˜ and G ˜ 0 —our desired edge of G, ˜ extension of ϕ to G: all we have to check is continuity at the vertices (where the edge homeomorphisms overlap), and this follows at once from our assumption that the two graphs and their individual edges all carry the subspace topology in R3 . ˜ →G ˜ 0 to In the third step we now extend our homeomorphism ϕ: G 2 all of S . This can be done analogously to the second step, face by face. ˜ and G ˜0 By Proposition 4.2.5, all face boundaries in G S are cycles. Now if ˜ and C its boundary, then σ f is a face of G ˜ (C) := { σ ˜ (e) | e ∈ E(C) } ˜ 0 . By Theorem 4.1.4, we may therefore extend bounds the face σ ˜ (f ) of G the homeomorphism ϕ: C → σ ˜ (C) defined so far to a homeomorphism from C ∪ f to σ ˜ (C) ∪ σ ˜ (f ). We finally take the union of all these home˜ as our desired homeomorphism omorphisms, one for every face f of G, ¤ ϕ: S 2 → S 2 ; as before, continuity is easily checked. So far, we have considered ways of comparing plane graphs. We now come to our actual goal, the definition of equivalence for planar embeddings. Let us call two planar embeddings σ1 , σ2 of a graph G topologically (respectively, combinatorially) equivalent if σ2 ◦ σ1−1 is a topological (respectively, combinatorial) isomorphism between σ1 (G) and σ2 (G). If G is 2-connected, the two definitions coincide by Theorem 4.3.1, and we simply speak of equivalent embeddings. Clearly, this is indeed an equivalence relation on the set of planar embeddings of any given graph. Note that two drawings of G resulting from inequivalent embeddings may well be topologically isomorphic (exercise): for the equivalence of two embeddings we ask not only that some (topological or combinatorial) isomorphism exist between the their images, but that the canonical isomorphism σ2 ◦ σ1−1 be a topological or combinatorial one. Even in this strong sense, 3-connected graphs have only one embedding up to equivalence: Theorem 4.3.2. (Whitney 1932) Any two planar embeddings of a 3-connected graph are equivalent.
equivalent embeddings
80 (4.2.10)
Proof . Let G be a 3-connected graph with planar embeddings σ1 : G → G1 and σ2 : G → G2 . By Theorem 4.3.1 it suffices to show that σ2 ◦ σ1−1 is a graph-theoretical isomorphism, i.e. that σ1 (C) bounds a face of G1 if and only if σ2 (C) bounds a face of G2 , for every subgraph C ⊆ G. This follows at once from Proposition 4.2.10. ¤
4.4 Planar graphs: Kuratowski’s theorem planar
A graph is called planar if it can be embedded in the plane: if it is isomorphic to a plane graph. A planar graph is maximal , or maximally planar , if it is planar but cannot be extended to a larger planar graph by adding an edge (but no vertex). Drawings of maximal planar graphs are clearly maximally plane. The converse, however, is not obvious: when we start to draw a planar graph, could it happen that we get stuck half-way with a proper subgraph that is already maximally plane? Our first proposition says that this can never happen, that is, a plane graph is never maximally plane just because it is badly drawn: Proposition 4.4.1. (i) Every maximal plane graph is maximally planar. (ii) A planar graph with n > 3 vertices is maximally planar if and only if it has 3n − 6 edges.
Proof . Apply Proposition 4.2.6 and Corollary 4.2.8.
Which graphs are planar? As we saw in Corollary 4.2.9, no planar graph contains K 5 or K3,3 as a topological minor. Our aim in this section is to prove the surprising converse, a classic theorem of Kuratowski: any graph without a topological K 5 or K3,3 minor is planar. Before we prove Kuratowski’s theorem, let us note that it suffices to consider ordinary minors rather than topological ones: Proposition 4.4.2. A graph contains K 5 or K3,3 as a minor if and only if it contains K 5 or K3,3 as a topological minor. (1.7.2)
Proof . By Proposition 1.7.2 it suffices to show that every graph G with a K 5 minor contains either K 5 as a topological minor or K3,3 as a minor. So suppose that G < K 5 , and let K ⊆ G be minimal such that K = M K 5 . Then every branch set of K induces a tree in K, and between any two branch sets K has exactly one edge. If we take the tree induced by a branch set Vx and add to it the four edges joining it to other branch sets, we obtain another tree, Tx say. By the minimality
4.4 Planar graphs: Kuratowski’s theorem
Vx Fig. 4.4.1. Every M K 5 contains a T K 5 or M K3,3
of K, Tx has exactly 4 leaves, the 4 neighbours of Vx in other branch sets (Fig. 4.4.1). If each of the five trees Tx is a T K1,4 then K is a T K 5 , and we are done. If one of the Tx is not a T K1,4 then it has exactly two vertices of degree 3. Contracting Vx onto these two vertices, and every other branch set to a single vertex, we obtain a graph on 6 vertices containing a K3,3 . Thus, G < K3,3 as desired. ¤ We first prove Kuratowski’s theorem for 3-connected graphs. This is the heart of the proof: the general case will then follow easily. Lemma 4.4.3. Every 3-connected graph G without a K 5 or K3,3 minor is planar. Proof . We apply induction on |G|. For |G| = 4 we have G = K 4 , and the assertion holds. Now let |G| > 4, and assume the assertion is true for smaller graphs. By Lemma 3.2.1, G has an edge xy such that G/xy is again 3-connected. Since the minor relation is transitive, G/xy has no K 5 or K3,3 minor either. Thus, by the induction hypothesis, G/xy has ˜ in the plane. Let f be the face of G ˜ − vxy containing the a drawing G point vxy , and let C be the boundary of f . Let X := NG (x) r { y } and Y := NG (y) r { x }; then X ∪ Y ⊆ V (C), because vxy ∈ f . Clearly, ˜ − { vxy v | v ˜ 0 := G G
Y rX }
may be viewed as a drawing of G − y, in which the vertex x is represented by the point vxy (Fig. 4.4.2). Our aim is to add y to this drawing to obtain a drawing of G. ˜ is 3-connected, G ˜ − vxy is 2-connected, so C is a cycle Since G (Proposition 4.2.5). Let x1 , . . . , xk be an enumeration along this cycle of the vertices in X, and let Pi = xi . . . xi+1 be the X-paths on C between them (i = 1, . . . , k; with xk+1 := x1 ). For each i, the set C r Pi is contained in one of the two faces of the cycle Ci := xxi Pi xi+1 x; we
(3.2.1) (4.2.5) xy
˜ G f, C X, Y ˜0 G
x1 , . . . , x k Pi Ci
x1 x5 f1
x (= vxy ) f x4
C x3
˜ 0 as a drawing of G − y: the vertex x is represented Fig. 4.4.2. G by the point vxy fi
denote the other face of Ci by fi . Since fi contains points of f (close to x) but no points of C, we have fi ⊆ f . Moreover, the plane edges xxj with j ∈/ { i, i + 1 } meet Ci only in x and end outside fi in C r Pi , so fi ˜ 0 , that is, fi is contained meets none of those edges. Hence fi ⊆ R2 r G 0 0 ˜ . (In fact, fi is a face of G ˜ , but we do not need this.) in a face of G 0 ˜ In order to turn G into a drawing of G, let us try to find an i such that Y ⊆ V (Pi ); we may then embed y into fi and link it up to its neighbours by arcs inside fi . Suppose there is no such i: how then can the vertices of Y be distributed around C? If y had a neighbour ˚i , it would also have one in C − Pi , so G would contain a in some P T K3,3 (with branch vertices x, y, xi , xi+1 and those two neighbours of y). Hence Y ⊆ X. Now if |Y | = |Y ∩ X| > 3, we have a T K 5 in G. So |Y | 6 2; in fact, |Y | = 2, because d(y) > κ(G) > 3. Since the two vertices of Y lie on no common Pi , we can once more find a T K3,3 in G, a contradiction. ¤ Compared with other proofs of Kuratowski’s theorem, the above proof has the attractive feature that it can easily be adapted to produce a drawing in which every inner face is convex (exercise); in particular, every edge can be drawn straight. Note that 3-connectedness is essential here: a 2-connected planar graph need not have a drawing with all inner faces convex (example?), although it always has a straight-line drawing (Exercise 12). It is not difficult, in principle, to reduce the general Kuratowski theorem to the 3-connected case by manipulating and combining partial drawings assumed to exist by induction. For example, if κ(G) = 2 and G = G1 ∪ G2 with V (G1 ∩ G2 ) = { x, y }, and if G has no T K 5 or T K3,3 subgraph, then neither G1 + xy nor G2 + xy has such a subgraph, and we may try to combine drawings of these graphs to one of G + xy. (If xy is already an edge of G, the same can be done with G1 and G2 .) For κ(G) 6 1, things become even simpler. However, the geometric operations involved require some cumbersome shifting and scaling, even if all the plane edges occurring are assumed to be straight.
The following more combinatorial route is just as easy, and may be a welcome alternative. Lemma 4.4.4. Let X be a set of 3-connected graphs. Let G be a graph with κ(G) 6 2, and let G1 , G2 be proper induced subgraphs of G such that G = G1 ∪ G2 and |G1 ∩ G2 | = κ(G). If G is edge-maximal without a topological minor in X , then so are G1 and G2 , and G1 ∩ G2 = K 2 .
Proof . Note first that every vertex v ∈ S := V (G1 ∩ G2 ) has a neighbour in every component of Gi − S, i = 1, 2: otherwise S r { v } would separate G, contradicting |S| = κ(G). By the maximality of G, every edge e added to G lies in a T X ⊆ G + e with X ∈ X . For all the choices of e considered below, the 3-connectedness of X will imply that the branch vertices of this T X all lie in the same Gi , say in G1 . (The position of e will always be symmetrical with respect to G1 and G2 , so this assumption entails no loss of generality.) Then the T X meets G2 at most in a path P corresponding to an edge of X. If S = ∅, we obtain an immediate contradiction by choosing e with one end in G1 and the other in G2 . If S = { v } is a singleton, let e join a neighbour v1 of v in G1 − S to a neighbour v2 of v in G2 − S (Fig. 4.4.3). Then P contains both v and the edge v1 v2 ; replacing vP v1 with the edge vv1 , we obtain a T X in G1 ⊆ G, a contradiction.
e v1
TX G1
Fig. 4.4.3. If G + e contains a T X, then so does G1 or G2
So |S| = 2, say S = { x, y }. If xy ∈/ G, we let e := xy, and in the arising T X replace e by an x–y path through G2 ; this gives a T X in G, a contradiction. Hence xy ∈ G, and G [ S ] = K 2 as claimed. It remains to show that G1 and G2 are edge-maximal without a topological minor in X . So let e0 be an additional edge for G1 , say. Replacing xP y with the edge xy if necessary, we obtain a T X either in G1 + e0 (which shows the edge-maximality of G1 , as desired) or in G2 (which contradicts G2 ⊆ G). ¤ Lemma 4.4.5. If |G| > 4 and G is edge-maximal with T K 5 , T K3,3 6⊆ G, then G is 3-connected.
x, y
84 (4.2.9) G1 , G2 x, y fi zi K
Proof . We apply induction on |G|. For |G| = 4, we have G = K 4 and the assertion holds. Now let |G| > 4, and let G be edge-maximal without a T K 5 or T K3,3 . Suppose κ(G) 6 2, and choose G1 and G2 as in Lemma 4.4.4. For X := { K 5 , K3,3 }, the lemma says that G1 ∩ G2 is a K 2 , with vertices x, y say. By Lemmas 4.4.4, 4.4.3 and the induction hypothesis, G1 and G2 are planar. For each i = 1, 2 separately, choose a drawing of Gi , a face fi with the edge xy on its boundary, and a vertex zi 6= x, y on the boundary of fi . Let K be a T K 5 or T K3,3 in the abstract graph G + z1 z2 (Fig. 4.4.4).
y G1
Fig. 4.4.4. A T K 5 or T K3,3 in G + z1 z2
If all the branch vertices of K lie in the same Gi , then either Gi + xzi or Gi + yzi (or Gi itself, if zi is already adjacent to x or y, respectively) contains a T K 5 or T K3,3 ; this contradicts Corollary 4.2.9, since these graphs are planar by the choice of zi . Since G + z1 z2 does not contain four independent paths between (G1 − G2 ) and (G2 − G1 ), these subgraphs cannot both contain a branch vertex of a T K 5 , and cannot both contain two branch vertices of a T K3,3 . Hence K is a T K3,3 with only one branch vertex v in, say, G2 − G1 . But then also the graph G1 + v + { vx, vy, vz1 }, which is planar by the choice of z1 , contains a T K3,3 . This contradicts Corollary 4.2.9. ¤
Theorem 4.4.6. (Kuratowski 1930; Wagner 1937) The following assertions are equivalent for graphs G: (i) G is planar; (ii) G contains neither K 5 nor K3,3 as a minor; (iii) G contains neither K 5 nor K3,3 as a topological minor.
Proof . Combine Corollary 4.2.9 and Proposition 4.4.2 with Lemmas 4.4.3 and 4.4.5. ¤ Corollary 4.4.7. Every maximal planar graph with at least four vertices is 3-connected. Proof . Apply Lemma 4.4.5 and Theorem 4.4.6.
4.5. Algebraic planarity criteria
4.5 Algebraic planarity criteria In this section we show that planarity can be characterized in purely algebraic terms, by a certain abstract property of its cycle space. Theorems relating such seemingly distant graph properties are rare, and their significance extends beyond their immediate applicability. In a sense, they indicate that both ways of viewing a graph—in our case, the topological and the algebraic way—are not just formal curiosities: if both are natural enough that, quite unexpectedly, each can be expressed in terms of the other, the indications are that they have the power to reveal some genuine insights into the structure of graphs and are worth pursuing. Let G = (V, E) be a graph. We call a subset F of its edge space E(G) simple if every edge of G lies in at most two sets of F. For example, the cut space C ∗ (G) has a simple basis: according to Proposition 1.9.3 it is generated by the cuts E(v) formed by all the edges at a given vertex v, and an edge xy ∈ G lies in E(v) only for v = x and for v = y. Theorem 4.5.1. (MacLane 1937) A graph is planar if and only if its cycle space has a simple basis. Proof . The assertion being trivial for graphs of order at most 2, we consider a graph G of order at least 3. If κ(G) 6 1, then G is the union of two proper induced subgraphs G1 , G2 with |G1 ∩ G2 | 6 1. Then C(G) is the direct sum of C(G1 ) and C(G2 ), and hence has a simple basis if and only if both C(G1 ) and C(G2 ) do (proof?). Moreover, G is planar if and only if both G1 and G2 are: this follows at once from Kuratowski’s theorem, but also from easy geometrical considerations. The assertion for G thus follows inductively from those for G1 and G2 . For the rest of the proof, we now assume that G is 2-connected. We first assume that G is planar and choose a drawing. By Lemma 4.2.5, the face boundaries of G are cycles, so they are elements of C(G). We shall show that the face boundaries generate all the cycles in G; then C(G) has a simple basis by Lemma 4.2.1. Let C ⊆ G be any cycle, and let f be its inner face. By Lemma 4.2.1, every edge e with ˚ e ⊆ f lies on exactly two face boundaries G [ f 0 ] with f 0 ⊆ f , and every edge of C lies on exactly one such face boundary. Hence the sum in C(G) of all those face boundaries is exactly C. Conversely, let { C1 , . . . , Ck } be a simple basis of C(G). Then, for every edge e ∈ G, also C(G − e) has a simple basis. Indeed, if e lies in just one of the sets Ci , say in C1 , then { C2 , . . . , Ck } is a simple basis of C(G − e); if e lies in two of the Ci , say in C1 and C2 , then { C1 + C2 , C3 , . . . , Ck } is such a basis. (Note that the two bases are indeed subsets of C(G − e) by Proposition 1.9.2.) Thus every subgraph of G has a cycle space with a simple basis. For our proof that G is planar, it thus suffices to show that the cycle spaces of K 5 and K3,3 (and hence
[ 4.6.3 ] (1.9.2) (1.9.6) (4.1.1) (4.2.1) (4.2.5) (4.4.6)
those of their subdivisions) do not have a simple basis: then G cannot contain a T K 5 or T K3,3 , and so is planar by Kuratowski’s theorem. Let us consider K 5 first. By Theorem 1.9.6, dim C(K 5 ) = 6; let B = { C1 , . . . , C6 } be a simple basis, and put C0 := C1 + . . . + C6 . As B is linearly independent, none of the sets C0 , . . . , C6 is empty, and so each of them contains at least three edges (cf. Proposition 1.9.2). The simplicity of B therefore implies 18 = 6 · 3 6 |C1 | + . . . + |C6 | 6 2 kK 5 k − |C0 | 6 2 · 10 − 3 = 17 , a contradiction; for the middle inequality note that every edge in C0 lies in just one of the sets C1 , . . . , C6 . For K3,3 , Theorem 1.9.6 gives dim C(K3,3 ) = 4; let B = { C1 , . . . , C4 } be a simple basis, and put C0 := C1 + . . . + C4 . Since K3,3 has girth 4, each Ci contains at least four edges, so 16 = 4 · 4 6 |C1 | + . . . + |C4 | 6 2 kK3,3 k − |C0 | 6 2 · 9 − 4 = 14 , a contradiction.
It is one of the hidden beauties of planarity theory that two such abstract and seemingly unintuitive results about generating sets in cycle spaces as MacLane’s theorem and Tutte’s theorem 3.2.3 conspire to produce a very tangible planarity criterion for 3-connected graphs:
(3.2.3) (4.2.1) (4.2.5) (4.2.10)
Theorem 4.5.2. (Tutte 1963) A 3-connected graph is planar if and only if every edge lies on at most (equivalently: exactly) two non-separating induced cycles. Proof . The forward implication follows from Propositions 4.2.10 and 4.2.1 (and Proposition 4.2.5 for the ‘exactly two’ version); the backward implication follows from Theorems 3.2.3 and 4.5.1. ¤
4.6 Plane duality
4.6 Plane duality In this section we shall use MacLane’s theorem to uncover another connection between planarity and algebraic structure: a connection between the duality of plane graphs, defined below, and the duality of the cycle and cut space hinted at in Chapters 1.9 and 3.5. A plane multigraph is a pair G = (V, E) of finite sets (of vertices and edges, respectively) satisfying the following conditions:
plane multigraph
(i) V ⊆ R2 ; (ii) every edge is either an arc between two vertices or a polygon containing exactly one vertex (its endpoint); (iii) apart from its own endpoint(s), an edge contains no vertex and no point of any other edge. We shall use terms defined for plane graphs freely for plane multigraphs. Note that, as in abstract multigraphs, both loops and double edges count as cycles. Let us consider the plane multigraph G shown in Figure 4.6.1. Let us place a new vertex inside each face of G and link these new vertices up to form another plane multigraph G∗ , as follows: for every edge e of G we link the two new vertices in the faces incident with e by an edge e∗ crossing e; if e is incident with only one face, we attach a loop e∗ to the new vertex in that face, again crossing the edge e. The plane multigraph G∗ formed in this way is then dual to G in the following sense: if we apply the same procedure as above to G∗ , we obtain a plane multigraph very similar to G; in fact, G itself may be reobtained from G∗ in this way.
e∗
G∗ Fig. 4.6.1. A plane graph and its dual
To make this idea more precise, let G = (V, E) and (V ∗ , E ∗ ) be any two plane multigraphs, and put F (G) =: F and F ((V ∗ , E ∗ )) =: F ∗ . We call (V ∗ , E ∗ ) a plane dual of G, and write (V ∗ , E ∗ ) =: G∗ , if there are bijections F →V ∗ E → E∗ V →F∗ f 7→ v ∗ (f ) e 7→ e∗ v 7→ f ∗ (v) satisfying the following conditions: (i) v ∗ (f )
f for all f
F;
plane dual G∗
88 (ii) |e∗ ∩ G| = |˚ e∗ ∩˚ e| = |e ∩ G∗ | = 1 for all e (iii) v ∈ f ∗ (v) for all v ∈ V .
4. Planar Graphs ∈
The existence of such bijections implies that both G and G∗ are connected (exercise). Conversely, every connected plane multigraph G has a plane dual G∗ : if we pick from each face f of G a point v ∗ (f ) as a vertex for G∗ , we can always link these vertices up by independent arcs as required by condition (ii), and there is always a bijection V → F ∗ satisfying (iii) (exercise). If G∗1 and G∗2 are two plane duals of G, then clearly G∗1 ' G∗2 ; in fact, one can show that the natural bijection v1∗ (f ) 7→ v2∗ (f ) is a topological isomorphism between G∗1 and G∗2 . In this sense, we may speak of the plane dual G∗ of G. Finally, G is in turn a plane dual of G∗ . Indeed, this is witnessed by the inverse maps of the bijections from the definition of G∗ : setting v ∗ (f ∗ (v)) := v and f ∗ (v ∗ (f )) := f for f ∗ (v) ∈ F ∗ and v ∗ (f ) ∈ V ∗ , we see that conditions (i) and (iii) for G∗ transform into (iii) and (i) for G, while condition (ii) is symmetrical in G and G∗ . Thus, the term ‘dual’ is also formally justified. Plane duality is fascinating not least because it establishes a connection between two natural but very different kinds of edge sets in a multigraph, between cycles and cuts: [ 6.5.2 ]
Proposition 4.6.1. For any connected plane multigraph G, an edge set E ⊆ E(G) is the edge set of a cycle in G if and only if E ∗ := { e∗ | e ∈ E } is a minimal cut in G∗ .
Proof . By conditions (i) and (ii) in the definition of G∗ , two vertices v ∗ (f1 ) and v ∗ (f2 ) of G∗ lie in the same component of G∗ − E ∗ if and S 2 every v ∗ (f1 )–v ∗ (f2 ) only if f1 and f2 lie in the same region of R r E: S ∗ ∗ 2 path in G − E is an arc between f1 and f2 in R r E, and conversely every such arc P (with P ∩ V (G) = ∅) defines a walk in G∗− E ∗ between v ∗ (f1 ) and v ∗ (f2 ). Now if C ⊆ G is a cycle and E = E(C) then, by the Jordan curve theorem and the above correspondence, G∗ − E ∗ has exactly two components, so E ∗ is a minimal cut in G∗ . Conversely, if E ⊆ E(G) is such that E ∗ is a cut in G∗ , then, by Proposition 4.2.3 and the above correspondence, E contains the edges of a cycle C ⊆ G. If E ∗ is minimal as a cut, then E cannot contain any further edges (by the implication shown before), so E = E(C). ¤
abstract dual
Proposition 4.6.1 suggests the following generalization of plane duality to a notion of duality for abstract multigraphs. Let us call a multigraph G∗ an abstract dual of a multigraph G if E(G∗ ) = E(G) and the minimal cuts in G∗ are precisely the edge sets of cycles in G. Note that any abstract dual of a multigraph is connected.
Proposition 4.6.2. If G∗ is an abstract dual of G, then the cut space of G∗ is the cycle space of G, i.e. C ∗ (G∗ ) = C(G) . Proof . By Lemma 1.9.4,5 C ∗ (G∗ ) is the subspace of E(G∗ ) = E(G) generated by the minimal cuts in G∗ . By assumption, these are precisely the edge sets of the cycles in G, and these generate C(G) in E(G). ¤
We finally come to one of the highlights of classical planarity theory: the planar graphs are characterized by the fact that they have an abstract dual. Although less obviously intuitive, this duality is just as fundamental a property as planarity itself; indeed the following theorem may well be seen as a topological characterization of the graphs that have a dual: Theorem 4.6.3. (Whitney 1933) A graph is planar if and only if it has an abstract dual. Proof . Let G be a graph. If G is plane, then every component C of G has a plane dual C ∗ . Let us consider these C ∗ as abstract multigraphs, pick a vertex in each of them, and identify these vertices. In the connected multigraph G∗ obtained, the set of minimal cuts is the union of the sets of minimal cuts in the multigraphs C ∗ . By Proposition 4.6.1, these cuts are precisely the edge sets of the cycles in G, so G∗ is an abstract dual of G. Conversely, suppose that G has an abstract dual G∗ . By Theorem 4.5.1 and Proposition 4.6.2 it suffices to show that C ∗ (G∗ ) has a simple basis, which it has by Proposition 1.9.3. ¤
Show that every graph can be embedded in R3 with all edges straight.
2.− Show directly by Lemma 4.1.2 that K3,3 is not planar. 3.− Find an Euler formula for disconnected graphs. 4.
Show that every connected planar graph with n vertices, m edges and g finite girth g satisfies m 6 g−2 (n − 2).
Show that every planar graph is a union of three forests.
5 Although the lemma was stated for graphs only, its proof remains the same for multigraphs.
Let G1 , G2 , . . . be an infinite sequence of pairwise non-isomorphic graphs. Show that if lim sup ε(Gi ) > 3 then the graphs Gi have unbounded genus—that is to say, there is no (closed) surface S in which all the Gi can be embedded. (Hint. You may use the fact that for every surface S there is a constant χ(S) 6 2 such that every graph embedded in S satisfies the generalized Euler formula of n − m + ` > χ(S).)
Find a direct proof for planar graphs of Tutte’s theorem on the cycle space of 3-connected graphs (Theorem 3.2.3).
8.− Show that the two plane graphs in Fig. 4.3.1 are not combinatorially (and hence not topologically) isomorphic. 9.
Show that the two graphs in Fig. 4.3.2 are combinatorially but not topologically isomorphic.
10.− Show that our definition of equivalence for planar embeddings does indeed define an equivalence relation. 11.
Find a 2-connected planar graph whose drawings are all topologically isomorphic but whose planar embeddings are not all equivalent.
12.+ Show that every plane graph is combinatorially isomorphic to a plane graph whose edges are all straight. (Hint. Given a plane triangulation, construct inductively a graphtheoretically isomorphic plane graph whose edges are straight. Which additional property of the inner faces could help with the induction?) Do not use Kuratowski’s theorem in the following two exercises. 13.
Show that any minor of a planar graph is planar. Deduce that a graph is planar if and only if it is the minor of a grid. (Grids are defined in Chapter 12.3.)
(i) Show that the planar graphs can in principle be characterized as in Kuratowski’s theorem, i.e., that there exists a set X of graphs such that a graph G is planar if and only if G has no topological minor in X . (ii) More generally, which graph properties can be characterized in this way?
15.− Does every planar graph have a drawing with all inner faces convex? 16.
Modify the proof of Lemma 4.4.3 so that all inner faces become convex.
Does every minimal non-planar graph G (i.e., every non-planar graph G whose proper subgraphs are all planar) contain an edge e such that G − e is maximally planar? Does the answer change if we define ‘minimal’ with respect to minors rather than subgraphs?
Show that adding a new edge to a maximal planar graph of order at least 6 always produces both a T K 5 and a T K3,3 subgraph.
Prove the general Kuratowski theorem from its 3-connected case by manipulating plane graphs, i.e. avoiding Lemma 4.4.5. (This is not intended as an exercise in elementary topology; for the topological parts of the proof, a rough sketch will do.)
A graph is called outerplanar if it has a drawing in which every vertex lies on the boundary of the outer face. Show that a graph is outerplanar if and only if it contains neither K 4 nor K2,3 as a minor.
Let G = G1 ∪ G2 , where |G1 ∩ G2 | 6 1. Show that C(G) has a simple basis if both C(G1 ) and C(G2 ) have one.
22.+ Find a cycle space basis among the face boundaries of a 2-connected plane graph. 23.
Show that a 2-connected plane graph is bipartite if and only if every face is bounded by an even cycle.
24.− Let G be a connected plane multigraph, and let G∗ be its plane dual. Prove the following two statements for every edge e ∈ G: (i) If e lies on the boundary of two distinct faces f1 , f2 of G, then e∗ = v ∗(f1 ) v ∗(f2 ). (ii) If e lies on the boundary of exactly one face f of G, then e∗ is a loop at v ∗ (f ). 25.− What does the plane dual of a plane tree look like? 26.− Show that the plane dual of a plane multigraph is connected. 27.+ Show that a plane multigraph has a plane dual if and only if it is connected. 28.
Let G, G∗ be mutually dual plane multigraphs, and let e ∈ E(G). Prove the following statements (with a suitable definition of G/e): (i) If e is not a bridge, then G∗ /e∗ is a plane dual of G − e. (ii) If e is not a loop, then G∗ − e∗ is a plane dual of G/e.
Show that any two plane duals of a plane multigraph are combinatorially isomorphic.
Let G, G∗ be mutually dual plane graphs. Prove the following statements: (i) If G is 2-connected, then G∗ is 2-connected. (ii) If G is 3-connected, then G∗ is 3-connected. (iii) If G is 4-connected, then G∗ need not be 4-connected.
Let G, G∗ be mutually dual plane graphs. Let B1 , . . . , Bn be the blocks of G. Show that B1∗ , . . . , Bn∗ are the blocks of G∗ .
Show that if G∗ is an abstract dual of a multigraph G, then G is an abstract dual of G∗ .
Show that a connected graph G = (V, E) is planar if and only if there exists a connected multigraph G0 = (V 0 , E) (i.e. with the same edge set) such that the following holds for every set F ⊆ E: the graph (V, F ) is a tree if and only if (V 0 , E r F ) is a tree.
Notes There is an excellent monograph on the embedding of graphs in surfaces, including the plane: B. Mohar & C. Thomassen, Graphs on Surfaces, Johns Hopkins University Press, to appear. Proofs of the results cited in Section 4.1, as well as all references for this chapter, can be found there. A good account of the Jordan curve theorem, both polygonal and general, is given also in J. Stillwell, Classical topology and combinatorial group theory, Springer 1980. The short proof of Corollary 4.2.8 uses a trick that deserves special mention: the so-called double counting of pairs, illustrated in the text by a bipartite graph whose edges can be counted alternatively by summing its degrees on the left or on the right. Double counting is a technique widely used in combinatorics, and there will be more examples later in the book. The material of Section 4.3 is not normally standard for an introductory graph theory course, and the rest of the chapter can be read independently of this section. However, the results of Section 4.3 are by no means unimportant. In a way, they have fallen victim to their own success: the shift from a topological to a combinatorial setting for planarity problems which they achieve has made the topological techniques developed there dispensable for most of planarity theory. In its original version, Kuratowski’s theorem was stated only for topological minors; the version for general minors was added by Wagner in 1937. Our proof of the 3-connected case (Lemma 4.4.3) can easily be strengthened to make all the inner faces convex (exercise); see C. Thomassen, Planarity and duality of finite and infinite graphs, J. Combin. Theory B 29 (1980), 244–271. The existence of such ‘convex’ drawings for 3-connected planar graphs follows already from the theorem of Steinitz (1922) that these graphs are precisely the 1-skeletons of 3-dimensional convex polyhedra. Compare also W.T. Tutte, How to draw a graph, Proc. London Math. Soc. 13 (1963), 743–767. As one readily observes, adding an edge to a maximal planar graph (of order at least 6) produces not only a topological K 5 or K3,3 , but both. In Chapter 8.3 we shall see that, more generally, every graph with n vertices and more than 3n − 6 edges contains a T K 5 and, with one easily described class of exceptions, also a T K3,3 . Seymour conjectures that every 5-connected non-planar graph contains a T K 5 (unpublished). The simple cycle space basis constructed in the proof of MacLane’s theorem, which consists of the inner face boundaries, is canonical in the following sense: for every simple basis B of the cycle space of a 2-connected planar graph there exists a drawing of that graph in which B is precisely the set of inner face boundaries. (This is proved in Mohar & Thomassen, who also mention some further planarity criteria.) Our proof of the backward direction of MacLane’s theorem is based on Kuratowski’s theorem. A more direct approach, in which
a planar embedding is actually constructed from a simple basis, is adopted in K. Wagner, Graphentheorie, BI Hochschultaschenb¨ ucher 1972. The proper setting for duality phenomena between cuts and cycles in abstract graphs (and beyond) is the theory of matroids; see J.G. Oxley, Matroid Theory, Oxford University Press 1992.
How many colours do we need to colour the countries of a map in such a way that adjacent countries are coloured differently? How many days have to be scheduled for committee meetings of a parliament if every committee intends to meet for one day and some members of parliament serve on several committees? How can we find a school timetable of minimum total length, based on the information of how often each teacher has to teach each class? A vertex colouring of a graph G = (V, E) is a map c: V → S such that c(v) 6= c(w) whenever v and w are adjacent. The elements of the set S are called the available colours. All that interests us about S is its size: typically, we shall be asking for the smallest integer k such that G has a k-colouring, a vertex colouring c: V → { 1, . . . , k }. This k is the (vertex-) chromatic number of G; it is denoted by χ(G). A graph G with χ(G) = k is called k-chromatic; if χ(G) 6 k, we call G k-colourable.
vertex colouring
chromatic number χ(G)
Fig. 5.0.1. A vertex colouring V → { 1, . . . , 4 }
Note that a k-colouring is nothing but a vertex partition into k independent sets, now called colour classes; the non-trivial 2-colourable graphs, for example, are precisely the bipartite graphs. Historically, the colouring terminology comes from the map colouring problem stated
edge colouring chromatic index χ0 (G)
5. Colouring
above, which leads to the problem of determining the maximum chromatic number of planar graphs. The committee scheduling problem, too, can be phrased as a vertex colouring problem—how? An edge colouring of G = (V, E) is a map c: E → S with c(e) 6= c(f ) for any adjacent edges e, f . The smallest integer k for which a k-edgecolouring exists, i.e. an edge colouring c: E → { 1, . . . , k }, is the edgechromatic number , or chromatic index , of G; it is denoted by χ0 (G). The third of our introductory questions can be modelled as an edge colouring problem in a bipartite multigraph (how?). Clearly, every edge colouring of G is a vertex colouring of its line graph L(G), and vice versa; in particular, χ0 (G) = χ(L(G)). The problem of finding good edge colourings may thus be viewed as a restriction of the more general vertex colouring problem to this special class of graphs. As we shall see, this relationship between the two types of colouring problem is reflected by a marked difference in our knowledge about their solutions: while there are only very rough estimates for χ, its sister χ0 always takes one of two values, either ∆ or ∆ + 1.
5.1 Colouring maps and planar graphs If any result in graph theory has a claim to be known to the world outside, it is the following four colour theorem (which implies that every map can be coloured with at most four colours): Theorem 5.1.1. (Four Colour Theorem) Every planar graph is 4-colourable. Some remarks about the proof of the four colour theorem and its history can be found in the notes at the end of this chapter. Here, we prove the following weakening: Proposition 5.1.2. (Five Colour Theorem) Every planar graph is 5-colourable. (4.1.1) (4.2.8) n, m
Proof . Let G be a plane graph with n > 6 vertices and m edges. We assume inductively that every plane graph with fewer than n vertices can be 5-coloured. By Corollary 4.2.8, d(G) = 2m/n 6 2 (3n − 6)/n < 6 ;
v H c
let v ∈ G be a vertex of degree at most 5. By the induction hypothesis, the graph H := G − v has a vertex colouring c: V (H) → { 1, . . . , 5 }. If c uses at most 4 colours for the neighbours of v, we can extend it to a 5colouring of G. Let us assume, therefore, that v has exactly 5 neighbours, and that these have distinct colours.
5.1 Colouring maps and planar graphs
Let D be an open disc around v, so small that it meets only those five straight edge segments of G that contain v. Let us enumerate these segments according to their cyclic position in D as s1 , . . . , s5 , and let vvi be the edge containing si (i = 1, . . . , 5; Fig. 5.1.1). Without loss of generality we may assume that c(vi ) = i for each i.
D s1 , . . . , s 5 v1 , . . . , v 5
v1 s1 s2 v5
D s4
s3 v3
v4 Fig. 5.1.1. The proof of the five colour theorem
Let us show first that every v1 – v3 path P ⊆ H separates v2 from v4 in H. Clearly, this is the case if and only if the cycle C := vv1 P v3 v separates v2 from v4 in G. We prove this by showing that v2 and v4 lie in different faces of C. Consider the two regions of D r (s1 ∪ s3 ). One of these regions meets s2 , the other s4 . Since C ∩ D ⊆ s1 ∪ s3 , the two regions are each contained within a face of C. Moreover, these faces are distinct: otherwise, D would meet only one face of C, contrary to the fact that v lies on the boundary of both faces (Theorem 4.1.1). Thus D ∩ s2 and D ∩ s4 lie in distinct faces of C. As C meets the edges vv2 ⊇ s2 and vv4 ⊇ s4 only in v, the same holds for v2 and v4 . Given i, j ∈ { 1, . . . , 5 }, let Hi,j be the subgraph of H induced by the vertices coloured i or j. We may assume that the component C1 of H1,3 containing v1 also contains v3 . Indeed, if we interchange the colours 1 and 3 at all the vertices of C1 , we obtain another 5-colouring of H; if v3 ∈/ C1 , then v1 and v3 are both coloured 3 in this new colouring, and we may assign colour 1 to v. Thus, H1,3 contains a v1 – v3 path P . As shown above, P separates v2 from v4 in H. Since P ∩ H2,4 = ∅, this means that v2 and v4 lie in different components of H2,4 . In the component containing v2 , we now interchange the colours 2 and 4, thus recolouring v2 with colour 4. Now v no longer has a neighbour coloured 2, and we may give it this colour. ¤ As a backdrop to the two famous theorems above, let us cite another well-known result: Theorem 5.1.3. (Gr¨ otzsch 1959) Every planar graph not containing a triangle is 3-colourable.
P C
Hi,j
5.2 Colouring vertices How do we determine the chromatic number of a given graph? How can we find a vertex-colouring with as few colours as possible? How does the chromatic number relate to other graph invariants, such as average degree, connectivity or girth? Straight from the definition of the chromatic number we may derive the following upper bound: Proposition 5.2.1. Every graph G with m edges satisfies q χ(G) 6 12 + 2m + 14 . Proof . Let c be a vertex colouring of G with k = χ(G) colours. Then G has at least one edge between any two colour classes: if not, we could have used the same colour for both classes. Thus, m > 12 k(k − 1). Solving this inequality for k, we obtain the assertion claimed. ¤ greedy algorithm
colouring number col(G)
One obvious way to colour a graph G with not too many colours is the following greedy algorithm: starting from a fixed vertex enumeration v1 , . . . , vn of G, we consider the vertices in turn and colour each vi with the first available colour—e.g., with the smallest positive integer not already used to colour any neighbour of vi among v1 , . . . , vi−1 . In this way, we never use more than ∆(G) + 1 colours, even for unfavourable choices of the enumeration v1 , . . . , vn . If G is complete or an odd cycle, then this is even best possible. In general, though, this upper bound of ∆ + 1 is rather generous, even for greedy colourings. Indeed, when we come to colour the vertex vi in the above algorithm, we only need a supply of dG[ v1 ,...,vi ] (vi ) + 1 rather than dG (vi ) + 1 colours to proceed; recall that, at this stage, the algorithm ignores any neighbours vj of vi with j > i. Hence in most graphs, there will be scope for an improvement of the ∆ + 1 bound by choosing a particularly suitable vertex ordering to start with: one that picks vertices of large degree early (when most neighbours are ignored) and vertices of small degree last. Locally, the number dG[ v1 ,...,vi ] (vi ) + 1 of colours required will be smallest if vi has minimum degree in G [ v1 , . . . , vi ]. But this is easily achieved: we just choose vn first, with d(vn ) = δ(G), then choose as vn−1 a vertex of minimum degree in G − vn , and so on. The least number k such that G has a vertex enumeration in which each vertex is preceded by fewer than k of its neighbours is called the colouring number col(G) of G. The enumeration we just discussed shows that col(G) 6 max H⊆G δ(H) + 1. But for H ⊆ G clearly also col(G) > col(H) and col(H) > δ(H) + 1, since the ‘back-degree’ of the last vertex in any enumeration of H is just its ordinary degree in H, which is at least δ(H). So we have proved the following:
5.2 Colouring vertices
Proposition 5.2.2. Every graph G satisfies χ(G) 6 col(G) = max { δ(H) | H ⊆ G } + 1 .
Corollary 5.2.3. Every graph G has a subgraph of minimum degree at least χ(G) − 1. ¤
[ 9.2.1 ] [ 9.2.3 ] [ 11.2.3 ]
The colouring number of a graph is closely related to its arboricity; see the remark following Theorem 3.5.4. As we have seen, every graph G satisfies χ(G) 6 ∆(G) + 1, with equality for complete graphs and odd cycles. In all other cases, this general bound can be improved a little: Theorem 5.2.4. (Brooks 1941) Let G be a connected graph. If G is neither complete nor an odd cycle, then χ(G) 6 ∆(G) . Proof . We apply induction on |G|. If ∆(G) 6 2, then G is a path or a cycle, and the assertion is trivial. We therefore assume that ∆ := ∆(G) > 3, and that the assertion holds for graphs of smaller order. Suppose that χ(G) > ∆. Let v ∈ G be a vertex and H := G − v. Then χ(H) 6 ∆ : by induction, every component H 0 of H satisfies χ(H 0 ) 6 ∆(H 0 ) 6 ∆ unless H 0 is complete or an odd cycle, in which case χ(H 0 ) = ∆(H 0 ) + 1 6 ∆ as every vertex of H 0 has maximum degree in H 0 and one such vertex is also adjacent to v in G. Since H can be ∆-coloured but G cannot, we have the following: Every ∆-colouring of H uses all the colours 1, . . . , ∆ on the neighbours of v; in particular, d(v) = ∆.
v1 , . . . , v ∆ Hi,j
(2) Ci,j
Otherwise we could interchange the colours i and j in one of those components; then vi and vj would be coloured the same, contrary to (1). Ci,j is always a vi – vj path.
v, H
Given any ∆-colouring of H, let us denote the neighbour of v coloured i by vi , i = 1, . . . , ∆. For all i 6= j, let Hi,j denote the subgraph of H spanned by all the vertices coloured i or j. For all i 6= j, the vertices vi and vj lie in a common component Ci,j of Hi,j .
Indeed, let P be a vi – vj path in Ci,j . As dH (vi ) 6 ∆ − 1, the neighbours of vi have pairwise different colours: otherwise we could recolour vi ,
contrary to (1). Hence the neighbour of vi on P is its only neighbour in Ci,j , and similarly for vj . Thus if Ci,j 6= P , then P has an inner vertex with three identically coloured neighbours in H; let u be the first such vertex on P (Fig. 5.2.1). Since at most ∆ − 2 colours are used on the neighbours of u, we may recolour u. But this makes P˚ u into a component of Hi,j , contradicting (2). vj
Ci,j
j i
v j i
P˚ u
Fig. 5.2.1. The proof of (3) in Brooks’s theorem
For distinct i, j, k, the paths Ci,j and Ci,k meet only in vi .
v1 , . . . , v ∆ c u c0
For if vi 6= u ∈ Ci,j ∩ Ci,k , then u has two neighbours coloured j and two coloured k, so we may recolour u. In the new colouring, vi and vj lie in different components of Hi,j , contrary to (2). The proof of the theorem now follows easily. If the neighbours of v are pairwise adjacent, then each has ∆ neighbours in N (v) ∪ { v } already, so G = G [ N (v) ∪ { v } ] = K ∆+1 . As G is complete, there is nothing to show. We may thus assume that v1 v2 ∈/ G, where v1 , . . . , v∆ derive their names from some fixed ∆-colouring c of H. Let u 6= v2 be the neighbour of v1 on the path C1,2 ; then c(u) = 2. Interchanging the colours 1 and 3 0 0 in C1,3 , we obtain a new colouring c0 of H; let vi0 , Hi,j , Ci,j etc. be defined 0 with respect to c in the obvious way. As a neighbour of v1 = v30 , our 0 , since c0 (u) = c(u) = 2. By (4) for c, however, vertex u now lies in C2,3 0 v1 C1,2 ⊆ C1,2 . the path ˚ v1 C1,2 retained its original colouring, so u ∈ ˚ 0 0 0 ∈ ¤ Hence u C2,3 ∩ C1,2 , contradicting (4) for c . As we have seen, a graph G of large chromatic number must have large maximum degree: at least χ(G) − 1. What else can we say about the structure of graphs with large chromatic number? One obvious possible cause for χ(G) > k is the presence of a K k subgraph. This is a local property of G, compatible with arbitrary values of global invariants such as ε and κ. Hence, the assumption of χ(G) > k does not tell us anything about those invariants for G itself. It does, however, imply the existence of a subgraph where those invariants are large: by Corollary 5.2.3, G has a subgraph H with δ(H) > k − 1, and hence by Theorem 1.4.2 a subgraph H 0 with κ(H 0 ) > b 14 (k − 1)c.
So are those somewhat denser subgraphs the ‘cause’ for the large value of χ? Do they, in turn, necessarily contain a graph of high chromatic number—maybe even one from some small collection of canonical such graphs, such as K k ? Interestingly, this is not so: those subgraphs of large but ‘constant’ average degree—bounded below only by a function of k, not of |G|—are not nearly dense enough to contain (necessarily) any particular graph of high chromatic number, let alone K k .1 Yet even if the above local structures do not appear to help, it might still be the case that, somehow, a high chromatic number forces the existence of certain canonical highly chromatic subgraphs. That this is in fact not the case will be our main result in Chapter 11: according to a classic result of Erd˝os, proved by probabilistic methods, there are graphs of arbitrarily large chromatic number and yet arbitrarily large girth (Theorem 11.2.2). Thus given any graph H that is not a forest, for every k ∈ N there are graphs G with χ(G) > k but H 6⊆ G.2 Thus, contrary to our initial guess that a large chromatic number might always be caused by some dense local substructure, it can in fact occur as a purely global phenomenon: after all, locally (around each vertex) a graph of large girth looks just like a tree, and is in particular 2-colourable there! So far, we asked what a high chromatic number implies: it forces the invariants δ, d, ∆ and κ up in some subgraph, but it does not imply the existence of any concrete subgraph of large chromatic number. Let us now consider the converse question: from what assumptions could we deduce that the chromatic number of a given graph is large? Short of a concrete subgraph known to be highly chromatic (such as K k ), there is little or nothing in sight: no values of the invariants studied so far imply that the graph considered has a large chromatic number. (Recall the example of Kn,n .) So what exactly can cause high chromaticity as a global phenomenon largely remains a mystery! Nevertheless, there exists a simple—though not always short— procedure to construct all the graphs of chromatic number > k. For each k ∈ N, let us define the class of k-constructible graphs recursively as follows: (i) K k is k-constructible. (ii) If G is k-constructible and x, y ∈ V (G) are non-adjacent, then also (G + xy)/xy is k-constructible. 1 This is obvious from the examples of Kn,n , which are 2-chromatic but whose connectivity and average degree n exceeds any constant bound. Which (non-constant) average degree exactly will force the existence of a given subgraph will be the topic of Chapter 7. 2 By Corollaries 5.2.3 and 1.5.4, of course, every graph of sufficiently high chromatic number will contain any given forest.
k-constructible
(iii) If G1 , G2 are k-constructible and there are vertices x, y1 , y2 such that G1 ∩ G2 = { x }, xy1 ∈ E(G1 ) and xy2 ∈ E(G2 ), then also (G1 ∪ G2 ) − xy1 − xy2 + y1 y2 is k-constructible (Fig. 5.2.2).
Fig. 5.2.2. The Haj´ os construction (iii)
One easily checks inductively that all k-constructible graphs—and hence their supergraphs—are at least k-chromatic. Indeed, if (G + xy)/xy as in (ii) has a colouring with fewer than k colours, then this defines such a colouring also for G, a contradiction. Similarly, in any colouring of the graph constructed in (iii), the vertices y1 and y2 do not both have the same colour as x, so this colouring induces a colouring of either G1 or G2 and hence uses at least k colours. It is remarkable, though, that the converse holds too: Theorem 5.2.5. (Haj´ os 1961) Let G be a graph and k ∈ N. Then χ(G) > k if and only if G has a k-constructible subgraph.
y1 x, xy2 H1 , H2 H20
v 0 etc.
Proof . Let G be a graph with χ(G) > k; we show that G has a kconstructible subgraph. Suppose not; then k > 3. Adding some edges if necessary, let us make G edge-maximal with the property that none of its subgraphs is k-constructible. Now G is not a complete r-partite graph for any r: for then χ(G) > k would imply r > k, and G would contain the k-constructible graph K k . Since G is not a complete multipartite graph, non-adjacency is not an equivalence relation on V (G). So there are vertices y1 , x, y2 such that y1 x, xy2 ∈/ E(G) but y1 y2 ∈ E(G). Since G is edge-maximal without a k-constructible subgraph, each edge xyi lies in some k-constructible subgraph Hi of G + xyi (i = 1, 2). Let H20 be an isomorphic copy of H2 that contains x and H2 − H1 but is otherwise disjoint from G, together with an isomorphism v 7→ v 0 from H2 to H20 that fixes H2 ∩ H20 pointwise. Then H1 ∩ H20 = { x }, so H := (H1 ∪ H20 ) − xy1 − xy20 + y1 y20 is k-constructible by (iii). One vertex at a time, let us identify in H each vertex v 0 ∈ H20 − G with its partner v; since vv 0 is never an edge of H,
each of these identifications amounts to a construction step of type (ii). Eventually, we obtain the graph (H1 ∪ H2 ) − xy1 − xy2 + y1 y2 ⊆ G ; this is the desired k-constructible subgraph of G.
5.3 Colouring edges Clearly, every graph G satisfies χ0 (G) > ∆(G). For bipartite graphs, we have equality here: Proposition 5.3.1. (K¨ onig 1916) Every bipartite graph G satisfies χ0 (G) = ∆(G). Proof . We apply induction on kGk. For kGk = 0 the assertion holds. Now assume that kGk > 1, and that the assertion holds for graphs with fewer edges. Let ∆ := ∆(G), pick an edge xy ∈ G, and choose a ∆edge-colouring of G − xy by the induction hypothesis. Let us refer to the edges coloured α as α-edges, etc. In G − xy, each of x and y is incident with at most ∆ − 1 edges. Hence there are α, β ∈ { 1, . . . , ∆ } such that x is not incident with an α-edge and y is not incident with a β-edge. If α = β, we can colour the edge xy with this colour and are done; so we may assume that α 6= β, and that x is incident with a β-edge. Let us extend this edge to a maximal walk W whose edges are coloured β and α alternately. Since no such walk contains a vertex twice (why not?), W exists and is a path. Moreover, W does not contain y: if it did, it would end in y on an α-edge (by the choice of β) and thus have even length, so W + xy would be an odd cycle in G (cf. Proposition 1.6.1). We now recolour all the edges on W , swapping α with β. By the choice of α and the maximality of W , adjacent edges of G − xy are still coloured differently. We have thus found a ∆-edge-colouring of G − xy in which neither x nor y is incident with a β-edge. Colouring xy with β, we extend this colouring to a ∆-edge-colouring of G. ¤
(1.6.1) ∆, xy α-edge α, β
Theorem 5.3.2. (Vizing 1964) Every graph G satisfies ∆(G) 6 χ0 (G) 6 ∆(G) + 1 . Proof . We prove the second inequality by induction on kGk. For kGk = 0 it is trivial. For the induction step let G = (V, E) with ∆ := ∆(G) > 0 be
V, E ∆
colouring α-edge
missing α/β - path
given, and assume that the assertion holds for graphs with fewer edges. Instead of ‘(∆ + 1)-edge-colouring’ let us just say ‘colouring’. An edge coloured α will again be called an α-edge. For every edge e ∈ G there exists a colouring of G − e, by the induction hypothesis. In such a colouring, the edges at a given vertex v use at most d(v) 6 ∆ colours, so some colour β ∈ { 1, . . . , ∆ + 1 } is missing at v. For any other colour α, there is a unique maximal walk (possibly trivial) starting at v, whose edges are coloured alternately α and β. This walk is a path; we call it the α/β - path from v. Suppose that G has no colouring. Then the following holds: Given xy ∈ E, and any colouring of G − xy in which the colour α is missing at x and the colour β is missing at y, the α/β - path from y ends in x.
xy0 G0 , c0 , α y1 , . . . , y k Gi
Otherwise we could interchange the colours α and β along this path and colour xy with α, obtaining a colouring of G (contradiction). Let xy0 ∈ G be an edge. By induction, G0 := G − xy0 has a colouring c0 . Let α be a colour missing at x in this colouring. Further, let y0 , y1 , . . . , yk be a maximal sequence of distinct neighbours of x in G, such that c0 (xyi ) is missing in c0 at yi−1 for each i = 1, . . . , k. For each of the graphs Gi := G − xyi we define a colouring ci , setting ½
ci (e) :=
c0 (xyj+1 ) c0 (e)
for e = xyj with j otherwise;
{ 0, . . . , i − 1 }
note that in each of these colourings the same colours are missing at x as in c0 . Now let β be a colour missing at yk in c0 . Clearly, β is still missing at yk in ck . If β were also missing at x, we could colour xyk with β and thus extend ck to a colouring of G. Hence, x is incident with a β-edge (in every colouring). By the maximality of k, therefore, there is an i ∈ { 1, . . . , k − 1 } such that
c0 (xyi ) = β .
Let P be the α/β - path from yk in Gk (with respect to ck ; Fig. 5.3.1). By (1), P ends in x, and it does so on a β-edge, since α is missing at x. As β = c0 (xyi ) = ck (xyi−1 ), this is the edge xyi−1 . In c0 , however, and hence also in ci−1 , β is missing at yi−1 (by (2) and the choice of yi ); let P 0 be the α/β - path from yi−1 in Gi−1 (with respect to ci−1 ). Since P 0 is uniquely determined, it starts with yi−1 P yk ; note that the edges of P˚ x are coloured the same in ci−1 as in ck . But in c0 , and hence in ci−1 , there is no β-edge at yk (by the choice of β). Therefore P 0 ends in yk , contradicting (1). ¤
5.3 Colouring edges
yi+1 β
x β
β α
yi−1
Fig. 5.3.1. The α/β - path P in Gk
Vizing’s theorem divides the finite graphs into two classes according to their chromatic index; graphs satisfying χ0 = ∆ are called (imaginatively) class 1 , those with χ0 = ∆ + 1 are class 2 .
5.4 List colouring In this section, we take a look at a relatively recent generalization of the concepts of colouring studied so far. This generalization may seem a little far-fetched at first glance, but it turns out to supply a fundamental link between the classical (vertex and edge) chromatic numbers of a graph and its other invariants. Suppose we are given a graph G = (V, E), and for each vertex of G a list of colours permitted at that particular vertex: when can we colour G (in the usual sense) so that each vertex receives a colour from its list? More formally, let (Sv )v ∈ V be a family of sets. We call a vertex colouring c of G with c(v) ∈ Sv for all v ∈ V a colouring from the lists Sv . The graph G is called k-list-colourable, or k-choosable, if, for every family (Sv )v ∈ V with |Sv | = k for all v, there is a vertex colouring of G from the lists Sv . The least integer k for which G is k-choosable is the list-chromatic number , or choice number ch(G) of G. List-colourings of edges are defined analogously. The least integer k such that G has an edge colouring from any family of lists of size k is the list-chromatic index ch0 (G) of G; formally, we just set ch0 (G) := ch(L(G)), where L(G) is the line graph of G. In principle, showing that a given graph is k-choosable is more difficult than proving it to be k-colourable: the latter is just the special case of the former where all lists are equal to { 1, . . . , k }. Thus, ch(G) > χ(G) for all graphs G.
ch0 (G) > χ0 (G)
k-choosable choice number ch(G) ch0 (G)
In spite of these inequalities, many of the known upper bounds for the chromatic number have turned out to be valid for the choice number, too. Examples for this phenomenon include Brooks’s theorem and Proposition 5.2.2; in particular, graphs of large choice number still have subgraphs of large minimum degree. On the other hand, it is easy to construct graphs for which the two invariants are wide apart (Exercise 24). Taken together, these two facts indicate a little how far those general upper bounds on the chromatic number may be from the truth. The following theorem shows that, in terms of its relationship to other graph invariants, the choice number differs fundamentally from the chromatic number. As mentioned before, there are 2-chromatic graphs of arbitrarily large minimum degree, e.g. the graphs Kn,n . The choice number, however, will be forced up by large values of invariants like δ, ε or κ: Theorem 5.4.1. (Alon 1993) There exists a function f : N → N such that, given any integer k, all graphs G with average degree d(G) > f (k) satisfy ch(G) > k. The proof of Theorem 5.4.1 uses probabilistic methods as introduced in Chapter 11. Empirically, the choice number’s different character is highlighted by another phenomenon: even in cases where known bounds for the chromatic number could be transferred to the choice number, their proofs have tended to be rather different. One of the simplest and most impressive examples for this is the list version of the five colour theorem: every planar graph is 5-choosable. This had been conjectured for almost 20 years, before Thomassen found a very simple induction proof. This proof does not use the five colour theorem—which thus gets reproved in a very different way. Theorem 5.4.2. (Thomassen 1994) Every planar graph is 5-choosable. (4.2.6)
Proof . We shall prove the following assertion for all plane graphs G with at least 3 vertices: Suppose that every inner face of G is bounded by a triangle and its outer face by a cycle C = v1 . . . vk v1 . Suppose further that v1 has already been coloured with the colour 1, and v2 has been coloured 2. Suppose finally that with every other vertex of C a list of at least 3 colours is associated, and with every vertex of G − C a list of at least 5 colours. Then the colouring of v1 and v2 can be extended to a colouring of G from the given lists.
5.4 List colouring
Let us check first that (∗) implies the assertion of the theorem. Let any plane graph be given, together with a list of 5 colours for each vertex. Add edges to this graph until it is a maximal plane graph G. By Proposition 4.2.6, G is a plane triangulation; let v1 v2 v3 v1 be the boundary of its outer face. We now colour v1 and v2 (differently) from their lists, and extend this colouring by (∗) to a colouring of G from the lists given. Let us now prove (∗), by induction on |G|. If |G| = 3, then G = C and the assertion is trivial. Now let |G| > 4, and assume (∗) for smaller graphs. If C has a chord vw, then vw lies on two unique cycles C1 , C2 ⊆ C + vw with v1 v2 ∈ C1 and v1 v2 ∈/ C2 . For i = 1, 2, let Gi denote the subgraph of G induced by the vertices lying on Ci or in its inner face (Fig. 5.4.1). Applying the induction hypothesis first to G1 and then—with the colours now assigned to v and w—to G2 yields the desired colouring of G.
v2 = w
v G2 Fig. 5.4.1. The induction step with a chord vw; here the case of w = v2
If C has no chord, let v1 , u1 , . . . , um , vk−1 be the neighbours of vk in their natural cyclic order order around vk ;3 by definition of C, all those neighbours ui lie in the inner face of C (Fig. 5.4.2). As the inner faces vk vk−1
P u3 u 2
v1 u1
C0 Fig. 5.4.2. The induction step without a chord 3
as in the first proof of the five colour theorem
u1 , . . . , u m
of C are bounded by triangles, P := v1 u1 . . . um vk−1 is a path in G, and C 0 := P ∪ (C − vk ) a cycle. We now choose two different colours j, ` 6= 1 from the list of vk and delete these colours from the lists of all the vertices ui . Then every list of a vertex on C 0 still has at least 3 colours, so by induction we may colour C 0 and its interior, i.e. the graph G − vk . At least one of the two colours j, ` is not used for vk−1 , and we may assign that colour to vk . ¤ As is often the case with induction proofs, the trick of the proof above lies in the delicately balanced strengthening of the assertion proved. Note that the proof uses neither traditional colouring arguments (such as swapping colours along a path) nor the Euler formula implicit in the standard proof of the five colour theorem. This suggests that maybe in other unsolved colouring problems too it might be of advantage to aim straight for their list version, i.e. to prove an assertion of the form ch(G) 6 k instead of the formally weaker χ(G) 6 k. Unfortunately, this approach fails for the four colour theorem: planar graphs are not in general 4-choosable. As mentioned before, the chromatic number of a graph and its choice number may differ a lot. Surprisingly, however, no such examples are known for edge colourings. Indeed it has been conjectured that none exist: List colouring conjecture. Every graph G satisfies ch0 (G) = χ0 (G).
N + (v) d+ (v)
We shall prove the list colouring conjecture for bipartite graphs. As a tool we shall use orientations of graphs, defined in Chapter 1.10. If D is a directed graph and v ∈ V (D), we denote by N + (v) the set, and by d+ (v) the number, of vertices w such that D contains an edge directed from v to w. To see how orientations come into play in the context of colouring, let us recall the greedy algorithm from Section 5.2. In order to apply the algorithm to a graph G, we first have to choose a vertex enumeration v1 , . . . , vn of G. The enumeration chosen defines an orientation of G: just orient every edge vi vj ‘backwards’, from vi to vj if i > j. Then, for each vertex vi to be coloured, the algorithm considers only those edges at vi that are directed away from vi : if d+ (v) < k for all vertices v, it will use at most k colours. Moreover, the first colour class U found by the algorithm has the following property: it is an independent set of vertices to which every other vertex sends an edge. The second colour class has the same property in G − U , and so on. The following lemma generalizes this to orientations D of G that do not necessarily come from a vertex enumeration, but may contain some directed cycles. Let us call an independent set U ⊆ V (D) a kernel of D
if, for every vertex v ∈ D − U , there is an edge in D directed from v to a vertex in U . Note that kernels of non-empty directed graphs are themselves non-empty. Lemma 5.4.3. Let H be a graph and (Sv )v ∈ V (H) a family of lists. If H has an orientation D with d+ (v) < |Sv | for every v, and such that every induced subgraph of D has a kernel, then H can be coloured from the lists Sv . Proof . We apply induction on |H|. For |H| = 0 we take the empty colouring. For the induction step, let |H| > 0. Let α be a colour occurring in one of the lists Sv , and let D be an orientation of H as stated. The vertices v with α ∈ Sv span a non-empty subgraph D0 in D; by assumption, D0 has a kernel U 6= ∅. Let us colour the vertices in U with α, and remove α from the lists of all the other vertices of D0 . Since each of those vertices sends an edge to U , the modified lists Sv0 for v ∈ D − U again satisfy the condition d+ (v) < |Sv0 | in D − U . Since D − U is an orientation of H − U , we can thus colour H − U from those lists by the induction hypothesis. As none of these lists contains α, this extends our colouring U → { α } to the desired list colouring of H. ¤
α D0 U
Theorem 5.4.4. (Galvin 1995) Every bipartite graph G satisfies ch0 (G) = χ0 (G). Proof . Let G =: (X ∪ Y, E), where { X, Y } is a vertex bipartition of G. Let us say that two edges of G meet in X if they share an end in X, and correspondingly for Y . Let χ0 (G) =: k, and let c be a k-edge-colouring of G. Clearly, ch0 (G) > k; we prove that ch0 (G) 6 k. Our plan is to use Lemma 5.4.3 to show that the line graph H of G is k-choosable. To apply the lemma, it suffices to find an orientation D of H with d+ (v) < k for every vertex v, and such that every induced subgraph of D has a kernel. To define D, consider adjacent e, e0 ∈ E, say with c(e) < c(e0 ). If e and e0 meet in X, we orient the edge ee0 ∈ H from e0 towards e; if e and e0 meet in Y , we orient it from e to e0 (Fig 5.4.3). Let us compute d+ (e) for given e ∈ E = V (D). If c(e) = i, say, then every e0 ∈ N + (e) meeting e in X has its colour in { 1, . . . , i − 1 }, and every e0 ∈ N + (e) meeting e in Y has its colour in { i + 1, . . . , k }. As any two neighbours e0 of e meeting e either both in X or both in Y are themselves adjacent and hence coloured differently, this implies d+ (e) < k as desired. It remains to show that every induced subgraph D0 of D has a kernel. We show this by induction on |D0 |. For D0 = ∅, the empty set is a kernel; so let |D0 | > 1. Let E 0 := V (D0 ) ⊆ E. For every x ∈ X at which E 0 has an edge, let ex ∈ E 0 be the edge at x with minimum
X, Y, E k c H
D0 E0
5. Colouring 1
Fig. 5.4.3. Orienting the line graph of G U
e, e0 U0
c-value, and let U denote the set of all those edges ex . Then every edge e0 ∈ E 0 r U meets some e ∈ U in X, and the edge ee0 ∈ D0 is directed from e0 to e. If U is independent, it is thus a kernel of D0 and we are home; let us assume, therefore, that U is not independent. Let e, e0 ∈ U be adjacent, and assume that c(e) < c(e0 ). By definition of U , e and e0 meet in Y , so the edge ee0 ∈ D0 is directed from e to e0 . By the induction hypothesis, D0 − e has a kernel U 0 . If e0 ∈ U 0 , then U 0 is also a kernel of D0 , and we are done. If not, there exists an e00 ∈ U 0 such that D0 has an edge directed from e0 to e00 . If e0 and e00 met in X, then c(e00 ) < c(e0 ) by definition of D, contradicting e0 ∈ U . Hence e0 and e00 meet in Y , and c(e0 ) < c(e00 ). Since e and e0 meet in Y , too, also e and e00 meet in Y , and c(e) < c(e0 ) < c(e00 ). So the edge ee00 is directed ¤ from e towards e00 , so again U 0 is also a kernel of D0 . By Proposition 5.3.1, we now know the exact list-chromatic index of bipartite graphs: Corollary 5.4.5. Every bipartite graph G satisfies ch0 (G) = ∆(G). ¤
5.5 Perfect graphs
ω(G) α(G)
As discussed in Section 5.2, a high chromatic number may occur as a purely global phenomenon: even when a graph has large girth, and thus locally looks like a tree, its chromatic number may be arbitrarily high. Since such ‘global dependence’ is obviously difficult to deal with, one may become interested in graphs where this phenomenon does not occur, i.e. whose chromatic number is high only when there is a local reason for it. Before we make this precise, let us note two definitions for a graph G. The greatest integer r such that K r ⊆ G is the clique number ω(G) of G, and the greatest integer r such that K r ⊆ G (induced) is the independence number α(G) of G. Clearly, α(G) = ω(G) and ω(G) = α(G).
A graph is called perfect if every induced subgraph H ⊆ G has chromatic number χ(H) = ω(H), i.e. if the trivial lower bound of ω(H) colours always suffices to colour the vertices of H. Thus, while proving an assertion of the form χ(G) > k may in general be difficult, even in principle, for a given graph G, it can always be done for a perfect graph simply by exhibiting some K k+1 subgraph as a ‘certificate’ for non-colourability with k colours. At first glance, the structure of the class of perfect graphs appears somewhat contrived: although it is closed under induced subgraphs (if only by explicit definition), it is not closed under taking general subgraphs or supergraphs, let alone minors (examples?). However, perfection is an important notion in graph theory: the fact that several fundamental classes of graphs are perfect (as if by fluke) may serve as a superficial indication of this.4 What graphs, then, are perfect? Bipartite graphs are, for instance. Less trivially, the complements of bipartite graphs are perfect, too— a fact equivalent to K¨ onig’s duality theorem 2.1.1 (Exercise 34). The so-called comparability graphs are perfect, and so are the interval graphs (see the exercises); both these turn up in numerous applications. In order to study at least one such example in some detail, we prove here that the chordal graphs are perfect: a graph is chordal (or triangulated ) if each of its cycles of length at least 4 has a chord, i.e. if it contains no induced cycles other than triangles. To show that chordal graphs are perfect, we shall first characterize their structure. If G is a graph with induced subgraphs G1 , G2 and S, such that G = G1 ∪ G2 and S = G1 ∩ G2 , we say that G arises from G1 and G2 by pasting these graphs together along S. Proposition 5.5.1. A graph is chordal if and only if it can be constructed recursively by pasting along complete subgraphs, starting from complete graphs. Proof . If G is obtained from two chordal graphs G1 , G2 by pasting them together along a complete subgraph, then G is clearly again chordal: any induced cycle in G lies in either G1 or G2 , and is hence a triangle by assumption. Since complete graphs are chordal, this proves that all graphs constructible as stated are chordal. Conversely, let G be a chordal graph. We show by induction on |G| that G can be constructed as described. This is trivial if G is complete. We therefore assume that G is not complete, in particular |G| > 1, and that all smaller chordal graphs are constructible as stated. Let a, b ∈ G 4 The class of perfect graphs has duality properties with deep connections to optimization and complexity theory, which are far from understood. Theorem 5.5.5 shows the tip of an iceberg here; for more, the reader is referred to Lov´ asz’s survey cited in the notes.
chordal
pasting [ 12.3.11 ]
112 X C G1 , G2 S
be two non-adjacent vertices, and let X ⊆ V (G) r { a, b } a minimal set of vertices separating a from b. Let C denote the component of G − X containing a, and put G1 := G [ V (C) ∪ X ] and G2 := G − C. Then G arises from G1 and G2 by pasting these graphs together along S := G [ X ]. Since G1 and G2 are both chordal (being induced subgraphs of G) and hence constructible by induction, it suffices to show that S is complete. Suppose, then, that s, t ∈ S are non-adjacent. By the minimality of X = V (S) as an a–b separator, both s and t have a neighbour in C. Hence, there is an X-path from s to t in G1 ; we let P1 be a shortest such path. Analogously, G2 contains a shortest X-path P2 from s to t. But then P1 ∪ P2 is a chordless cycle of length > 4 (Fig. 5.5.1), contradicting our assumption that G is chordal. ¤
s P2
Fig. 5.5.1. If G1 and G2 are chordal, then so is G
Proposition 5.5.2. Every chordal graph is perfect. Proof . Since complete graphs are perfect, it suffices by Proposition 5.5.1 to show that any graph G obtained from perfect graphs G1 , G2 by pasting them together along a complete subgraph S is again perfect. So let H ⊆ G be an induced subgraph; we show that χ(H) 6 ω(H). Let Hi := H ∩ Gi for i = 1, 2, and let T := H ∩ S. Then T is again complete, and H arises from H1 and H2 by pasting along T . As an induced subgraph of Gi , each Hi can be coloured with ω(Hi ) colours. Since T is complete and hence coloured injectively, two such colourings, one of H1 and one of H2 , may be combined into a colouring of H with max { ω(H1 ), ω(H2 ) } 6 ω(H) colours—if necessary by permuting the colours in one of the Hi . ¤ We now come to the main result in the theory of perfect graphs, the perfect graph theorem: perfect graph theorem
Theorem 5.5.3. (Lov´ asz 1972) A graph is perfect if and only if its complement is perfect.
We shall give two proofs of Theorem 5.5.3. The first of these is Lov´asz’s original proof, which is still unsurpassed in its clarity and the amount of ‘feel’ for the problem it conveys. Our second proof, due to Gasparian (1996), is in fact a very short and elegant linear algebra proof of another theorem of Lov´asz’s (Theorem 5.5.5), which easily implies Theorem 5.5.3. Let us prepare our first proof of the perfect graph theorem by a lemma. Let G be a graph and x ∈ G a vertex, and let G0 be obtained from G by adding a vertex x0 and joining it to x and all the neighbours of x. We say that G0 is obtained from G by expanding the vertex x to an edge xx0 (Fig. 5.5.2). x
expanding a vertex
x0 G0
H X r{x}
Fig. 5.5.2. Expanding the vertex x in the proof of Lemma 5.5.4
Lemma 5.5.4. Any graph obtained from a perfect graph by expanding a vertex is again perfect. Proof . We use induction on the order of the perfect graph considered. Expanding the vertex of K 1 yields K 2 , which is perfect. For the induction step, let G be a non-trivial perfect graph, and let G0 be obtained from G by expanding a vertex x ∈ G to an edge xx0 . For our proof that G0 is perfect it suffices to show χ(G0 ) 6 ω(G0 ): every proper induced subgraph H of G0 is either isomorphic to an induced subgraph of G or obtained from a proper induced subgraph of G by expanding x; in either case, H is perfect by assumption and the induction hypothesis, and can hence be coloured with ω(H) colours. Let ω(G) =: ω ; then ω(G0 ) ∈ { ω, ω + 1 }. If ω(G0 ) = ω + 1, then
x, x0
χ(G0 ) 6 χ(G) + 1 = ω + 1 = ω(G0 ) and we are done. So let us assume that ω(G0 ) = ω. Then x lies in no K ω ⊆ G: together with x0 , this would yield a K ω+1 in G0 . Let us colour G with ω colours. Since every K ω ⊆ G meets the colour class X of x but not x itself, the graph H := G − (X r { x }) has clique number ω(H) < ω (Fig. 5.5.2). Since G is perfect, we may thus colour H with ω − 1 colours. Now X is independent, so the set (X r { x }) ∪ { x0 } = V (G0 − H) is also independent. We can therefore extend our (ω − 1)-colouring of H to an ω-colouring of G0 , showing that χ(G0 ) 6 ω = ω(G0 ) as desired. ¤
X H
G = (V, E) K α A
Proof of Theorem 5.5.3. Applying induction on |G|, we show that the complement G of any perfect graph G = (V, E) is again perfect. For |G| = 1 this is trivial, so let |G| > 2 for the induction step. Let K denote the set of all vertex sets of complete subgraphs of G. Put α(G) =: α, and let A be the set of all independent vertex sets A in G with |A| = α. Every proper induced subgraph of G is the complement of a proper induced subgraph of G, and is hence perfect by induction. For the perfection of G it thus suffices to prove χ(G) 6 ω(G) (= α). To this end, we shall find a set K ∈ K such that K ∩ A 6= ∅ for all A ∈ A; then ω(G − K) = α(G − K) < α = ω(G) , so by the induction hypothesis χ(G) 6 χ(G − K) + 1 = ω(G − K) + 1 6 ω(G)
AK Gx k(x)
as desired. Suppose there is no such K; thus, for every K ∈ K there exists a set AK ∈ A with K ∩ AK = ∅. Let us replace in G every vertex x by a complete graph Gx of order ¯ k(x) := ¯{ K
K|x
¯ AK }¯ ,
joining all the vertices of Gx to all the vertices of Gy whenever S x and y are adjacent in G. The graph G0 thus obtained has vertex set x ∈ V V (Gx ), and two vertices v ∈ Gx and w ∈ Gy are adjacent in G0 if and only if x = y or xy ∈ E. Moreover, G0 can be obtained by repeated vertex expansion from the graph G [ { x ∈ V | k(x) > 0 } ]. Being an induced subgraph of G, this latter graph is perfect by assumption, so G0 is perfect by Lemma 5.5.4. In particular, χ(G0 ) 6 ω(G0 ) .
In order to obtain a contradiction to (1), we now compute in turn the actual values of ω(G0 ) and χ(G0 ). By construction of G0 , every maximal S 0 0 complete subgraph of G has the form G [ x ∈ X Gx ] for some X ∈ K. So there exists a set X ∈ K such that ω(G0 ) =
k(x)
x∈X
¯ = ¯{ (x, K) : x ∈ X, K X |X ∩ AK | =
K, x
¯ AK }¯
K ∈K
6 |K| − 1 ;
the last inequality follows from the fact that |X ∩ AK | 6 1 for all K (since AK is independent but G [ X ] is complete), and |X ∩ AX | = 0 (by the choice of AX ). On the other hand, |G0 | =
x∈V
¯ = ¯{ (x, K) : x X |AK | =
V, K
= |K| · α . As α(G0 ) 6 α by construction of G0 , this implies χ(G0 ) >
|G0 | |G0 | > = |K| . 0 α(G ) α
Putting (2) and (3) together we obtain χ(G0 ) > |K| > |K| − 1 > ω(G0 ) , ¤
a contradiction to (1).
Since the following characterization of perfection is symmetrical in G and G, it clearly implies Theorem 5.5.3. As our proof of Theorem 5.5.5 will again be from first principles, we thus obtain a second and independent proof of the perfect graph theorem. Theorem 5.5.5. (Lov´ asz 1972) A graph G is perfect if and only if |H| 6 α(H) · ω(H)
for all induced subgraphs H ⊆ G. Proof . Let us write V (G) =: V =: { v1 , . . . , vn }, and put α := α(G) and ω := ω(G). The necessity of (∗) is immediate: if G is perfect, then every induced subgraph H of G can be partitioned into at most ω(H) colour classes each containing at most α(H) vertices, and (∗) follows. To prove sufficiency, we apply induction on n = |G|. Assume that every induced subgraph H of G satisfies (∗), and suppose that G is not perfect. By the induction hypothesis, every proper induced subgraph of G is perfect. Hence, every non-empty independent set U ⊆ V satisfies χ(G − U ) = ω(G − U ) = ω .
V, vi , n α, ω
Indeed, while the first equality is immediate from the perfection of G − U , the second is easy: ‘6’ is obvious, while χ(G − U ) < ω would imply χ(G) 6 ω, so G would be perfect contrary to our assumption. Let us apply (1) to a singleton U = { u } and consider an ω-colouring of G − u. Let K be the vertex set of any K ω in G. Clearly, if u ∈/ K then K meets every colour class of G − u; if u A0
Ai Ki
K then K meets all but exactly one colour class of G − u. (3)
Let A0 = { u1 , . . . , uα } be an independent set in G of size α. Let A1 , . . . , Aω be the colour classes of an ω-colouring of G − u1 , let Aω+1 , . . . , A2ω be the colour classes of an ω-colouring of G − u2 , and so on; altogether, this gives us αω + 1 independent sets A0 , A1 , . . . , Aαω in G. For each i = 0, . . . , αω, there exists by (1) a K ω ⊆ G − Ai ; we denote its vertex set by Ki . Note that if K is the vertex set of any K ω in G, then K ∩ Ai = ∅ for exactly one i
J A
{ 0, . . . , αω + 1 }.
Indeed, if K ∩ A0 = ∅ then K ∩ Ai 6= ∅ for all i 6= 0, by definition of Ai and (2). Similarly if K ∩ A0 6= ∅, then |K ∩ A0 | = 1, so K ∩ Ai = ∅ for exactly one i 6= 0: apply (3) to the unique vertex u ∈ K ∩ A0 , and (2) to all the other vertices u ∈ A0 . Let J be the real (αω + 1) × (αω + 1) matrix with zero entries in the main diagonal and all other entries 1. Let A be the real (αω + 1) × n matrix whose rows are the incidence vectors of the subsets Ai ⊆ V : if ai1 , . . . , ain denote the entries of the ith row of A, then aij = 1 if vj ∈ Ai , and aij = 0 otherwise. Similarly, let B denote the real n × (αω + 1) matrix whose columns are the incidence vectors of the subsets Ki ⊆ V . Now while |Ki ∩ Ai | = 0 for all i by the choice of Ki , we have Ki ∩ Aj 6= ∅ and hence |Ki ∩ Aj | = 1 whenever i 6= j, by (4). Thus, AB = J. Since J is non-singular, this implies that A has rank αω + 1. In particular, n > αω + 1, which contradicts (∗) for H := G. ¤ By definition, every induced subgraph of a perfect graph is again perfect. The property of perfection can therefore be characterized by forbidden induced subgraphs: there exists a set H of imperfect graphs such that any graph is perfect if and only if it has no induced subgraph isomorphic to an element of H. (For example, we may choose as H the set of all imperfect graphs with vertices in N.) Naturally, it would be desirable to keep H as small as possible. In fact, one of the best known conjectures in graph theory says that H
need only contain two types of graph: the odd cycles of length > 5 and their complements. (Neither of these are perfect—why?) Or, rephrased slightly: Perfect Graph Conjecture. (Berge 1966) A graph G is perfect if and only if neither G nor G contains an odd cycle of length at least 5 as an induced subgraph. Clearly, this conjecture implies the perfect graph theorem. In fact, that theorem had also been conjectured by Berge: until its proof, it was known as the ‘weak’ version of the perfect graph conjecture, the above conjecture being the ‘strong’ version. Graphs G such that neither G nor G contains an induced odd cycle of length at least 5 have been called Berge graphs. Thus all perfect graphs are Berge graphs, and the perfect graph conjecture claims that all Berge graphs are perfect. This has been approximately verified by Pr¨omel & Steger (1992), who proved that the proportion of perfect graphs to Berge graphs on n vertices tends to 1 as n → ∞.
Exercises 1.− Show that the four colour theorem does indeed solve the map colouring problem stated in the first sentence of the chapter. Conversely, does the 4-colourability of every map imply the four colour theorem? 2.− Show that, for the map colouring problem above, it suffices to consider maps such that no point lies on the boundary of more than three countries. How does this affect the proof of the four colour theorem? 3.
Try to turn the proof of the five colour theorem into one of the four colour theorem, as follows. Defining v and H as before, assume inductively that H has a 4-colouring; then proceed as before. Where does the proof fail?
Calculate the chromatic number of a graph in terms of the chromatic numbers of its blocks.
5.− Show that every graph G has a vertex ordering for which the greedy algorithm uses only χ(G) colours. 6.
For every n > 1, find a bipartite graph on 2n vertices, ordered in such a way that the greedy algorithm uses n rather than 2 colours.
Consider the following approach to vertex colouring. First, find a maximal independent set of vertices and colour these with colour 1; then find a maximal independent set of vertices in the remaining graph and colour those 2, and so on. Compare this algorithm with the greedy algorithm: which is better?
Show that the bound of Proposition 5.2.2 is always at least as sharp as that of Proposition 5.2.1.
Find a function f such that every graph of arboricity at least f (k) has colouring number at least k, and a function g such that every graph of colouring number at least g(k) has arboricity at least k, for all k ∈ N. (The arboricity of a graph is defined in Chapter 3.5.)
10.− A k-chromatic graph is called critically k-chromatic, or just critical , if χ(G − v) < k for every v ∈ V (G). Show that every k-chromatic graph has a critical k-chromatic induced subgraph, and that any such subgraph has minimum degree at least k − 1. 11.
Determine the critical 3-chromatic graphs.
12.+ Show that every critical k-chromatic graph is (k − 1) - edge-connected. 13.
Given k ∈ N, find a constant ck > 0 such that every graph G with |G| > 3k and α(G) 6 k contains a cycle of length at least ck |G|.
14.− Find a graph G for which Brooks’s theorem yields a significantly weaker bound on χ(G) than Proposition 5.2.2. 15.+ Show that, in order to prove Brooks’s theorem for a graph G = (V, E), we may assume that κ(G) > 2 and ∆(G) > 3. Prove the theorem under these assumptions, showing first the following two lemmas. (i) Let v1 , . . . , vn be an enumeration of V . If every vi (i < n) has a neighbour vj with j > i, and if v1 vn , v2 vn ∈ E but v1 v2 ∈/ E, then the greedy algorithm uses at most ∆(G) colours. (ii) If G is not complete and vn has maximum degree in G, then vn has neighbours v1 , v2 as in (i). 16.
Given a graph G and k ∈ N, let PG (k) denote the number of vertex colourings V (G) → { 1, . . . , k }. Show that PG is a polynomial in k of degree n := |G|, in which the coefficient of kn is 1 and the coefficient of kn−1 is −kGk. (PG is called the chromatic polynomial of G.) (Hint. Apply induction on kGk. In the induction step, compare the values of PG (k), PG−e (k) and PG/e (k).)
17.+ Determine the class of all graphs G for which PG (k) = k (k − 1)n−1 . (As in the previous exercise, let n := |G|, and let PG denote the chromatic polynomial of G.) 18.
In the definition of k-constructible graphs, replace the axiom (ii) by (ii)0 Every supergraph of a k-constructible graph is k-constructible; and the axiom (iii) by (iii)0 If G is a graph with vertices x, y1 , y2 such that y1 y2 ∈ E(G) but xy1 , xy2 ∈/ E(G), and if both G + xy1 and G + xy2 are kconstructible, then G is k-constructible. Show that a graph is k-constructible with respect to this new definition if and only if its chromatic number is at least k.
19.− An n × n - matrix with entries from { 1, . . . , n } is called a Latin square if every element of { 1, . . . , n } appears exactly once in each column and exactly once in each row. Recast the problem of constructing Latin squares as a colouring problem. Without using Proposition 5.3.1, show that χ0 (G) = k for every kregular bipartite graph G.
20. 21. +
Prove Proposition 5.3.1 from the statement of the previous exercise. For every k
N, construct a triangle-free k-chromatic graph.
Without using Theorem 5.4.2, show that every plane graph is 6-listcolourable. For every integer k, find a 2-chromatic graph whose choice number is at least k.
25.− Find a general upper bound for ch0 (G) in terms of χ0 (G). 26.
Compare the choice number of a graph with its colouring number: which is greater? Can you prove the analogue of Theorem 5.4.1 for the colouring number?
27.+ Prove that the choice number of K2r is r. 28.
The total chromatic number χ00 (G) of a graph G = (V, E) is the least number of colours needed to colour the vertices and edges of G simultaneously so that any adjacent or incident elements of V ∪ E are coloured differently. The total colouring conjecture says that χ00 (G) 6 ∆(G) + 2. Bound the total chromatic number from above in terms of the listchromatic index, and use this bound to deduce a weakening of the total colouring conjecture from the list colouring conjecture.
29.− Find a directed graph that has no kernel. 30.+ Prove Richardson’s theorem: every directed graph without odd directed cycles has a kernel. 31.
Show that every bipartite planar graph is 3-list-colourable. (Hint. Apply the previous exercise and Lemma 5.4.3.)
32.− Show that perfection is closed neither under edge deletion nor under edge contraction. 33.− Deduce Theorem 5.5.5 from the perfect graph conjecture. 34.
Use K¨ onig’s Theorem 2.1.1 to show that the complement of any bipartite graph is perfect.
Using the results of this chapter, find a one-line proof of the following theorem of K¨ onig, the dual of Theorem 2.1.1: in any bipartite graph without isolated vertices, the minimum number of edges meeting all vertices equals the maximum number of independent vertices.
A graph is called a comparability graph if there exists a partial ordering of its vertex set such that two vertices are adjacent if and only if they are comparable. Show that every comparability graph is perfect.
A graph G is called an interval graph if there exists a set { Iv | v ∈ V (G) } of real intervals such that Iu ∩ Iv 6= ∅ if and only if uv ∈ E(G).
(i) Show that every interval graph is chordal. (ii) Show that the complement of any interval graph is a comparability graph. (Conversely, a chordal graph is an interval graph if its complement is a comparability graph; this is a theorem of Gilmore and Hoffman (1964).) 38. +
Show that χ(H)
{ ω(H) , ω(H) + 1 } for every line graph H.
Characterize the graphs whose line graphs are perfect.
Show that a graph G is perfect if and only if every non-empty induced subgraph H of G contains an independent set A ⊆ V (H) such that ω(H − A) < ω(H).
41.+ Consider the graphs G for which every induced subgraph H has the property that every maximal complete subgraph of H meets every maximal independent vertex set in H. (i) Show that these graphs G are perfect. (ii) Show that these graphs G are precisely the graphs not containing an induced copy of P 3 . 42.+ Show that in every perfect graph G one can find a set A of independent vertex sets and aSset O of vertex sets of complete subgraphs such that S A = V (G) = O and every set in A meets every set in O. (Hint. Lemma 5.5.4.) +
Let G be a perfect graph. As in the proof of Theorem 5.5.3, replace every vertex x of G with a perfect graph Gx (not necessarily complete). Show that the resulting graph G0 is again perfect.
Let H1 and H2 be two sets of imperfect graphs, each minimal with the property that a graph is perfect if and only if it has no induced subgraph in Hi (i = 1, 2). Do H1 and H2 contain the same graphs, up to isomorphism?
Notes The authoritative reference work on all questions of graph colouring is T.R. Jensen & B. Toft, Graph Coloring Problems, Wiley 1995. Starting with a brief survey of the most important results and areas of research in the field, this monograph gives a detailed account of over 200 open colouring problems, complete with extensive background surveys and references. Most of the remarks below are discussed comprehensively in this book, and all the references for this chapter can be found there. The four colour problem, whether every map can be coloured with four colours so that adjacent countries are shown in different colours, was raised by a certain Francis Guthrie in 1852. He put the question to his brother Frederick, who was then a mathematics undergraduate in Cambridge. The problem was
first brought to the attention of a wider public when Cayley presented it to the London Mathematical Society in 1878. A year later, Kempe published an incorrect proof, which was in 1890 modified by Heawood into a proof of the five colour theorem. In 1880, Tait announced ‘further proofs’ of the four colour conjecture, which never materialized; see the notes for Chapter 10. The first generally accepted proof of the four colour theorem was published by Appel and Haken in 1977. The proof builds on ideas that can be traced back as far as Kempe’s paper, and were developed largely by Birkhoff and Heesch. Very roughly, the proof sets out first to show that every plane triangulation must contain at least one of 1482 certain ‘unavoidable configurations’. In a second step, a computer is used to show that each of those configurations is ‘reducible’, i.e., that any plane triangulation containing such a configuration can be 4-coloured by piecing together 4-colourings of smaller plane triangulations. Taken together, these two steps amount to an inductive proof that all plane triangulations, and hence all planar graphs, can be 4coloured. Appel & Haken’s proof has not been immune to criticism, not only because of their use of a computer. The authors responded with a 741 page long algorithmic version of their proof, which addresses the various criticisms and corrects a number of errors (e.g. by adding more configurations to the ‘unavoidable’ list): K. Appel & W. Haken, Every Planar Map is Four Colorable, American Mathematical Society 1989. A much shorter proof, which is based on the same ideas (and, in particular, uses a computer in the same way) but can be more readily verified both in its verbal and its computer part, has been given by N. Robertson, D. Sanders, P.D. Seymour & R. Thomas, The four-colour theorem, J. Combin. Theory B 70 (1997), 2–44. A relatively short proof of Gr¨ otzsch’s theorem was found by C. Thomassen, Gr¨ otzsch’s 3-color theorem and its counterparts for the torus and the projective plane, J. Combin. Theory B 62 (1994), 268–279. Although not touched upon in this chapter, colouring problems for graphs embedded in surfaces other than the plane form a substantial and interesting part of colouring theory; see B. Mohar & C. Thomassen, Graphs on Surfaces, Johns Hopkins University Press, to appear. The proof of Brooks’s theorem indicated in Exercise 15, where the greedy algorithm is applied to a carefully chosen vertex ordering, is due to Lov´ asz (1973). Lov´ asz (1968) was also the first to construct graphs of arbitrarily large girth and chromatic number, graphs whose existence Erd˝ os had proved by probabilistic methods ten years earlier. A. Urquhart, The graph constructions of Haj´ os and Ore, J. Graph Theory 26 (1997), 211–215, showed that not only do the graphs of chromatic number at least k each contain a k-constructible graph (as by Haj´ os’s theorem); they are in fact all themselves k-constructible. Algebraic tools for showing that the chromatic number of a graph is large have been developed by Kleitman & Lov´ asz (1982), and by Alon & Tarsi (1992); see Alon’s paper cited below. List colourings were first introduced in 1976 by Vizing. Among other things, Vizing proved the list-colouring equivalent of Brooks’s theorem. Voigt (1993) constructed a plane graph of order 238 that is not 4-choosable; thus, Thomassen’s list version of the five colour theorem is best possible. A stimulating survey on the list-chromatic number and how it relates to the more
classical graph invariants (including a proof of Theorem 5.4.1) is given by N. Alon, Restricted colorings of graphs, in (K. Walker, ed.) Surveys in Combinatorics, LMS Lecture Notes 187, Cambridge University Press 1993. Both the list colouring conjecture and Galvin’s proof of the bipartite case are originally stated for multigraphs. Kahn (1994) proved that the conjecture is asymptotically correct, as follows: given any ² > 0, every graph G with large enough maximum degree satisfies ch0 (G) 6 (1 + ²)∆(G). The total colouring conjecture was proposed around 1965 by Vizing and by Behzad; see Jensen & Toft for details. A gentle introduction to the basic facts about perfect graphs and their applications is given by M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press 1980. Our first proof of the perfect graph theorem follows L. Lov´ asz’s survey on perfect graphs in (L.W. Beineke and R.J. Wilson, eds.) Selected Topics in Graph Theory 2, Academic Press 1983. The theorem was also proved independently, and only a little later, by Fulkerson. Our second proof, the proof of Theorem 5.5.5, is due to G.S. Gasparian, Minimal imperfect graphs: a simple approach, Combinatorica 16 (1996), 209–212. The approximate proof of the perfect graph conjecture is due to H.J. Pr¨ omel & A. Steger, Almost all Berge graphs are perfect, Combinatorics, Probability and Computing 1 (1992), 53–79.
Let us view a graph as a network: its edges carry some kind of flow—of water, electricity, data or similar. How could we model this precisely? For a start, we ought to know how much flow passes through each edge e = xy, and in which direction. In our model, we could assign a positive integer k to the pair (x, y) to express that a flow of k units passes through e from x to y, or assign −k to (x, y) to express that k units of flow pass through e the other way, from y to x. For such an assignment f : V 2 → Z we would thus have f (x, y) = −f (y, x) whenever x and y are adjacent vertices of G. Typically, a network will have only a few nodes where flow enters or leaves the network; at all other nodes, the total amount of flow into that node will equal the total amount of flow out of it. For our model this means that, at most nodes x, the function f will satisfy Kirchhoff ’s law X f (x, y) = 0 . y ∈ N (x)
In this chapter, we call any map f : V 2 → Z with the above two properties a ‘flow’ on G. Sometimes, we shall replace Z with another group, and as a rule we consider multigraphs rather than graphs.1 As it turns out, the theory of those ‘flows’ is not only useful as a model for real flows: it blends so well with other parts of graph theory that some deep and surprising connections become visible, connections particularly with connectivity and colouring problems. 1 For consistency, we shall phrase some of our proposition for graphs only: those whose proofs rely on assertions proved (for graphs) earlier in the book. However, all those results remain true for multigraphs.
6. Flows
6.1 Circulations G = (V, E)
In the context of flows, we have to be able to speak about the ‘directions’ of an edge. Since, in a multigraph G = (V, E), an edge e = xy is not identified uniquely by the pair (x, y) or (y, x), we define directed edges as triples: →
E := { (e, x, y) | e
direction (e, x, y) ←
E; x, y
V ; e = xy } .
Thus, an edge e = xy with x 6= y has the two directions (e, x, y) and (e, y, x); a loop e = xx has only one direction, the triple (e, x, x). For → → ← ∈ E, we set e := (e, y, x), and for an arbitrary set given e = (e, x, y) → → F ⊆ E of edge directions we put ←
F := { ← e |→ e ∈ F }.
Note that E itself is symmetrical: E = E. For X, Y ⊆ V and F ⊆ E, define →
F (X, Y ) := { (e, x, y)
F (X, Y ) →
F (x, Y )
Y ; x 6= y } ,
Here, as below, X denotes the complement V r X of a vertex set X ⊆ V. Note that→ any loops at→vertices x ∈ X ∩ Y are disregarded in the definitions of F (X, Y ) and F (x). Let H be an abelian semigroup,2 written→additively with zero 0. Given vertex sets X, Y ⊆ V and a function f : E → H, let X
f (X, Y ) := ~ e
X; y
F (x) := F (x, V ) = F ({ x }, { x }) .
F |x
abbreviate F ({ x }, Y ) to F (x, Y ) etc., and write
F (x) X
~ (X,Y ∈E
f (→ e) . )
Instead of f ({ x }, Y ) we again write f (x, Y ), etc. From now on, we assume that H is a group. We call f a circulation on G (with values in H), or an H-circulation, if f satisfies the following two conditions: (F1) f (e, x, y) = −f (e, y, x) for all (e, x, y) (F2) f (v, V ) = 0 for all v 2
E with x 6= y;
This chapter contains no group theory. The only semigroups we ever consider for H are the natural numbers, the integers, the reals, the cyclic groups Zk , and (once) the Klein four-group.
6.1 Circulations
If f satisfies (F1), then f (X, X) = 0 for all X ⊆ V . If f satisfies (F2), then X f (x, V ) = 0 . f (X, V ) = x∈X
Together, these two basic observations imply that, in a circulation, the net flow across any cut is zero: Proposition 6.1.1. If f is a circulation, then f (X, X) = 0 for every set X ⊆ V . Proof . f (X, X) = f (X, V ) − f (X, X) = 0 − 0 = 0.
Since bridges form cuts by themselves, Proposition 6.1.1 implies that circulations are always zero on bridges: Corollary 6.1.2. If f is a circulation and e = xy is a bridge in G, then f (e, x, y) = 0. ¤
6.2 Flows in networks In this section we give a brief introduction to the kind of network flow theory that is now a standard proof technique in areas such as matching and connectivity. By way of example, we shall prove a classic result of this theory, the so-called max-flow min-cut theorem of Ford and Fulkerson. This theorem alone implies Menger’s theorem without much difficulty (Exercise 3), which indicates some of the natural power lying in this approach. Consider the task of modelling a network with one source s and one sink t, in which the amount of flow through a given link between two nodes is subject to a certain capacity of that link. Our aim is to determine the maximum net amount of flow through the network from s to t. Somehow, this will depend both on the structure of the network and on the various capacities of its connections—how exactly, is what we wish to find out. Let G = (V, E) be a multigraph, s, t ∈ V two fixed vertices, and → c: E → N a map; we call c a capacity function on G, and the tuple N := (G, s, t, c) a network . Note that c is defined independently for → the two directions of an edge. A function f : E → R is a flow in N if it satisfies the following three conditions (Fig. 6.2.1):
G = (V, E) s, t, c, N network flow
(F1) f (e, x, y) = −f (e, y, x) for all (e, x, y) (F20 ) f (v, V ) = 0 for all v ∈ V r { s, t }; → (F3) f ( → e) 6 c( → e) for all → e ∈ E. integral
We call f integral if all its values are integers. 1 1 3
Fig. 6.2.1. A network flow in short notation: all values refer to the direction indicated (capacities are not shown) f cut in N capacity
Let f be a flow in N . If S ⊆ V is such that s ∈ S and t ∈ S, we call the pair (S, S) a cut in N , and c(S, S) the capacity of this cut. Since f now has to satisfy only (F20 ) rather than (F2), we no longer have f (X, X) = 0 for all X ⊆ V (as in Proposition 6.1.1). However, the value is the same for all cuts: Proposition 6.2.1. Every cut (S, S) in N satisfies f (S, S) = f (s, V ). Proof . As in the proof of Proposition 6.1.1, we have f (S, S) = f (S, V ) − f (S, S) X f (v, V ) − 0 = f (s, V ) + (F1)
v ∈ Sr{ s }
=0 f (s, V ) .
(F2 )
total value |f |
The common value of f (S, S) in Proposition 6.2.1 will be called the total value of f and denoted by |f |;3 the flow shown in Figure 6.2.1 has total value 3. By (F3), we have |f | = f (S, S) 6 c(S, S) for every cut (S, S) in N . Hence the total value of a flow in N is never larger than the smallest capacity of a cut. The following max-flow mincut theorem states that this upper bound is always attained by some flow: 3 Thus, formally, |f | may be negative. In practice, however, we can change the sign of |f | simply by swapping the roles of s and t.
6.2 Flows in networks
Theorem 6.2.2. (Ford & Fulkerson 1956) In every network, the maximum total value of a flow equals the minimum capacity of a cut.
max-flow min-cut theorem
Proof . Let N = (G, s, t, c) be a network, and G =: (V, E). We shall define a sequence f0 , f1 , f2 , . . . of integral flows in N of strictly increasing total value, i.e. with |f0 | < |f1 | < |f2 | < . . . Clearly, the total value of an integral flow is again an integer, so in fact |fn+1 | > |fn | + 1 for all n. Since all these numbers are bounded above by the capacity of any cut in N , our sequence will terminate with some flow fn . Corresponding to this flow, we shall find a cut of capacity cn = |fn |. Since no flow can have a total value greater than cn , and no cut can have a capacity less than |fn |, this number is simultaneously the maximum and the minimum referred to in→the theorem. e) := 0 for all → e ∈ E. Having defined an integral For f0 , we set f0 ( → flow fn in N for some n ∈ N, we denote by Sn the set of all vertices v such that G contains an s–v walk x0 e0 . . . e`−1 x` with
fn (e→i ) < c(e→i ) for all i < `; here, e→i := (ei , xi , xi+1 ) (and, of course, x0 = s and x` = v). If t ∈ Sn , let W = x0 e0 . . . e`−1 x` be the corresponding s–t walk; without loss of generality we may assume that W does not repeat any vertices. Let ² := min { c(e→i ) − fn (e→i ) | i < ` } . Then ² > 0, and since fn (like c) is integral by assumption, ² is an integer. Let → → → fn ( e) + ² for e = ei , i = 0, . . . , ` − 1; e 7→ fn+1 : → e) − ² for → e = e←i , i = 0, . . . , ` − 1; fn ( → e) for e ∈/ W . fn ( → Intuitively, fn+1 is obtained from fn by sending additional flow of value ² along W from s to t (Fig. 6.2.2). 1 1 1 3
Fig. 6.2.2. An ‘augmenting path’ W with increment ² = 2, for constant flow fn = 0 and capacities c = 3
Clearly, fn+1 is again an integral flow in N . Let us compute its total value |fn+1 | = fn+1 (s, V ). Since W contains the vertex s only once, e→0 is the only triple (e, x, y) with x = s and y ∈ V whose f -value was changed. This value, and hence that of fn+1 (s, V ) was raised. Therefore |fn+1 | > |fn | as desired. If t ∈/ Sn , then (Sn , Sn ) is a cut in N . By (F3) for fn , and the definition of Sn , we have e) = c( → e) fn ( → →
e ∈ E(Sn , Sn ), so for all → |fn | = fn (Sn , Sn ) = c(Sn , Sn ) as desired.
Since the flow constructed in the proof of Theorem 6.2.2 is integral, we have also proved the following: Corollary 6.2.3. In every network (with integral capacity function) there exists an integral flow of maximum total value. ¤
6.3 Group-valued flows f +g −f nowhere zero H-flow
Let G = (V, E) be a multigraph and H an abelian group. If f and e 7→ f ( → e) + g( → e) and g are two H-circulations then, clearly, (f + g): → → → −f : e 7→ −f ( e) are again H-circulations. The H-circulations on G thus form a group in a natural way. → → e) 6= 0 for all → e ∈ E. An A function f : E → H is nowhere zero if f ( → H-circulation that is nowhere zero is called an H-flow .4 Note that the set of H-flows on G is not closed under addition: if two H-flows add up to zero on some edge → e, then their sum is no longer an H-flow. By Corollary 6.1.2, a graph with an H-flow cannot have a bridge. For finite groups H, the number of H-flows on G—and, in particular, their existence—surprisingly depends only on the order of H, not on H itself: Theorem 6.3.1. (Tutte 1954) For every multigraph G there exists a polynomial P such¡ that, for ¢ any finite abelian group H, the number of H-flows on G is P |H| − 1 . 4 This terminology seems simplest for our purposes but is not standard; see the notes.
6.3 Group-valued flows
Proof . Let G =: (V, E); we use induction on m := |E|. Let us assume first that all the edges of G are loops. Then, given any finite→abelian → group H, every map E → H r { 0 }¡is an H-flow ¢m on G. Since |E| = |E| such maps, and P := xm when all edges are loops, there are |H| − 1 is the polynomial sought. Now assume there is an edge e0 = xy ∈ E that is not a loop; let e→0 := (e0 , x, y) and E 0 := E r { e0 }. We consider the multigraphs G1 := G − e0
e0 = xy E0
and G2 := G/e0 .
By the induction hypothesis, there are polynomials Pi for i = 1, 2 such that, for any finite abelian group H and k := |H| − 1, the number of H-flows on Gi is Pi (k). We shall prove that the number of H-flows on G equals P2 (k) − P1 (k); then P := P2 − P1 is the desired polynomial. Let H be given, and denote the set of all H-flows on G by F . We are trying to show that |F | = P2 (k) − P1 (k) .
P1 , P2 k
(1) →
The H-flows on G1 are precisely the restrictions to E 0 of those H-circulations on G that are zero on e0 but nowhere else. Let us denote the set of these circulations on G by F1 ; then
P1 (k) = |F1 | . Our aim is to show that, likewise, the H-flows on G2 correspond bijectively to those H-circulations on G that are nowhere zero except possibly on e0 . The set F2 of those circulations on G then satisfies
P2 (k) = |F2 | , and F2 is the disjoint union of F1 and F . This will prove (1), and hence the theorem. E 0 (x, y)
v0 G2
Fig. 6.3.1. Contracting the edge e0
In G2 , let v0 := ve0 be the vertex contracted from e0 (Fig. 6.3.1; see Chapter 1.10). We are looking for a bijection f 7→ g between F2
and the set of H-flows on G2 . Given f , let g be the restriction of f to → → E 0 r E 0 (y, x). (As the x–y edges e ∈ E 0 become loops in G2 , they have only the one direction (e, v0 , v0 ) there; as its g-value, we choose f (e, x, y).) Then g is indeed an H-flow on G2 ; note that (F2) holds at v0 by Proposition 6.1.1 for G, with X := { x, y }. It remains to show that the map f 7→ g is a bijection. If we are given f→ 7→ g, then f ( → e) is an H-flow g on G2 and try to find an f ∈ F2 with → → → → 0 ∈ E r E 0 (y, x); by (F1), we already determined as f ( e) = g( e) for all e → further have f ( → e) = −f ( ← e) for all → e ∈ E 0 (y, x). Thus our map f 7→ g is bijective if and only if for given g there is always a unique way to define the remaining values of f (e→0 ) and f (e←0 ) so that f satisfies (F1) in e0 and (F2) in x and y. This is indeed the case. Let V 0 := V r { x, y }. As g satisfies (F2), the f -values fixed already are such that f (x, V 0 ) + f (y, V 0 ) = g(v0 , V 0 ) = 0 . With h := ~ e
f (→ e)
→ ∈ E 0 (x,y)
³ =
(2) ´ g(e, v0 , v0 ) ,
e ∈ E 0 (x,y)
(F2) for f requires 0 = f (x, V ) = f (e→0 ) + h + f (x, V 0 ) and 0 = f (y, V ) = f (e←0 ) − h + f (y, V 0 ) , so we have to set f (e→0 ) := −f (x, V 0 ) − h
and f (e←0 ) := −f (y, V 0 ) + h .
Then f (e→0 ) + f (e←0 ) = 0 by (2), so f also satisfies (F1) in e0 . flow polynomial
The polynomial P of Theorem 6.3.1 is known as the flow polynomial of G. Corollary 6.3.2. If H and H 0 are two finite abelian groups of equal order, then G has an H-flow if and only if G has an H 0 -flow. ¤ Corollary 6.3.2 has fundamental implications for the theory of algebraic flows: it indicates that crucial difficulties in existence proofs of H-flows are unlikely to be of a group-theoretic nature. On the other hand, being able to choose a convenient group can be quite helpful; we shall see a pretty example for this in Proposition 6.4.5.
Let k > 1 be an integer and G = (V, E) a multigraph. A Z-flow f → on G such that 0 < |f ( → e)| < k for all → e ∈ E is called a k-flow . Clearly, any k-flow is also an `-flow for all ` > k. Thus, we may ask which is the least integer k such that G admits a k-flow—assuming that such a k exists. We call this least k the flow number of G and denote it by ϕ(G); if G has no k-flow for any k, we put ϕ(G) := ∞. The task of determining flow numbers quickly leads to some of the deepest open problems in graph theory. We shall consider these later in the chapter. First, however, let us see how k-flows are related to the more general concept of H-flows. There is an intimate connection between k-flows and Zk -flows. Let σk denote the natural homomorphism i 7→ i from Z to Zk . By composition with σk , every k-flow defines a Zk -flow. As the following theorem shows, the converse holds too: from every Zk -flow on G we can construct a k-flow on G. In view of Corollary 6.3.2, this means that the general question about the existence of H-flows for arbitrary groups H reduces to the corresponding question for k-flows. Theorem 6.3.3. (Tutte 1950) A multigraph admits a k-flow if and only if it admits a Zk -flow. Proof . Let g be a Zk -flow on a multigraph G = (V, E); we construct a k-flow f on G. We may assume without loss of generality that G has → no loops. Let F be the→ set of all functions f : E → Z that satisfy (F1), |f ( → e)| < k for all → e ∈ E, and σk ◦ f = g; note that, like g, any f ∈ F is nowhere zero. Let us show first that F 6= ∅. Since we can express every value → ∈ Zk as i with |i| < k and then put f ( e) := i, there is clearly a map g( → e) → → → → f : E → Z such that |f ( e)| < k for all e ∈ E and σk ◦ f = g. For each edge e ∈ E, let us choose →one of its two directions and denote this by → e. We may then define f 0 : E → Z by setting f 0 ( → e) := f ( → e) and f 0 ( ← e) := −f ( → e) for every e ∈ E. Then f 0 is a function satisfying (F1) and with values in the desired range; it remains to show that σk ◦ f 0 and g agree not only on the chosen directions → e but also on their inverses ← e. Since σk is a homomorphism, this is indeed so:
k k-flow
flow number ϕ(G)
σk
[ 6.4.1 ] [ 6.4.2 ] [ 6.4.3 ] [ 6.4.5 ] g F
(σk ◦ f 0 )( ← e) = σk (−f ( → e)) = −(σk ◦ f )( → e) = −g( → e) = g( ← e) . Hence f 0 ∈ F , so F is indeed non-empty. Our aim is to find an f ∈ F that satisfies Kirchhoff’s law (F2), and is thus a k-flow. As a candidate, let us consider an f ∈ F for which the sum
K(f ) :=
|f (x, V )|
of all deviations from Kirchhoff’s law is least possible. We shall prove that K(f ) = 0; then, clearly, f (x, V ) = 0 for every x, as Pdesired. Suppose K(f ) 6= 0. Since f satisfies (F1), and hence x ∈ V f (x, V ) = f (V, V ) = 0, there exists a vertex x with f (x, V ) > 0 .
Let X ⊆ V be the set of all vertices x0 for which G contains a walk x0 e0 . . . e`−1 x` from x to x0 such that f (ei , xi , xi+1 ) > 0 for all i < `; furthermore, let X 0 := X r { x }. We first show that X 0 contains a vertex x0 with f (x0 , V ) < 0. By definition of X, we have f (e, x0 , y) 6 0 for all edges e = x0 y such that x0 ∈ X and y ∈ X. In particular, this holds for x0 = x. Thus, (1) implies f (x, X 0 ) > 0. Then f (X 0 , x) < 0 by (F1), as well as f (X 0 , X 0 ) = 0. Therefore X f (x0 , V ) = f (X 0 , V ) = f (X 0 , X) + f (X 0 , x) + f (X 0 , X 0 ) < 0 , x0 ∈ X 0
so some x0
X 0 must indeed satisfy f (x0 , V ) < 0 .
W f0
As x0 ∈ X, there is an x–x0 walk W = x0 e0 . . . e`−1 x` such that f (ei , xi , xi+1 ) > 0 for all i→< `. We now modify f by sending some flow back along W , letting f 0 : E → Z be given by → f ( e) − k 0 → f : e 7→ e) + k f (→ → f ( e)
for → e = (ei , xi , xi+1 ), i = 0, . . . , ` − 1; → for e = (ei , xi+1 , xi ), i = 0, . . . , ` − 1; for e ∈/ W . →
e)| < k for all → e ∈ E. Hence f 0 , like f , By definition of W , we have |f 0 ( → lies in F . How does the modification of f affect K? At all inner vertices v of W , as well as outside W , the deviation from Kirchhoff’s law remains unchanged: f 0 (v, V ) = f (v, V )
V r { x, x0 }.
and f 0 (x0 , V ) = f (x0 , V ) + k .
for all v
For x and x0 , on the other hand, we have f 0 (x, V ) = f (x, V ) − k
Since g is a Zk -flow and hence σk (f (x, V )) = g(x, V ) = 0
σk (f (x0 , V )) = g(x0 , V ) = 0
Zk ,
f (x, V ) and f (x0 , V ) are both multiples of k. Thus f (x, V ) > k and f (x0 , V ) 6 −k, by (1) and (2). But then (4) implies that |f 0 (x, V )| < |f (x, V )|
and |f 0 (x0 , V )| < |f (x0 , V )| .
Together with (3), this gives K(f 0 ) < K(f ), a contradiction to the choice of f . Therefore K(f ) = 0 as claimed, and f is indeed a k-flow. ¤ Since the sum of two Zk -circulations is always another Zk -circulation, Zk -flows are often easier to construct (by summing over suitable partial flows) than k-flows. In this way, Theorem 6.3.3 may be of considerable help in determining whether or not some given graph has a k-flow. In the following sections we shall meet a number of examples for this.
6.4 k-Flows for small k Trivially, a graph has a 1-flow (the empty set) if and only if it has no edges. In this section we collect a few simple examples of sufficient conditions under which a graph has a 2-, 3- or 4-flow. More examples can be found in the exercises. Proposition 6.4.1. A graph has a 2-flow if and only if all its degrees are even.
Proof . By Theorem 6.3.3, a graph G = (V, E) has a → 2-flow if and only if it has a Z2 -flow, i.e. if and only if the constant map E → Z2 with value 1 satisfies (F2). This is the case if and only if all degrees are even. ¤
For the remainder of this chapter, let us call a graph even if all its vertex degrees are even. Proposition 6.4.2. A cubic graph has a 3-flow if and only if it is bipartite.
even graph
134 (1.6.1) (6.3.3)
Proof . Let G = (V, E) be a cubic graph. Let us assume first that G has a 3-flow, and hence also a Z3 -flow f . We show that any cycle C = x0 . . . x` x0 in G has even length (cf. Proposition 1.6.1). Consider two consecutive edges on C, say ei−1 := xi−1 xi and ei := xi xi+1 . If f assigned the same value to these edges in the direction of the forward orientation of C, i.e. if f (ei−1 , xi−1 , xi ) = f (ei , xi , xi+1 ), then f could not satisfy (F2) at xi for any non-zero value of the third edge at xi . Therefore f assigns the values 1 and 2 to the edges of C alternately, and in particular C has even length. Conversely, let G be bipartite, with vertex bipartition { X, Y }. → Since G is cubic, the map E → Z3 defined by f (e, x, y) := 1 and f (e, y, x) := 2 for all edges e = xy with x ∈ X and y ∈ Y is a Z3 flow on G. By Theorem 6.3.3, then, G has a 3-flow. ¤ What are the flow numbers of the complete graphs K n ? For odd n > 1, we have ϕ(K n ) = 2 by Proposition 6.4.1. Moreover, ϕ(K 2 ) = ∞, and ϕ(K 4 ) = 4; this is easy to see directly (and it follows from Propositions 6.4.2 and 6.4.5). Interestingly, K 4 is the only complete graph with flow number 4: Proposition 6.4.3. For all even n > 4, ϕ(K n ) = 3.
Proof . Proposition 6.4.1 implies that ϕ(K n ) > 3 for even n. We show, by induction on n, that every G = K n with even n > 4 has a 3-flow. For the induction start, let n = 6. Then G is the edge-disjoint union of three graphs G1 , G2 , G3 , with G1 , G2 = K 3 and G3 = K3,3 . Clearly G1 and G2 each have a 2-flow, while G3 has a 3-flow by Proposition 6.4.2. The union of all these flows is a 3-flow on G. Now let n > 6, and assume the assertion holds for n − 2. Clearly, G is the edge-disjoint union of a K n−2 and a graph G0 = (V 0 , E 0 ) with G0 = K n−2 ∗ K 2 . The K n−2 has a 3-flow by induction. By Theorem 6.3.3, it thus suffices to find a Z3 -flow on G0 . For every vertex z of the K n−2 ⊆ G0 , let fz be a Z3 -flow on the→ triangle zxyz ⊆ G0 , where e = xy is the edge of the K 2 in G0 . Let f : E 0 → Z3 be the sum of these flows. Clearly, f is nowhere zero, except possibly in (e, x, y) and (e, y, x). If f (e, x, y) 6= 0, then f is the desired Z3 -flow on G0 . If f (e, x, y) = 0, then f + fz (for ¤ any z) is a Z3 -flow on G0 . Proposition 6.4.4. Every 4-edge-connected graph has a 4-flow.
(3.5.2) f1,e , f2,e
Proof . Let G be a 4-edge-connected graph. By Corollary 3.5.2, G has two edge-disjoint spanning trees Ti , i = 1, 2. For each edge e ∈/ Ti , let Ci,e be the unique cycle in Ti + e, and let fi,e be a Z4 -flow of value i around Ci,e —more precisely: a Z4 -circulation on G with values i and −i on the edges of Ci,e and zero otherwise.
6.4 k-Flows for small k
P Let f1 := e ∈/ T1 f1,e . Since each e ∈/ T1 lies on only one cycle C1,e0 (namely, for e = e0 ), f1 takes only the values 1 and −1 (= 3) outside T1 . Let F := { e
E(T1 ) | f1 (e) = 0 }
P and f2 := e ∈ F f2,e . As above, f2 (e) = 2 = −2 for all e ∈ F . Now f := f1 + f2 is the sum of Z4 -circulations, and hence itself a Z4 -circulation. Moreover, f is nowhere zero: on edges in F it takes the value 2, on edges of T1 − F it agrees with f1 (and is hence non-zero by the choice of F ), and on all edges outside T1 it takes one of the values 1 or 3. Hence, f is a Z4 -flow on G, and the assertion follows by Theorem 6.3.3. ¤
f2 f
The following proposition describes the graphs with a 4-flow in terms of those with a 2-flow: Proposition 6.4.5. (i) A graph has a 4-flow if and only if it is the union of two even subgraphs. (ii) A cubic graph has a 4-flow if and only if it is 3-edge-colourable. Proof . Let Z22 = Z2 × Z2 be the Klein four-group. (Thus, the elements of Z22 are the pairs (a, b) with a, b ∈ Z2 , and (a, b) + (a0 , b0 ) = (a + a0 , b + b0 ).) By Corollary 6.3.2 and Theorem 6.3.3, a graph has a 4-flow if and only if it has a Z22 -flow. (i) now follows directly from Proposition 6.4.1. (ii) Let G = (V, E) be a cubic graph. We assume first that G has a 2 Z22 -flow f , and define an edge colouring E → Z→ 2 r { 0 }. As a = −a for → ← → 2 all a ∈ Z2 , we have f ( e) = f ( e) for every e ∈ E; let us colour the edge e with this colour f ( → e). Now if two edges with a common end v had the same colour, then these two values of f would sum to zero; by (F2), f would then assign zero to the third edge at v. As this contradicts the definition of f , our edge colouring is correct. Conversely, since the three non-zero elements of Z22 sum to zero, every 3-edge-colouring c: E → Z22→r { 0 } defines a Z22 -flow on G by letting f (→ e) = f ( ← e) = c(e) for all → e ∈ E. ¤ Corollary 6.4.6. Every cubic 3-edge-colourable graph is bridgeless. ¤
6.5 Flow-colouring duality
G = (V, E) G∗
F∗
cycle with orientation
In this section we shall see a surprising connection between flows and colouring: every k-flow on a plane multigraph gives rise to a k-vertexcolouring of its dual, and vice versa. In this way, the investigation of k-flows appears as a natural generalization of the familiar map colouring problems in the plane. Let G = (V, E) and G∗ = (V ∗ , E ∗ ) be dual plane multigraphs. For simplicity, let us assume that G and G∗ have neither bridges nor loops and are non-trivial. For edge sets F ⊆ E, let us write F ∗ := { e∗
E∗ | e
F }.
Conversely, if a subset of E ∗ is given, we shall usually write it immediately in the form F ∗ , and thus let F ⊆ E be defined implicitly via the bijection e 7→ e∗ . Suppose we are given a circulation g on G∗ : how can we employ the duality between G and G∗ to derive from g some information about G? The most general property of all circulations is Proposition 6.1.1, which says that g(X, X) = 0 for all X ⊆ V ∗ . By Proposition 4.6.1, the minimal cuts E ∗ (X, X) in G∗ correspond precisely to the cycles in G. Thus if we take the composition f of the maps e 7→ e∗ and g, and sum its values over the edges of a cycle in G, then this sum should again be zero. Of course, there is still a technical hitch: since g takes its arguments → f as→above: we first have not in E ∗ but in E ∗ , we cannot simply define → ∗ to refine the bijection e → 7 e into one from E to E ∗ , i.e. assign to every → → ∈ e E canonically one of the two directions of e∗ . This will be the purpose of our first lemma. After that, we shall show that f does indeed sum to zero along any cycle in G. If C = v0 . . . v`−1 v0 is a cycle with edges ei = vi vi+1 (and v` := v0 ), we shall call → C := { (ei , vi , vi+1 ) | i < ` } →
a cycle with orientation. Note that this definition of C depends on the vertex enumeration chosen to denote C: every cycle has two orientations. → Conversely, of course, C can be reconstructed from the set C . In practice, → we shall therefore speak about C freely even when, formally, only C has been defined. →
Lemma 6.5.1. There exists a bijection ∗ : → e 7→ → e ∗ from E to E ∗ with the following properties. e ∗ is always e∗ , i.e. → e ∗ is one of the two (i) The underlying edge of → → ← ∗ ∗ ∗ directions e , e of e . (ii) If C ⊆ G is a cycle, F := E(C), and if X ⊆ V ∗ →is such that X), → then there exists an orientation C of C with F ∗ = E ∗ (X, → e∗ | → e ∈ C } = E ∗ (X, X). {→
The proof of Lemma 6.5.1 is not entirely trivial: it is based on the so-called orientability of the plane, and we cannot give it here. Still, the assertion of the lemma is intuitively plausible. Indeed if we define for e = vw and e∗ = xy the assignment (e, v, w) 7→ (e, v, w)∗ ∈ { (e∗ , x, y), (e∗ , y, x) } simply by turning e and its ends clockwise onto e∗ (Fig. 6.5.1), then the resulting map → e 7→ → e ∗ satisfies the two assertions of the lemma.
X →
Fig. 6.5.1. Oriented cycle-cut duality →
Given an abelian group H, let f : E → H and g: E ∗ → H be two maps such that e) = g( → e ∗) f (→ →
for all → e ∈ E. For F ⊆ E, we set →
f (F ) :=
X ~ e
f (→ e) .
f ( C ) etc.
~ ∈F
Lemma 6.5.2. (i) The map g satisfies (F1) if and only if f does. (ii) The map g is a circulation on→G∗ if and only if f satisfies (F1) → and f (C ) = 0 for every cycle C with orientation. Proof . Assertion (i) follows from Lemma 6.5.1 (i) and the fact that → e 7→ → e ∗ is bijective. For the forward implication of (ii), let us assume that g is a circulation on G∗ , and consider a cycle C ⊆ G with some given orientation. Let F := E(C). By Proposition 4.6.1, F ∗ is a minimal cut in G∗ , i.e. F ∗ = E ∗ (X, X) for some suitable X ⊆ V ∗ . By definition of f and g, Lemma 6.5.1 (ii) and Proposition 6.1.1 give X → X → → f (C ) = f ( e) = g( d) = g(X, X) = 0 ~ e
~ ∈C
→ d~ ∈ E ∗ (X,X) →
for one of the two orientations C of C. Then, by f ( C ) = −f (C ), also
B F ∗, F
the corresponding value for our given orientation of C must be zero. For the backward implication it suffices by (i) to show that g satisfies (F2), i.e. that g(x, V ∗ ) = 0 for every x ∈ V ∗ . We shall prove that g(x, V (B)) = 0 for every block B of G∗ containing x; since every edge of G∗ at x lies in exactly one such block, this will imply g(x, V ∗ ) = 0. So let x ∈ V ∗ be given, and let B be any block of G∗ containing x. Since G∗ is a non-trivial plane dual, and hence connected, we have B − x 6= ∅. Let F ∗ be the set of all edges of B at x (Fig. 6.5.2),
Fig. 6.5.2. The cut F ∗ in G∗ X
and let X be the vertex set of the component of G∗ − F ∗ containing x. Then ∅ 6= V (B − x) ⊆ X, by the maximality of B as a cutvertex-free subgraph. Hence (1) F ∗ = E ∗ (X, X) by definition of X, i.e. F ∗ is a cut in G∗ . As a dual, G∗ is connected, so G∗ [ X ] too is connected. Indeed, every vertex of X is linked to x by a path P ⊆ G∗ whose last edge lies in F ∗ . Then P − x is a path in G∗ [ X ] meeting B. Since x does not separate B, this shows that G∗ [ X ] is connected. Thus, X and X are both connected in G∗ , so F ∗ is even a minimal cut in G∗ . Let C ⊆ G be the cycle with E(C) = F that→ exists by Proposition→4.6.1. → By Lemma 6.5.1 (ii), C has an orientation →C such that → {→ e∗ | → e ∈ C } = E ∗ (X, X). By (1), however, E ∗ (X, X) = E ∗ (x, V (B)), so → g(x, V (B)) = g(X, X) = f (C ) = 0 ¤
by definition of f and g.
P v0 → v ` path
With the help of Lemma 6.5.2, we can now prove our colouring-flow duality theorem for plane multigraphs. If P = v0 . . . v` is a path with edges ei = vi vi+1 (i < `), we set (depending on our vertex enumeration of P ) → P := { (ei , vi , vi+1 ) | i < ` } →
and call P a v0 → v` path. Again, P may be given implicitly by P .
Theorem 6.5.3. (Tutte 1954) For every dual pair G, G∗ of plane multigraphs, χ(G) = ϕ(G∗ ) . Proof . Let G =: (V, E) and G∗ =: (V ∗ , E ∗ ). For |G| ∈ { 1, 2 } the assertion is easily checked; we shall assume that |G| > 3, and apply induction on the number of bridges in G. If e ∈ G is a bridge then e∗ is a loop, and G∗ − e∗ is a plane dual of G/e (why?). Hence, by the induction hypothesis,
(1.5.5) V, E V ∗, E∗
χ(G) = χ(G/e) = ϕ(G∗ − e∗ ) = ϕ(G∗ ) ; for the first and the last equality we use that, by |G| > 3, e is not the only edge of G. So all that remains to be checked is the induction start: let us assume that G has no bridge. If G has a loop, then G∗ has a bridge, and χ(G) = ∞ = ϕ(G∗ ) by convention. So we may also assume that G has no loop. Then χ(G) is finite; we shall prove for given k > 2 that G is k-colourable if and only if G∗ has a k-flow. As G—and hence G∗ — has neither loops nor bridges, we may apply Lemmas → 6.5.1 and 6.5.2 → e 7→ → e ∗ be the bijection between E and E ∗ from to G and G∗ . Let → Lemma 6.5.1. We first assume that G∗ has a k-flow. Then G∗ also has a Zk -flow g. → As before, let f : E → Zk be defined by f ( → e) := g( → e ∗ ). We shall use f to define a vertex colouring c: V → Zk of G. Let T be a normal spanning tree of G, with→root r, say.→Put c(r) := 0. For every other vertex v ∈ V let c(v) := f (P ), where P is the r → v path in T . To check that this is a proper colouring, consider an edge e = vw ∈ E. As T is normal, we may assume that v < w in the tree order of T . If e is an edge of T then c(w) − c(v) = f (e, v, w) by definition of c, so c(v) 6= c(w) since g (and hence f ) is nowhere zero. If e ∈/ T , let → P denote the v → w path in T . Then
g f
c(w) − c(v) = f (P ) = −f (e, w, v) 6= 0 by Lemma 6.5.2 (ii). Conversely, we now assume that G has a k-colouring c. Let us define → f : E → Z by
f (e, v, w) := c(w) − c(v) ,
and g: E ∗ → Z by g( → e ∗ ) := f ( → e). Clearly, f satisfies (F1) and takes values in { ±1, . . . , ±(k − 1) }, so by Lemma→6.5.2 (i) the same holds → for g. By definition of f , we further have f (C ) = 0 for every cycle C with orientation. By Lemma 6.5.2 (ii), therefore, g is a k-flow. ¤
6.6 Tutte’s flow conjectures How can we determine the flow number of a graph? Indeed, does every (bridgeless) graph have a flow number, a k-flow for some k? Can flow numbers, like chromatic numbers, become arbitrarily large? Can we characterize the graphs admitting a k-flow, for given k? Of these four questions, we shall answer the second and third in this section: we prove that every bridgeless graph has a 6-flow. In particular, a graph has a flow number if and only if it has no bridge. The question asking for a characterization of the graphs with a k-flow remains interesting for k = 3, 4, 5. Partial answers are suggested by the following three conjectures of Tutte, who initiated algebraic flow theory. The oldest and best known of the Tutte conjectures is his 5-flow conjecture: Five-Flow Conjecture. (Tutte 1954) Every bridgeless multigraph has a 5-flow. Which graphs have a 4-flow? By Proposition 6.4.4, the 4-edgeconnected graphs are among them. The Petersen graph (Fig. 6.6.1), on the other hand, is an example of a bridgeless graph without a 4-flow: since it is cubic but not 3-edge-colourable (Ex. 19, Ch. 5), it cannot have a 4-flow by Proposition 6.4.5 (ii).
Fig. 6.6.1. The Petersen graph
Tutte’s 4-flow conjecture states that the Petersen graph must be present in every graph without a 4-flow: Four-Flow Conjecture. (Tutte 1966) Every bridgeless multigraph not containing the Petersen graph as a minor has a 4-flow. By Proposition 1.7.2, we may replace the word ‘minor’ in the 4-flow conjecture by ‘topological minor’.
6.6 Tutte’s flow conjectures
Even if true, the 4-flow conjecture will not be best possible: a K 11 , for example, contains the Petersen graph as a minor but has a 4-flow, even a 2-flow. The conjecture appears more natural for sparser graphs, and indeed the cubic graphs form an important special case. (See the notes.) A cubic bridgeless graph or multigraph without a 4-flow (equivalently, without a 3-edge-colouring) is called a snark . The 4-flow conjecture for cubic graphs says that every snark contains the Petersen graph as a minor; in this sense, the Petersen graph has thus been shown to be the smallest snark. Snarks form the hard core both of the four colour theorem and of the 5-flow conjecture: the four colour theorem is equivalent to the assertion that no snark is planar (exercise), and it is not difficult to reduce the 5-flow conjecture to the case of snarks.5 However, although the snarks form a very special class of graphs, none of the problems mentioned seems to become much easier by this reduction.6
Three-Flow Conjecture. (Tutte 1972) Every multigraph without a cut consisting of exactly one or exactly three edges has a 3-flow. Again, the 3-flow conjecture will not be best possible: it is easy to construct graphs with three-edge cuts that have a 3-flow (exercise). By our duality theorem (6.5.3), all three flow conjectures are true for planar graphs and thus motivated: the 3-flow conjecture translates to Gr¨otzsch’s theorem (5.1.3), the 4-flow conjecture to the four colour theorem (since the Petersen graph is not planar, it is not a minor of a planar graph), the 5-flow conjecture to the five colour theorem. We finish this section with the main result of the chapter: Theorem 6.6.1. (Seymour 1981) Every bridgeless graph has a 6-flow. Proof . Let G = (V, E) be a bridgeless graph. Since 6-flows on the components of G will add up to a 6-flow on G, we may assume that G is connected; as G is bridgeless, it is then 2-edge-connected. Note that any two vertices in a 2-edge-connected graph lie in some common even connected subgraph—for example, in the union of two edge-disjoint paths linking these vertices by Menger’s theorem (3.3.5 (ii)). We shall use this fact repeatedly. 5 The same applies to another well-known conjecture, the cycle double cover conjecture; see Exercise 13. 6 That snarks are elusive has been known to mathematicians for some time; cf. Lewis Carroll, The Hunting of the Snark , Macmillan 1876.
142 H0 , . . . , Hn F1 , . . . , F n Vi , Ei Hi V i, Ei
n Xi
We shall construct a sequence H0 , . . . , Hn of disjoint connected and even subgraphs of G, together with a sequence F1 , . . . , Fn of non-empty sets of edges between them. The sets Fi will each contain only one or two edges, between Hi and H0 ∪ . . . ∪ Hi−1 . We write Hi =: (Vi , Ei ), H i := (H0 ∪ . . . ∪ Hi ) + (F1 ∪ . . . ∪ Fi ) and H i =: (V i , E i ). Note that each H i = (H i−1 ∪ Hi ) + Fi is connected (induction on i). Our assumption that Hi is even implies by Proposition 6.4.1 (or directly by Proposition 1.2.1) that Hi has no bridge. As H0 we choose any K 1 in G. Now assume that H0 , . . . , Hi−1 and F1 , . . . , Fi−1 have been defined for some i > 0. If V i−1 = V , we terminate the construction and set i − 1 =: n. Otherwise, we let Xi ⊆ V i−1 be minimal such that Xi 6= ∅ and ¯ ¯ ¯E(Xi , V i−1 r Xi )¯ 6 1
(Fig. 6.6.2); such an Xi exists, because V i−1 is a candidate. Since G is 2-edge-connected, (1) implies that E(Xi , V i−1 ) 6= ∅. By the minimality of Xi , the graph G [ Xi ] is connected and bridgeless, i.e. 2-edgeconnected or a K 1 . As the elements of Fi we pick one or two edges from E(Xi , V i−1 ), if possible two. As Hi we choose any connected even subgraph of G [ Xi ] containing the ends in Xi of the edges in Fi . V i−1 r Xi
H i−1 Fi
Hi Xi
V i−1 Fig. 6.6.2. Constructing the Hi and Fi H E0 fn , . . . , f 0 →
Ce fe fn
When our construction is complete, we set H n =: H and E 0 := E r E(H). By definition of n, H is a spanning connected subgraph of G. We now define, by ‘reverse’ induction, a →sequence fn , . . . , f0 of Z3 circulations on G. For every edge e ∈ E 0 , let Ce be a cycle (with orienta→ tion) in H + e containing e, and fe a positive flow around→Ce ; formally, → ← we let fe be a Z3 -circulation on G such that fe−1 (0) = E r (Ce ∪ Ce ). Let fn be the sum of all these fe . Since each e0 ∈ E 0 lies on just one of → the cycles Ce (namely, on Ce0 ), we have fn ( → e) 6= 0 for all → e ∈ E0.
Assume now that Z3 -circulations fn , . . . , fi on G have been defined for some i 6 n, and that →
fi ( → e) 6= 0 for all → e ∈ E0 ∪
Fj ,
j>i →
e ∈ E | e ∈ Fj }. Our aim is to define fi−1 in such a way where Fj := { → that (2) also holds for i − 1. We first consider the case that |Fi | = 1, say Fi = { e }. We then let fi−1 := fi , and thus have to show that fi is non-zero on (the two directions of) e. Our assumption of |Fi | = 1 implies by the choice of Fi that G contains no Xi –V i−1 edge other than e. Since G is 2-edgeconnected, it therefore has at least—and thus, by (1), exactly—one edge e0 between Xi and V i−1 r Xi . We show that fi is non-zero on e0 ; as { e, e0 } is a cut in G, this implies by Proposition 6.1.1 that fi is also non-zero on e. 0 0 ∈ To S show that fi is 0 non-zero on e , we use (2): we show that e 0 0 E ∪ j>i Fj , i.e. that e lies in no Hk and in no Fj with j 6 i. Since e has both ends in V i−1 , it clearly lies in no Fj with j 6 i and in no Hk with k < i. But every Hk with k > i is a subgraph of G [ V i−1 ]. Since e0 is a bridge of G [ V i−1 ] but Hk has no bridge, this means that e0 ∈/ Hk . Hence, fi−1 does indeed satisfy (2) for i − 1 in the case considered. It remains to consider the case that |Fi | = 2, say Fi = { e1 , e2 }. Since Hi and H i−1 are both connected, we can find a cycle C in H i = (Hi ∪ H i−1 ) + Fi that contains e1 and e2 . If fi is non-zero on both these edges, we again let fi−1 := fi . Otherwise, there are directions e→1 and → e→2 of e1 and e2 such→that, without loss of generality, f→ i (e1 ) = 0 and → → fi (e2 ) ∈ { 0, 1 }. Let C be→the orientation of C with e2 ∈ C , and let g be let←g be a Z3 -circulation on G such a flow of value 1 around C (formally: → → that g(e→2 ) = 1 and g −1 (0) = E r (C ∪ C )). We then let fi−1 := fi + g. → By choice of the directions e→1 and e→ 2 , fS i−1 is→non-zero on both edges. Since fi−1 agrees with fi on all of E 0 ∪ j>i Fj and (2) holds for i, we again have (2) also for i − 1. Eventually, f0 will be a Z3 -circulation on G that is nowhere zero except possibly on edges of H0 ∪ . . . ∪ Hn . Composing f0 with the map h 7→ 2h from Z3 to Z6 (h ∈ { 1, 2 }), we obtain a Z6 -circulation f on G with values in { 0, 2, 4 } for all edges lying in some Hi , and with values in { 2, 4 } for all other edges. Adding to f a 2-flow on each Hi (formally: a Z6 -circulation on G with values in { 1, −1 } on the edges of Hi and 0 otherwise; this exists by Proposition 6.4.1), we obtain a Z6 -circulation on G that is nowhere zero. Hence, G has a 6-flow by Theorem 6.3.3. ¤
e1 , e2 C
Exercises 1.− Prove Proposition 6.2.1 by induction on |S|. 2.
(i)− Given n ∈ N, find a capacity function for the network below such that the algorithm from the proof of the max-flow min-cut theorem will need more than n augmenting paths W if these are badly chosen.
(ii)+ Show that, if all augmenting paths are chosen as short as possible, their number is bounded by a function of the size of the network. 3.+ Derive Menger’s Theorem 3.3.4 from the max-flow min-cut theorem. (Hint. The edge version is easy. For the vertex version, apply the edge version to a suitable auxiliary graph.) 4.− Let f be an H-circulation on G and g: H → H 0 a group homomorphism. Show that g ◦ f is an H 0 -circulation on G. Is g ◦ f an H 0 -flow if f is an H-flow? 5.− Given k > 1, show that a graph has a k-flow if and only if each of its blocks has a k-flow. 6.− Show that ϕ(G/e) 6 ϕ(G) whenever G is a multigraph and e an edge of G. Does this imply that, for every k, the class of all multigraphs admitting a k-flow is closed under taking minors? 7.− Work out the flow number of K 4 directly, without using any results from the text. 8.
Let H be a finite abelian group, G a graph, and T a spanning tree of G. Show that every mapping from the directions of E(G) r E(T ) to H that satisfies (F1) extends uniquely to an H-circulation on G.
Do not use the 6-flow Theorem 6.6.1 for the following three exercises. 9. 10.
Show that ϕ(G) < ∞ for every bridgeless multigraph G. Assume that a graph G has m spanning trees such that no edge of G lies in all of these trees. Show that ϕ(G) 6 2m .
11.+ Let G be a bridgeless connected graph with n vertices and m edges. By considering a normal spanning tree of G, show that ϕ(G) 6 m − n + 2. 12.
Show that every graph with a Hamilton cycle has a 4-flow. (A Hamilton cycle of G is a cycle in G that contains all the vertices of G.)
A family of (not necessarily distinct) cycles in a graph G is called a cycle double cover of G if every edge of G lies on exactly two of these cycles. The cycle double cover conjecture asserts that every bridgeless multigraph has a cycle double cover. Prove the conjecture for graphs with a 4-flow.
14.− Determine the flow number of C 5 ∗ K 1 , the wheel with 5 spokes. 15.
Find bridgeless graphs G and H = G − e such that 2 < ϕ(G) < ϕ(H).
Prove Proposition 6.4.1 without using Theorem 6.3.3.
Prove Heawood’s theorem that a plane triangulation is 3-colourable if and only if all its vertices have even degree.
18.− Find a bridgeless graph that has both a 3-flow and a cut of exactly three edges. 19.
Show that the 3-flow conjecture for planar multigraphs is equivalent to Gr¨ otzsch’s Theorem 5.1.3.
(i)− Show that the four colour theorem is equivalent to the non-existence of a planar snark, i.e. to the statement that every cubic bridgeless planar multigraph has a 4-flow. (ii) Can ‘bridgeless’ in (i) be replaced by ‘3-connected’ ?
21.+ Show that a graph G = (V, E) has a k-flow if and only if it admits an orientation D that directs, for every X ⊆ V , at least 1/k of the edges in E(X, X) from X towards X. 22.− Generalize the 6-flow Theorem 6.6.1 to multigraphs.
Notes Network flow theory is an application of graph theory that has had a major and lasting impact on its development over decades. As is illustrated already by the fact that Menger’s theorem can be deduced easily from the max-flow min-cut theorem (Exercise 3), the interaction between graphs and networks may go either way: while ‘pure’ results in areas such as connectivity, matching and random graphs have found applications in network flows, the intuitive power of the latter has boosted the development of proof techniques that have in turn brought about theoretic advances. The standard reference for network flows is L.R. Ford & D.R. Fulkerson, Flows in Networks, Princeton University Press 1962. A more recent and comprehensive account is given by R.K. Ahuja, T.L. Magnanti & J.B. Orlin, Network flows, Prentice-Hall 1993. For more theoretical aspects, see A. Frank’s chapter in the Handbook of Combinatorics (R.L. Graham, M. Gr¨ otschel & L. Lov´ asz, eds.), North-Holland 1995. A general introduction to graph algorithms is given in A. Gibbons, Algorithmic Graph Theory, Cambridge University Press 1985. If one recasts the maximum flow problem in linear programming terms, one can derive the max-flow min-cut theorem from the linear programming duality theorem; see A. Schrijver, Theory of integer and linear programming, Wiley 1986. The more algebraic theory of group-valued flows and k-flows has been developed largely by Tutte; he gives a thorough account in his monograph W.T. Tutte, Graph Theory, Addison-Wesley 1984. Tutte’s flow conjectures are
covered also in F. Jaeger’s survey, Nowhere-zero7 flow problems, in (L.W. Beineke & R.J. Wilson, eds.) Selected Topics in Graph Theory 3, Academic Press 1988. For the flow conjectures, see also T.R. Jensen & B. Toft, Graph Coloring Problems, Wiley 1995. Seymour’s 6-flow theorem is proved in P.D. Seymour, Nowhere-zero 6-flows, J. Combin. Theory B 30 (1981), 130–135. This paper also indicates how Tutte’s 5-flow conjecture reduces to snarks. In 1998, Robertson, Sanders, Seymour and Thomas announced a proof of the 4-flow conjecture for cubic graphs. Finally, Tutte discovered a 2-variable polynomial associated with a graph, which generalizes both its chromatic polynomial and its flow polynomial. What little is known about this Tutte polynomial can hardly be more than the tip of the iceberg: it has far-reaching, and largely unexplored, connections to areas as diverse as knot theory and statistical physics. See D.J.A. Welsh, Complexity: knots, colourings and counting (LMS Lecture Notes 186), Cambridge University Press 1993.
7 In the literature, the term ‘flow’ is often used to mean what we have called ‘circulation’, i.e. flows are not required to be nowhere zero unless this is stated explicitly.
Substructures in Dense Graphs
In this chapter and the next, we study how global parameters of a graph, such as its edge density or chromatic number, have a bearing on the existence of certain local substructures. How many edges, for instance, do we have to give a graph on n vertices to be sure that, no matter how these edges happen to be arranged, the graph will contain a K r subgraph for some given r? Or at least a K r minor? Or a topological K r minor? Will some sufficiently high average degree or chromatic number ensure that one of these substructures occurs? Questions of this type are among the most natural ones in graph theory, and there is a host of deep and interesting results. Collectively, these are known as extremal graph theory. Extremal graph problems in this sense fall neatly into two categories, as follows. If we are looking for ways to ensure by global assumptions that a graph G contains some given graph H as a minor (or topological minor), it will suffice to raise kGk above the value of some linear function of |G| (depending on H), i.e. to make ε(G) large enough. The existence of such a function was already established in Theorem 3.6.1. The precise growth rate needed will be investigated in Chapter 8, where we study substructures of such ‘sparse’ graphs. Since a large enough value of ε gives rise to an H minor for any given graph H, its occurrence could be forced alternatively by raising some other global invariants (such as κ or χ) which, in turn, force up the value of ε, at least in some subgraph. This, too, will be a topic for Chapter 8. On the other hand, if we ask what global assumptions might imply the existence of some given graph H as a subgraph, it will not help to raise any of the invariants ε, κ or χ, let alone any of the other invariants discussed in Chapter 1. Indeed, as mentioned in Chapter 5.2,
dense edge density
7. Substructures in Dense Graphs
given any graph H that contains at least one cycle, there are graphs of arbitrarily large chromatic number not containing H as a subgraph (Theorem 11.2.2). By Corollary 5.2.3 and Theorem 1.4.2, such graphs have subgraphs of arbitrarily large average degree and connectivity, so these invariants too can be large without the presence of an H subgraph. Thus, unless H is a forest, the only way to force the presence of an H subgraph in an arbitrary graph G by global assumptions on G is to raise kGk substantially above any value implied by large values of the above invariants. If H is not bipartite, then any function f such that f (n) edges on n vertices force an H subgraph must even grow quadratically with n: since complete bipartite graphs can have 14 n2 edges, f (n) must exceed 14 n2 . Graphs with a number of edges roughly1 quadratic ±¡ in¢ their number of vertices are usually called dense; the number kGk |G| 2 —the proportion of its potential edges that G actually has—is the edge density of G. The question of exactly which edge density is needed to force a given subgraph is the archetypal extremal graph problem in its original (narrower) sense; it is the topic of this chapter. Rather than attempting to survey the wide field of (dense) extremal graph theory, however, we shall concentrate on its two most important results and portray one powerful general proof technique. The two results are Tur´ an’s classic extremal graph theorem for H = K r , a result that has served as a model for countless similar theorems for other graphs H, and the fundamental Erd˝ os-Stone theorem, which gives precise asymptotic information for all H at once (Section 7.1). The proof technique, one of increasing importance in the extremal theory of dense graphs, is the use of the Szemer´edi regularity lemma. This lemma is presented and proved in Section 7.2. In Section 7.3, we outline a general method for applying the regularity lemma, and illustrate this in the proof of the Erd˝ os-Stone theorem postponed from Section 7.1. Another application of the regularity lemma will be given in Chapter 9.2.
7.1 Subgraphs Let H be a graph and n > |H|. How many edges will suffice to force an H subgraph in any graph on n vertices, no matter how these edges are arranged? Or, to rephrase the problem: which is the greatest possible number of edges that a graph on n vertices can have without containing a copy of H as a subgraph? What will such a graph look like? Will it be unique? 1 Note that, formally, the notions of sparse and dense make sense only for families of graphs whose order tends to infinity, not for individual graphs.
7.1 Subgraphs
A graph G 6⊇ H on n vertices with the largest possible number of edges is called extremal for n and H; its number of edges is denoted by ex(n, H). Clearly, any graph G that is extremal for some n and H will also be edge-maximal with H 6⊆ G. Conversely, though, edge-maximality does not imply extremality: G may well be edge-maximal with H 6⊆ G while having fewer than ex(n, H) edges (Fig. 7.1.1).
extremal ex(n, H)
Fig. 7.1.1. Two graphs that are edge-maximal with P 3 6⊆ G; is the right one extremal?
As a case in point, we consider our problem for H = K r (with r > 1). A moment’s thought suggests some obvious candidates for extremality here: all complete (r − 1)-partite graphs are edge-maximal without containing K r . But which among these have the greatest number of edges? Clearly those whose partition sets are as equal as possible, i.e. differ in size by at most 1: if V1 , V2 are two partition sets with |V1 | − |V2 | > 2, we may increase the number of edges in our complete (r − 1)-partite graph by moving a vertex from V1 across to V2 . The unique complete (r − 1)-partite graphs on n > r − 1 vertices whose partition sets differ in size by at most 1 are called Tur´ an graphs; we denote them by T r−1 (n) and their number of edges by tr−1 (n) (Fig. 7.1.2). For n < r − 1 we shall formally continue to use these definitions, with the proviso that—contrary to our usual terminology— the partition sets may now be empty; then, clearly, T r−1 (n) = K n for all n 6 r − 1.
Fig. 7.1.2. The Tur´ an graph T 3 (8)
The following theorem tells us that T r−1 (n) is indeed extremal for n and K r , and as such unique; in particular, ex(n, K r ) = tr−1 (n).
T r−1 (n) tr−1 (n)
Theorem 7.1.1. (Tur´ an 1941) For all integers r, n with r > 1, every graph G 6⊇ K r with n vertices and ex(n, K r ) edges is a T r−1 (n). Proof . We apply induction on n. For n 6 r − 1 we have G = K n = T r−1 (n) as claimed. For the induction step, let now n > r. Since G is edge-maximal without a K r subgraph, G has a subgraph K = K r−1 . By the induction hypothesis, G − K has at most tr−1 (n − r + 1) edges, and each vertex of G − K has at most r − 2 neighbours in K. Hence, µ ¶ r−1 kGk 6 tr−1 (n − r + 1) + (n − r + 1)(r − 2) + = tr−1 (n) ; (1) 2 the equality on the right follows by inspection of the Tur´ an graph T r−1 (n) (Fig. 7.1.3). r−2
¡r−1¢
tr−1 (n − r + 1)
Fig. 7.1.3. The equation from (1) for r = 5 and n = 14
x1 , . . . , xr−1 V1 , . . . , Vr−1
Since G is extremal for K r (and T r−1 (n) 6⊇ K r ), we have equality in (1). Thus, every vertex of G − K has exactly r − 2 neighbours in K— just like the vertices x1 , . . . , xr−1 of K itself. For i = 1, . . . , r − 1 let Vi := { v
V (G) | vxi ∈/ E(G) }
be the set of all vertices of G whose r − 2 neighbours in K are precisely the vertices other than xi . Since K r 6⊆ G, each of the sets Vi is independent, and they partition V (G). Hence, G is (r − 1)-partite. As T r−1 (n) is the unique (r − 1)-partite graph with n vertices and the maximum number of edges, our claim that G = T r−1 (n) follows from the assumed extremality of G. ¤ The Tur´ an graphs T r−1 (n) are dense: in order of magnitude, they have about n2 edges. More exactly, for every n and r we have tr−1 (n) 6 12 n2
r−2 , r−1
with equality whenever r − 1 divides n (Exercise 8). It is therefore remarkable that just ²n2 more edges (for any fixed ² > 0 and n large) an’s theorem) but a Ksr for give us not only a K r subgraph (as does Tur´ any given integer s—a graph itself teeming with K r subgraphs: Theorem 7.1.2. (Erd˝ os & Stone 1946) For all integers r > 2 and s > 1, and every ² > 0, there exists an integer n0 such that every graph with n > n0 vertices and at least tr−1 (n) + ²n2 edges contains Ksr as a subgraph. We shall prove this theorem in Section 7.3. The Erd˝ os-Stone theorem is interesting not only in its own right: it also has a most interesting corollary. In fact, it was this entirely unexpected corollary that established the theorem as a kind of meta-theorem for the extremal theory of dense graphs, and thus made it famous. Given¡ a¢ graph H and an integer n, consider the number hn := ex(n, H)/ n2 : the maximum edge density that an n-vertex graph can have without containing a copy of H. Could it be that this critical density is essentially just a function of H, that hn converges as n → ∞? Theorem 7.1.2 implies this, and more: the limit of hn is determined by a very simple function of a natural invariant of H—its chromatic number! Corollary 7.1.3. For every graph H with at least one edge, µ ¶−1 χ(H) − 2 n lim ex(n, H) . = n→∞ χ(H) − 1 2 For the proof of Corollary 7.1.3 we need as a lemma that tr−1 (n) never deviates much from ¡the ¢ value it takes when r − 1 divides n (see above), and that tr−1 (n)/ n2 converges accordingly. The proof of the lemma is left as an easy exercise with hint (Exercise 9). Lemma 7.1.4.
µ ¶−1 n r−2 . = 2 r−1
lim tr−1 (n)
n→∞
Proof of Corollary 7.1.3. Let r := χ(H). Since H cannot be coloured with r − 1 colours, we have H 6⊆ T r−1 (n) for all n ∈ N, and hence tr−1 (n) 6 ex(n, H) . On the other hand, H ⊆ Ksr for all sufficiently large s, so ex(n, H) 6 ex(n, Ksr )
for all those s. Let us fix such an s. For every ² > 0, Theorem 7.1.2 implies that eventually (i.e. for large enough n) ex(n, Ksr ) < tr−1 (n) + ²n2 . Hence for n large, ¡ n¢
tr−1 (n)/
6 ex(n, H)/ 6 < = 6
¡ n¢
Therefore,¡ since tr−1 (n)/ ¢ ex(n, H)/ n2 . Thus
2 ¡ n¢ r ex(n, Ks )/ 2 ¡ ¢ ¡ ¢ tr−1 (n)/ n2 + ²n2 / n2 ¡ ¢ tr−1 (n)/ n2 + 2²/(1 − n1 ) ¡ ¢ (assume tr−1 (n)/ n2 + 4²
converges to
r−2 r−1
n > 2).
(Lemma 7.1.4), so does
µ ¶−1 r−2 n = r−1 2
lim ex(n, H)
as claimed.
For ¡ ¢bipartite graphs H, Corollary 7.1.3 says that substantially fewer than n2 edges suffice to force an H subgraph. It turns out that 2
c1 n2− r+1 6 ex(n, Kr,r ) 6 c2 n2− r
for suitable constants c1 , c2 depending on r; the lower bound is obtained by random graphs,2 the upper bound is calculated in Exercise 13. If H is a forest, then H ⊆ G as soon as ε(G) is large enough, so ex(n, H) is at most linear in n (Exercise 5). Erd˝ os and S´ os conjectured in 1963 that ex(n, T ) 6 12 (k − 1)n for all trees with k > 2 edges; as a general bound for all n, this is best possible for every T . See Exercises 15–18 for details. 2
see Chapter 11
7.2 Szemer´edi’s regularity lemma
7.2 Szemer´edi’s regularity lemma More than 20 years ago, in the course of the proof of a major result on the Ramsey properties of arithmetic progressions, Szemer´edi developed a graph theoretical tool whose fundamental importance has been realized more and more in recent years: his so-called regularity or uniformity lemma. Very roughly, the lemma says that all graphs can be approximated by random graphs in the following sense: every graph can be partitioned, into a bounded number of equal parts, so that most of its edges run between different parts and the edges between any two parts are distributed fairly uniformly—just as we would expect it if they had been generated at random. In order to state the regularity lemma precisely, we need some definitions. Let G = (V, E) be a graph, and let X, Y ⊆ V be disjoint. Then we denote by kX, Y k the number of X–Y edges of G, and call d(X, Y ) :=
kX, Y k |X| |Y |
the density of the pair (X, Y ). (This is a real number between 0 and 1.) Given some ² > 0, we call a pair (A, B) of disjoint sets A, B ⊆ V ²-regular if all X ⊆ A and Y ⊆ B with |X| > ² |A| satisfy
kX, Y k
d(X, Y ) density ²-regular pair
and |Y | > ² |B|
¯ ¯ ¯d(X, Y ) − d(A, B)¯ 6 ² .
The edges in an ²-regular pair are thus distributed fairly uniformly: the smaller ², the more uniform their distribution. Consider a partition { V0 , V1 , . . . , Vk } of V in which one set V0 has been singled out as an exceptional set. (This exceptional set V0 may be empty.3 ) We call such a partition an ²-regular partition of G if it satisfies the following three conditions: (i) |V0 | 6 ² |V |; (ii) |V1 | = . . . = |Vk |; (iii) all but at most ²k 2 of the pairs (Vi , Vj ) with 1 6 i < j 6 k are ²-regular. The role of the exceptional set V0 is one of pure convenience: it makes it possible to require that all the other partition sets have exactly the same size. Since condition (iii) affects only the sets V1 , . . . , Vk , we 3 So V0 may be an exception also to our terminological rule that partition sets are not normally empty.
exceptional set
²-regular partition
may think of V0 as a kind of bin: its vertices are disregarded when the uniformity of the partition is assessed, but there are only few such vertices.
Lemma 7.2.1. (Regularity Lemma) For every ² > 0 and every integer m > 1 there exists an integer M such that every graph of order at least m admits an ²-regular partition { V0 , V1 , . . . , Vk } with m 6 k 6 M . The regularity lemma thus says that, given any ² > 0, every graph has an ²-regular partition into a bounded number of sets. The upper bound M on the number of partition sets ensures that for large graphs the partition sets are large too; note that ²-regularity is trivial when the partition sets are singletons, and a powerful property when they are large. In addition, the lemma allows us to specify a lower bound m on the number of partition sets; by choosing m large, we may increase the proportion of edges running between different partition sets (rather than inside one), i.e. the proportion of edges that are subject to the regularity assertion. Note that the regularity lemma is designed for use with dense graphs:4 for sparse graphs it becomes trivial, because all densities of pairs—and hence their differences—tend to zero (Exercise 22). The remainder of this section is devoted to the proof of the regularity lemma. Although the proof is not difficult, a reader meeting the regularity lemma here for the first time is likely to draw more insight from seeing how the lemma is typically applied than from studying the technicalities of its proof. Any such reader is encouraged to skip to the start of Section 7.3 now and come back to the proof at his or her leisure.
G = (V, E) n q(A, B)
q(A, B)
We shall need the following inequality for reals µ1 , . . . , µk > 0 and e1 , . . . , ek > 0: P 2 X e2 ( ei ) i > P . (1) µi µi P 2P 2 P This follows from the Cauchy-Schwarz inequality ai bi > ( ai bi )2 √ √ by taking ai := µi and bi := ei / µi . Let G = (V, E) be a graph and n := |V |. For disjoint sets A, B ⊆ V we define 2 |A| |B| 2 kA, Bk q(A, B) := d (A, B) = . 2 n |A| |B| n2 For partitions A of A and B of B we set X q(A0 , B 0 ) , q(A, B) := A0 ∈ A; B 0 ∈ B 4
Sparse versions do exist, though; see the notes.
and for a partition P = { C1 , . . . , Ck } of V we let q(P) :=
q(Ci , Cj ) .
q(P)
i<j
However, if P = { C0 , C1 , . . . , Ck } is a partition of V with exceptional set C0 , we treat C0 as a set of singletons and define ˜ , q(P) := q(P) ª © ª © where P˜ := C1 , . . . , Ck ∪ { v } : v ∈ C0 . The function q(P) plays a pivotal role in the proof of the regularity lemma. On the one hand, it measures the uniformity of the partition P: if P has too many irregular pairs (A, B), we may take the pairs (X, Y ) of subsets violating the regularity of the pairs (A, B) and make those sets X and Y into partition sets of their own; as we shall prove, this refines P into a partition for which q is substantially greater than for P. Here, ‘substantial’ means that the increase of q(P) is bounded below by some constant depending only on ². On the other hand, q(P) =
q(Ci , Cj )
X |Ci | |Cj | d2 (Ci , Cj ) 2 n i<j 1 X |Ci | |Cj | n2 i<j
6 1. The number of times that q(P) can be increased by a constant is thus also bounded by a constant—in other words, after some bounded number of refinements our partition will be ²-regular! To complete the proof of the regularity lemma, all we have to do then is to note how many sets that last partition can possibly have if we start with a partition into m sets, and to choose this number as our desired bound M . Let us make all this precise. We begin by showing that, when we refine a partition, the value of q will not decrease: Lemma 7.2.2. (i) Let C, D ⊆ V be disjoint. If C is a partition of C and D is a partition of D, then q(C, D) > q(C, D). (ii) If P, P 0 are partitions of V and P 0 refines P, then q(P 0 ) > q(P).
˜ P
Proof . (i) Let C =: { C1 , . . . , Ck } and D =: { D1 , . . . , D` }. Then q(C, D) =
q(Ci , Dj )
i,j 2 1 X kCi , Dj k = 2 n i,j |Ci | |Dj | ¢2 ¡P 1 i,j kCi , Dj k > 2 P (1) n i,j |Ci | |Dj | 2
kC, Dk 1 ¢¡ P ¢ ¡P 2 n i |Ci | j |Dj |
= q(C, D) . (ii) Let P =: { C1 , . . . , Ck }, and for i = 1, . . . , k let Ci be the partition of Ci induced by P 0 . Then q(P) =
6 q(P 0 ) , since q(P 0 ) =
P i
q(Ci ) +
P i<j
q(Ci , Cj ).
Next, we show that refining a partition by subpartitioning an irregular pair of partition sets increases the value of q a little; since we are dealing here with a single pair only, the amount of this increase will still be less than any constant. Lemma 7.2.3. Let ² > 0, and let C, D ⊆ V be disjoint. If (C, D) is not ²-regular, then there are partitions C = (C1 , C2 ) of C and D = (D1 , D2 ) of D such that |C| |D| . q(C, D) > q(C, D) + ²4 n2 Proof . Suppose (C, D) is not ²-regular. Then there are sets C1 ⊆ C and D1 ⊆ D with |C1 | > ² |C| and |D1 | > ² |D| such that |η| > ² η
for η := d(C1 , D1 ) − d(C, D). Let C := { C1 , C2 } and D := { D1 , D2 }, where C2 := C r C1 and D2 := D r D1 .
Let us show that C and D satisfy the conclusion of the lemma. We shall write ci := |Ci |, di := |Di |, eij := kCi , Dj k, c := |C|, d := |D| and e := kC, Dk. As in the proof of Lemma 7.2.2,
ci , di , eij c, d, e
1 X e2ij n2 i,j ci dj µ 2 X e2ij ¶ 1 e11 = 2 + n c1 d1 i+j>2 ci dj µ 2 ¶ (e − e11 )2 1 e11 . + > 2 c1 d1 cd − c1 d1 (1) n
q(C, D) =
By definition of η, we have e11 = c1 d1 e/cd + ηc1 d1 , so ¶2 c1 d1 e + ηc1 d1 cd µ ¶2 1 cd − c1 d1 e − ηc1 d1 + cd − c1 d1 cd
1 n q(C, D) > c1 d1 2
c1 d1 e2 2eηc1 d1 + η 2 c1 d1 + c2 d2 cd η 2 c21 d21 cd − c1 d1 2 2eηc1 d1 + + e − 2 2 c d cd cd − c1 d1 e2 + η 2 c1 d1 > cd =
e2 + ²4 cd cd
since c1 > ²c and d1 > ²d by the choice of C1 and D1 .
Finally, we show that if a partition has enough irregular pairs of partition sets to fall short of the definition of an ²-regular partition, then subpartitioning all those pairs at once results in an increase of q by a constant: Lemma 7.2.4. Let 0 < ² 6 1/4, and let P = { C0 , C1 , . . . , Ck } be a partition of V , with exceptional set C0 of size |C0 | 6 ²n and |C1 | = . . . = |Ck | =: c. If P is not ²-regular, then there is a partition P 0 = { C00 , C10 , . . . , C`0 } of V with exceptional set C00 , where k 6 ` 6 k4k , such that |C00 | 6 |C0 | + n/2k , all other sets Ci0 have equal size, and q(P 0 ) > q(P) + ²5/2 .
158 Cij
Proof . For all 1 6 i < j 6 k, let us define a partition Cij of Ci and a partition Cji of Cj , as follows. If the pair (Ci , Cj ) is ²-regular, we let Cij := { Ci } and Cji := { Cj }. If not, then by Lemma 7.2.3 there are partitions Cij of Ci and Cji of Cj with |Cij | = |Cji | = 2 and q(Cij , Cji ) > q(Ci , Cj ) + ²4
²4 c2 |Ci | |Cj | = q(C , C ) + . i j n2 n2
For each i = 1, . . . , k, let Ci be the unique minimal partition of Ci that refines every partition Cij with j 6= i. (In other words, if we consider two elements of Ci as equivalent whenever they lie in the same partition set of Cij for every j 6= i, then Ci is the set of equivalence classes.) Thus, |Ci | 6 2k−1 . Now consider the partition k [
C := { C0 } ∪
of V , with C0 as exceptional set. Then C refines P, and k 6 |C| 6 k2k . C0
© ª Let C0 := { v } : v ∈ C0 . Now if P is not ²-regular, then for more than ²k 2 of the pairs (Ci , Cj ) with 1 6 i < j 6 k the partition Cij is non-trivial. Hence, by our definition of q for partitions with exceptional set, and Lemma 7.2.2 (i), q(C) =
q(Ci , Cj ) +
16i<j
q(Cij , Cji ) +
q(C0 , Ci ) +
q(Ci )
X ¡ ¢ q C0 , { Ci } + q(C0 ) 16i
q(Ci , Cj ) + ²k 2
= q(P) + ²5
kc n
¶2
¢ ²4 c2 X ¡ + q C0 , { Ci } + q(C0 ) 2 n 16i
> q(P) + ²5/2 .
(For the last inequality, recall that |C0 | 6 ²n 6 14 n, so kc > 34 n.) In order to turn C into our desired partition P 0 , all that remains to do is to cut its sets up into pieces of some common size, small enough that all remaining vertices can be collected into the exceptional set without making this too large. Let C10 , . . . , C`0 be a maximal collection of disjoint sets of size d := bc/4k c such that each Ci0 is contained in some
S C ∈ C r { C0 }, and put C00 := V r Ci0 . Then P 0 = { C00 , C10 , . . . , C`0 } ˜ so is indeed a partition of V . Moreover, P˜ 0 refines C,
q(P 0 ) > q(C) > q(P) + ²5/2 by Lemma 7.2.2 (ii). Since each set Ci0 6= C00 is also contained in one of the sets C1 , . . . , Ck , but no more than 4k sets Ci0 can lie inside the same Cj (by the choice of d), we also have k 6 ` 6 k4k as required. Finally, the sets C10 , . . . , C`0 use all but at most d vertices from each set C 6= C0 of C. Hence, |C00 | 6 |C0 | + d |C| c 6 |C0 | + k k2k 4 (4) = |C0 | + ck/2k 6 |C0 | + n/2k .
The proof of the regularity lemma now follows easily by repeated application of Lemma 7.2.4: Proof of Lemma 7.2.1. Let ² > 0 and m > 1 be given; without loss of generality, ² 6 1/4. Let s := 2/²5 . This number s is an upper bound on the number of iterations of Lemma 7.2.4 that can be applied to a partition of a graph before it becomes ²-regular; recall that q(P) 6 1 for all partitions P. There is one formal requirement which a partition { C0 , C1 , . . . , Ck } with |C1 | = . . . = |Ck | has to satisfy before Lemma 7.2.4 can be (re-) applied: the size |C0 | of its exceptional set must not exceed ²n. With each iteration of the lemma, however, the size of the exceptional set can grow by up to n/2k . (More precisely, by up to n/2` , where ` is the number of other sets in the current partition; but ` > k by the lemma, so n/2k is certainly an upper bound for the increase.) We thus want to choose k large enough that even s increments of n/2k add up to at most 12 ²n, and n large enough that, for any initial value of |C0 | < k, we have |C0 | 6 12 ²n. (If we give our starting partition k non-exceptional sets C1 , . . . , Ck , we should allow an initial size of up to k for C0 , to be able to achieve |C1 | = . . . = |Ck |.) So let k > m be large enough that 2k−1 > s/². Then s/2k 6 ²/2, and hence s (5) k + k n 6 ²n 2 whenever k/n 6 ²/2, i.e. for all n > 2k/². Let us now choose M . This should be an upper bound on the number of (non-exceptional) sets in our partition after up to s iterations
², m s
of Lemma 7.2.4, where in each iteration this number may grow from its current value r to at most r4r . So let f be the function x 7→ x4x , and take M := max { f s (k), 2k/² }; the second term in the maximum ensures that any n > M is large enough to satisfy (5). We finally have to show that every graph G = (V, E) of order at least m has an ²-regular partition { V0 , V1 , . . . , Vk } with m 6 k 6 M . So let G be given, and let n := |G|. If n 6 M , we partition G into k := n singletons, choosing V0 := ∅ and |V1 | = . . . = |Vk | = 1. This partition of G is clearly ²-regular. Suppose now that n > M . Let C0 ⊆ V be minimal such that k divides |V r C0 |, and let { C1 , . . . , Ck } be any partition of V r C0 into sets of equal size. Then |C0 | < k, and hence |C0 | 6 ²n by (5). Starting with { C0 , C1 , . . . , Ck } we apply Lemma 7.2.4 again and again, until the partition of G obtained is ²-regular; this will happen after at most s iterations, since by (5) the size of the exceptional set in the partitions stays below ²n, so the lemma could indeed be reapplied up to the theoretical maximum of s times. ¤
7.3 Applying the regularity lemma The purpose of this section is to illustrate how the regularity lemma is typically applied in the context of (dense) extremal graph theory. Suppose we are trying to prove that a certain edge density of a graph G suffices to force the occurrence of some given subgraph H, and that we have an ²-regular partition of G. The edges inside almost all the pairs (Vi , Vj ) of partition sets are distributed uniformly, although their density may depend on the pair. But since G has many edges, this density cannot be zero for all the pairs: some sizeable proportion of the pairs will have positive density. Now if G is large, then so are the pairs: recall that the number of partition sets is bounded, and they have equal size. But any large enough bipartite graph with equal partition sets, fixed positive edge density (however small!) and a uniform distribution of edges will contain any given bipartite subgraph5 —this will be made precise below. Thus if enough pairs in our partition of G have positive density that H can be written as the union of bipartite graphs each arising in one of those pairs, we may hope that H ⊆ G as desired. These ideas will be formalized by Lemma 7.3.2 below. We shall then use this and the regularity lemma to prove the Erd˝ os-Stone theorem from Section 7.1; another application will be given later, in the proof of Theorem 9.2.2. Before we state Lemma 7.3.2, let us note a simple consequence of the ²-regularity of a pair (A, B): for any subset Y ⊆ B that is not too 5 Readers already acquainted with random graphs may find it instructive to compare this statement with Proposition 11.3.1.
7.3 Applying the regularity lemma
small, most vertices of A have about the expected number of neighbours in Y : Lemma 7.3.1. Let (A, B) be an ²-regular pair, of density d say, and let Y ⊆ B have size |Y | > ² |B|. Then all but at most ² |A| of the vertices in A have (each) at least (d − ²)|Y | neighbours in Y . Proof . Let X ⊆ A be the set of vertices with fewer than (d − ²)|Y | neighbours in Y . Then kX, Y k < |X|(d − ²)|Y |, so d(X, Y ) =
kX, Y k < d − ² = d(A, B) − ² . |X| |Y |
Since (A, B) is ²-regular, this implies that |X| < ² |A|.
Let G be a graph with an ²-regular partition { V0 , V1 , . . . , Vk }, with exceptional set V0 and |V1 | = . . . = |Vk | =: `. Given d ∈ (0, 1 ], let R be the graph with vertices V1 , . . . , Vk in which two vertices are adjacent if and only if they form an ²-regular pair in G of density > d. We shall call R a regularity graph of G with parameters ², ` and d. Given s ∈ N, let us now replace every vertex Vi of R by a set Vis of s vertices, and every edge by a complete bipartite graph between the corresponding s-sets. The resulting graph will be denoted by Rs . (For R = K r , for example, we have Rs = Ksr .) The following lemma says that subgraphs of Rs can also be found in G, provided that ² is small enough and the Vi are large enough. In fact, the values of ² and ` required depend only on (d and) the maximum degree of the subgraph: Lemma 7.3.2. For all d ∈ (0, 1 ] and ∆ > 1 there exists an ²0 > 0 with the following property: if G is any graph, H is a graph with ∆(H) 6 ∆, s ∈ N, and R is any regularity graph of G with parameters ² 6 ²0 , ` > s/²0 and d, then
regularity graph Vis Rs
H ⊆ Rs ⇒ H ⊆ G . Proof . Given d and ∆, choose ²0 < d small enough that ∆+1 ²0 6 1 ; (d − ²0 )∆
d, ∆
²0
such a choice is possible, since (∆ + 1)²/(d − ²)∆ → 0 as ² → 0. Now let G, H, s and R be given as stated. Let { V0 , V1 , . . . , Vk } be the ²-regular partition of G that gave rise to R; thus, ² 6 ²0 , V (R) = { V1 , . . . , Vk } and |V1 | = . . . = |Vk | = `. Let us assume that H is actually a subgraph
G, H, R, Rs Vi ², k, `
162 ui , h σ vi
of Rs (not just isomorphic to one), with vertices u1 , . . . , uh say. Each vertex ui lies in one of the s-sets Vjs of Rs ; this defines a map σ: i 7→ j. Our aim is to define an embedding ui 7→ vi ∈ Vσ(i) of H in G; thus, v1 , . . . , vh will be distinct, and vi vj will be an edge of G whenever ui uj is an edge of H. Our plan is to choose the vertices v1 , . . . , vh inductively. Throughout the induction, we shall have a ‘target set’ Yi ⊆ Vσ(i) assigned to each i; this contains the vertices that are still candidates for the choice of vi . Initially, Yi is the entire set Vσ(i) . As the embedding proceeds, Yi will get smaller and smaller (until it collapses to { vi } when vi is chosen): whenever we choose a vertex vj with j < i and uj ui ∈ E(H), we delete all those vertices from Yi that are not adjacent to vj . The set Yi thus evolves as Vσ(i) = Yi0 ⊇ . . . ⊇ Yii = { vi } , where Yij denotes the version of Yi current after the definition of vj (and any corresponding deletion of vertices from Yij−1 ). In order to make this approach work, we have to ensure that the target sets Yi do not get too small. When we come to embed a vertex uj , we consider all the indices i > j with uj ui ∈ E(H); there are at most ∆ such i. For each of these i, we wish to select vj so that Yij = N (vj ) ∩ Yij−1
is large, i.e. not much smaller than Yij−1 . Now this can be done by Lemma 7.3.1 (with A = Vσ(j) , B = Vσ(i) and Y = Yij−1 ): unless Yij−1 is tiny (of size less than ²`), all but at most ²` choices of vj will be such that (2) implies (3) |Yij | > (d − ²)|Yij−1 | . Doing this simultaneously for all of the at most ∆ values of i considered, we find that all but at most ∆²` choices of vj from Vσ(j) , and in particular from Yjj−1 ⊆ Vσ(j) , satisfy (3) for all i. It remains to show that the sets Y considered for Lemma 7.3.1 above are indeed never tiny, and that |Yjj−1 | − ∆²` > s to ensure that a suitable choice for vj exists: since σ(j 0 ) = σ(j) for at most s − 1 of the vertices uj 0 with j 0 < j, a choice between s suitable candidates for vj will suffice to keep vj distinct from v1 , . . . , vj−1 . But all this follows from our choice of ²0 . Indeed, the initial target sets Yi0 have size `, and each Yi has vertices deleted from it only when some vj with j < i and uj ui ∈ E(H) is defined, which happens at most ∆ times. Thus, |Yij | − ∆²` > (d − ²)∆ ` − ∆²` > (d − ²0 )∆ ` − ∆²0 ` > ²0 ` > s (3)
whenever j < i, so in particular |Yij | > ²0 ` > ²` and |Yjj−1 | − ∆²` > s. ¤
We are now ready to prove the Erd˝ os-Stone theorem. Proof of Theorem 7.1.2. Let r > 2 and s > 1 be given as in the statement of the theorem. For s = 1 the assertion follows from Tur´ an’s theorem, so we assume that s > 2. Let γ > 0 be given; this γ will play the role of the ² of the theorem. Let G be a graph with |G| =: n and kGk > tr−1 (n) + γn2 .
1 > 0; m
Ms . ²0 (1 − ²)
and `=
Since this number is at least m, the regularity lemma provides us with an ²-regular partition { V0 , V1 , . . . , Vk } of G, where m 6 k 6 M ; let |V1 | = . . . = |Vk | =: `. Then n > k` ,
m, ²
1 this is possible, since 2γ − d − m > 0. On input ² and m, the regularity lemma returns an integer M . Let us assume that
n>
d, ∆ ²0
To apply the regularity lemma, let m > 1/γ and choose ² > 0 small enough that ² 6 ²0 and δ := 2γ − ²2 − 4² − d −
r, s γ
(Thus, γ < 1.) We want to show that Ksr ⊆ G if n is large enough. Our plan is to use the regularity lemma to show that G has a reguan’s theorem. Then larity graph R dense enough to contain a K r by Tur´ Rs contains a Ksr , so we may hope to use Lemma 7.3.2 to deduce that Ksr ⊆ G. On input d := γ and ∆ := ∆(Ksr ), Lemma 7.3.2 returns an ²0 > 0; since the lemma’s assertion about ²0 becomes weaker when ²0 is made smaller, we may assume that ²0 < γ/2 < 1 .
k `
n − ²n 1−² s n − |V0 | > =n > k M M ²0
by the choice of n. Let R be the regularity graph of G with parameters ², `, d corresponding to the above partition. Since ² 6 ²0 and ` > s/²0 , the regularity graph R satisfies the premise of Lemma 7.3.2, and by definition of ∆ we have ∆(Ksr ) = ∆. Thus in order to conclude by Lemma 7.3.2
that Ksr ⊆ G, all that remains to be checked is that K r ⊆ R (and hence Ksr ⊆ Rs ). an’s theorem. We thus have to Our plan was to show K r ⊆ R by Tur´ check that R has enough edges, i.e. that enough ²-regular pairs (Vi , Vj ) have density at least d. This should follow from our assumption that G has at least tr−1 (n) + γn2 edges, i.e. an edge density of about r−2 r−1 + 2γ: this lies substantially above the approximate edge density r−2 r−1 of the Tur´ an graph T r−1 (k), and hence substantially above any density that G could have if no more than tr−1 (k) of the pairs (Vi , Vj ) had density > d—even if all those pairs had density 1! Let us then estimate kRk more precisely. How many edges of G ¡ ¢ lie outside ²-regular pairs? At most |V20 | edges lie inside V0 , and by condition (i) in the definition of ²-regularity these are at most 12 (²n)2 edges. At most |V0 |k` 6 ²nk` edges join V0 to other partition sets. The at most ²k 2 other pairs (Vi , Vj ) that are not ²-regular contain at most `2 edges each, together at most ²k 2 `2 . The ²-regular pairs of insufficient 2 density (< d) each contain no more than d` ¡ ` ¢edges, altogether at most 1 2 2 2 k d` edges. Finally, there are at most 2 edges inside each of the partition sets V1 , . . . , Vk , together at most 12 `2 k edges. All other edges of G lie in ²-regular pairs of density at least d, and thus contribute to edges of R. Since each edge of R corresponds to at most `2 edges of G, we thus have in total kGk ≤ 12 ²2 n2 + ²nk` + ²k 2 `2 + 12 k 2 d`2 + 12 `2 k + kRk `2 . Hence, for all sufficiently large n, kGk − 12 ²2 n2 − ²nk` − ²k 2 `2 − 12 dk 2 `2 − 12 k`2 1 2 2 2k ` ¶ µ 1 2 2 2 tr−1 (n) + γn − 2 ² n − ²nk` 1 − 2² − d − ≥ 21 k 2 n2 /2 k (1,2) ¶ µ tr−1 (n) 1 + 2γ − ²2 − 4² − d − ≥ 12 k 2 n2 /2 m (2) ¶ ¶ µ µ ¶−1µ 1 n 1 2 +δ 1− = 2 k tr−1 (n) 2 n
kRk ≥ 12 k 2
> 12 k 2
> tr−1 (k) . (The strict inequality follows from Lemma 7.1.4.) Therefore K r ⊆ R by Theorem 7.1.1, as desired. ¤
Exercises 1.− Show that K1,3 is extremal without a P 3 . 2.− Given k > 0, determine the extremal graphs of chromatic number at most k. N.
Determine the value of ex(n, K1,r ) for all r, n
Is there a graph that is edge-maximal without a K 3 minor but not extremal?
Show that, for every forest F , the value of ex(n, F ) is bounded above by a linear function of n.
6.+ Given k > 0, determine the extremal graphs without a matching of size k. (Hint. Theorem 2.2.3 and Ex. 10, Ch. 2.) 7.
Without using Tur´ an’s theorem, show that the maximum number of edges in a triangle-free graph of order n > 1 is bn2 /4c.
Show that tr−1 (n) 6
1 2 n 2
with equality whenever r − 1 divides n. 9.
¡n¢
Show that tr−1 (n)/ (Hint.
converges to (r − 2)/(r − 1) as n → ∞.
2 n tr−1 (r − 1)b r−1 c
n ) 6 tr−1 (n) 6 tr−1 ((r − 1)d r−1 e).)
10.+ Given non-adjacent vertices u, v in a graph G, denote by G [ u → v ] the graph obtained from G by first deleting all the edges at u and then joining u to all the neighbours of v. Show that K r 6⊆ G [ u → v ] if K r 6⊆ G. Applying this operation repeatedly to a given extremal graph for n and K r , prove that ex(n, K r ) = tr−1 (n): in each iteration step, choose u and v so that the number of edges will not decrease, and so that eventually a complete multipartite graph is obtained. 11.
Show that deleting at most (m − s)(n − t)/s edges from a Km,n will never destroy all its Ks,t subgraphs.
For 0 < s 6 t 6 n let z(n, s, t) denote the maximum number of edges in a bipartite graph whose partition sets both have size n, and which does not contain a Ks,t . Show that 2 ex(n, Ks,t ) ≤ z(n, s, t) ≤ ex(2n, Ks,t ).
13.+ Let 1 6 r 6 n be integers. Let G be a bipartite graph with bipartition { A, B }, where |A| = |B| = n, and assume that Kr,r 6⊆ G. Show that
X µd(x)¶
x∈A
µ ¶
6 (r − 1)
n . r
Using the previous exercise, deduce that ex(n, Kr,r ) 6 cn2−1/r for some constant c depending only on r.
The upper density of an infinite graph G is the infimum of all reals α ¡ ¢−1 such that the finite graphs H ⊆ G with kHk |H| > α have bounded 2 order. Show that this number always takes one of the countably many values 0, 1, 12 , 23 , 34 , . . .. (Hint. Erd˝ os-Stone.)
Prove the following weakening of the Erd˝ os-S´ os conjecture (stated at the end of Section 7.1): given integers 2 6 k < n, every graph with n vertices and at least (k − 1)n edges contains every tree with k edges as a subgraph.
Show that, as a general bound for arbitrary n, the bound on ex(n, T ) claimed by the Erd˝ os-S´ os conjecture is best possible for every tree T . Is it best possible even for every n and every T ?
17.− Prove the Erd˝ os-S´ os conjecture for the case when the tree considered is a star. 18.
Prove the Erd˝ os-S´ os conjecture for the case when the tree considered is a path. (Hint. Use the result of the next exercise.)
Show that every connected graph G contains a path of length at least min { 2δ(G), |G| − 1 }.
20.− In the definition of an ²-regular pair, what is the purpose of the requirement that |X| > ² |A| and |Y | > ² |B|? 21.− Show that any ²-regular pair in G is also ²-regular in G. 22.
Prove the regularity lemma for sparse graphs, that is, for every sequence (Gn )n ∈ N of graphs Gn of order n such that kGn k/n2 → 0 as n → ∞.
Notes The standard reference work for results and open problems in extremal graph theory (in a very broad sense) is still B. Bollob´ as, Extremal Graph Theory, Academic Press 1978. A kind of update on the book is given by its author in his chapter of the Handbook of Combinatorics (R.L. Graham, M. Gr¨ otschel & L. Lov´ asz, eds.), North-Holland 1995. An instructive survey of extremal graph theory in the narrower sense of our chapter is given by M. Simonovits in (L.W. Beineke & R.J. Wilson, eds.) Selected Topics in Graph Theory 2, Academic Press 1983. This paper focuses among other things on the particular role played by the Tur´ an graphs. A more recent survey by the same author can be found in (R.L. Graham & J. Neˇsetˇril, eds.) The Mathematics of Paul Erd˝ os, Vol. 2, Springer 1996. Tur´ an’s theorem is not merely one extremal result among others: it is the result that sparked off the entire line of research. Our proof of Tur´ an’s theorem is essentially the original one; the proof indicated in Exercise 10 is due to Zykov.
Our version of the Erd˝ os-Stone theorem is a slight simplification of the original. A direct proof, not using the regularity lemma, is given in L. Lov´ asz, Combinatorial Problems and Exercises (2nd edn.), North-Holland 1993. Its most fundamental application, Corollary 7.1.3, was only found 20 years after the theorem, by Erd˝ os and Simonovits (1966). Of our two bounds on ex(n, Kr,r ) the upper one is thought to give the correct order of magnitude. For vastly off-diagonal complete bipartite graphs this was verified by J. Koll´ ar, L. R´ onyai & T. Szab´ o, Norm-graphs and bipartite Tur´ an numbers, Combinatorica 16 (1996), 399–406, who proved that 1 ex(n, Kr,s ) > cr n2− r when s > r! . Details about the Erd˝ os-S´ os conjecture, including an approximate solution for large k, can be found in the survey by Koml´ os and Simonovits cited below. The case where the tree T is a path (Exercise 18) was proved by Erd˝ os & Gallai in 1959. It was this result, together with the easy case of stars (Exercise 17) at the other extreme, that inspired the conjecture as a possible unifying result. The regularity lemma is proved in E. Szemer´edi, Regular partitions of graphs, Colloques Internationaux CNRS 260—Probl`emes Combinatoires et Th´eorie des Graphes, Orsay (1976), 399–401. Our rendering follows an account by Scott (personal communication). A broad survey on the regularity lemma and its applications is given by J. Koml´ os & M. Simonovits in (D. Mikl´ os, V.T. S´ os & T. Sz˝ onyi, eds.) Paul Erd˝ os is 80, Vol. 2, Proc. Colloq. Math. Soc. J´ anos Bolyai (1996); the concept of a regularity graph and Lemma 7.3.2 are taken from this paper. An adaptation of the regularity lemma for use with sparse graphs was developed independently by Kohayakawa and by R¨ odl; see Y. Kohayakawa, Szemer´edi’s regularity lemma for sparse graphs, in (F. Cucker & M. Shub, eds.) Foundations of Computational Mathematics, Selected papers of a conference held at IMPA in Rio de Janeiro, January 1997, Springer 1997.
Substructures in Sparse Graphs
In this chapter we study how global assumptions about a graph—on its average degree, chromatic number, or even (large) girth—can force it to contain a given graph H as a minor or topological minor. As we know already from Mader’s theorem 3.6.1, there exists a function h such that an average degree of d(G) > h(r) suffices to create a T K r subgraph in G, and hence a (topological) H minor if r > |H|. Since a graph with n vertices and average degree d has 12 dn edges this shows that, for every H, there is a ‘constant’ c (depending on H but not on n) such that a topological H minor occurs in every graph with n vertices and at least cn edges. Such graphs with a number of edges about linear1 in their order are called sparse—so this is a chapter about substructures in sparse graphs. The first question, then, will be the analogue of Tur´ an’s theorem: given a positive integer r, what is the minimum value of the above ‘constant’ c for H = K r , i.e. the smallest growth rate of a function h(r) as in Theorem 3.6.1? This was a major open problem until very recently; we present its solution, which builds on some fascinating methods the problem has inspired over time, in Section 8.1. If raising the average degree suffices to force the occurrence of a certain minor, then so does raising any other invariant which in turn forces up the average degree. For example, if d(G) > c implies H 4 G, then so will χ(G) > c + 1 (by Corollary 5.2.3). However, is this best possible? Even if the value of c above is least possible for d(G) > c to imply H 4 G, it need not be so for χ(G) > c + 1 to imply H 4 G. One of the most famous conjectures in graph theory, the Hadwiger conjecture, 1
Compare the footnote at the beginning of Chapter 7.
8. Substructures in Sparse Graphs
√ suggests that there is indeed a gap here: while a value of c = c0 r log r (where c0 is independent of both n and r) is best possible for d(G) > c to imply H 4 G (Section 8.2), the conjecture says that χ(G) > r will do the same! Thus, if true, then Hadwiger’s conjecture shows that the effect of a large chromatic number on the occurrence of minors somehow goes beyond that part which is well-understood: its effect via mere edge density. We shall consider Hadwiger’s conjecture in Section 8.3.
8.1 Topological minors In this section we prove that an average degree of cr2 suffices to force the occurrence of a topological K r minor in a graph; complete bipartite graphs show that, up to the constant c, this is best possible (Exercise 5). The following theorem was proved independently around 1996 by Bollob´ as & Thomason and by Koml´os & Szemer´edi. Theorem 8.1.1. There exists a c ∈ R such that, for every r ∈ N, every graph G of average degree d(G) > cr2 contains K r as a topological minor.
linked (k, `)-linked
The proof of this theorem, in which we follow Bollob´ as & Thomason, will occupy us for the remainder of this section. A set U ⊆ V (G) will be called linked (in G) if for any distinct vertices u1 , . . . , u2h ∈ U there are h disjoint paths Pi = u2i−1 . . . u2i in G, i = 1, . . . , h.2 The graph G itself is (k, `)-linked if every k-set of its vertices contains a linked `-set. How can we hope to find the T K r in G claimed to exist by Theorem 8.1.1? Our basic approach will be to identify first some r-set X as a set of branch vertices, and to choose for each x ∈ X a set Yx of r − 1 neighbours, one for every edge incident with x in the K r . If the 2 constant c from S the theorem is large enough, the r + r(r − 1) = r vertices of X ∪ Yx can be chosen distinct: by Proposition 1.2.2, G has a subgraph of minimum degree at least ε(G) = 12 d(G) > 12 cr2 , so we can choose X and its neighbours inside this subgraph. Having fixed X and the S sets Yx , we then have to link up the correct pairs of vertices in Y := Yx by disjoint paths in G − X, to obtain the desired T K r . This would be possible at once if Y were linked in G − X. Unfortunately, this is unrealistic to hope for: no average degree, however large, will force every r(r − 1)-set to be linked. (Why not?) However, if we pick for X significantly more than the r vertices needed eventually, and for each x ∈ X significantly more than r − 1 neighbours as Yx , then Y might become so large that the high average degree of G guarantees the 2 Thus, in a k-linked graph—see Chapter 3.6—every set of up to 2k + 1 vertices is linked.
8.1 Topological minors
existence of some large linked subset Z ⊆ Y . This would be the case if G were (k, `)-linked for some k 6 |Y | and ` > |Z|. As above, a large enough constant c will easily ensure that X and Y can be chosen with many vertices to spare. Another problem, however, is more serious: it will not be enough to make ` (and hence Z) large in absolute terms. Indeed, if k (and Y ) is much larger still, it might happen that Z, although large, consists of neighbours of only a few vertices in X! We thus have to ensure that ` is large also relative to k. This will be the purpose of our first lemma (8.1.2): it establishes a sufficient condition for G to be (k, dk/2e)-linked. What is this sufficient condition? It is the assumption that G has a particularly dense minor H, one whose minimum degree exceeds 12 |H| by a positive fraction of k. (In particular, H will be dense in the sense of Chapter 7.) In view of Theorem 3.6.2, it is not surprising that such a dense graph H is highly linked. Given sufficiently high connectivity of G (which again follows easily if c is large enough), we may then try to link up the vertices of any Y as above to distinct branch sets of H by disjoint paths in G avoiding most of the other branch sets, and thus to transfer the linking properties of H to a dk/2e-set Z ⊆ Y (Fig. 8.1.1).
Y Z X
Fig. 8.1.1. Finding a T K 3 in G with branch vertices x1 , x2 , x3
What is all the more surprising, however, is that the existence of such a dense minor H can be deduced from our assumption of d(G) > cr2 . This will be shown in another lemma (8.1.3); the assertion of the theorem itself will then follow easily. Lemma 8.1.2. If G is k-connected and has a minor H with 2δ(H) > |H| + 32 k, then G is (k, dk/2e)-linked.
172 (3.3.1) V, Vx v1 , . . . , v k linkage link
P P1 , . . . , Pk f (P )
Proof . Let V := { Vx | x ∈ V (H) } be the set of branch sets in G corresponding to the vertices of H. For our proof that G is (k, dk/2e)linked, let k distinct vertices v1 , . . . , vk ∈ G be given. Let us call a sequence P1 , . . . , Pk of disjoint paths in G a linkage if the Pi each start in vi and end in pairwise distinct sets V ∈ V; the paths Pi themselves will be called links. Since our assumptions about H imply that |H| > k, and G is k-connected, such linkages exist: just pick k vertices from pairwise distinct sets V ∈ V, and link them disjointly to { v1 , . . . , vk } by Menger’s theorem. NowSlet P = (P1 , . . . , Pk ) be a linkage whose total number of edges outside V ∈ V G [ V ] is as small as possible. Thus, if f (P ) denotes the number ofPedges of P not lying in any G [ Vx ], we choose P so as to k minimize i=1 f (Pi ). Then for every V ∈ V that meets a path Pi ∈ P there exists one such path that ends in V : if not, we could terminate Pi in V and reduce f (Pi ). Thus, exactly k of the branch sets of H meet a link. Let us divide these sets into two classes:
U := { V
W := { V
V | V meets exactly one link } V | V meets more than one link } .
Since H is dense and each U ∈ U meets only one link, it will be easy to show that the starting vertices vi of those links form a linked set in G. Hence, our aim is to show that |U| > dk/2e, i.e. that U is no smaller than W. (Recall that |U| + |W| = k.) To this end, we first prove the following: Every V ∈ W is met by some link which leaves V again and next meets a set from U (where it ends). x
Suppose Vx
W is a counterexample to (1). Since 2δ(H) > |H| + 32 k > δ(H) + 32 k ,
Pi Pi0
we have δ(H) > 32 k. As |U ∪ W| = k, this implies that x has a neighbour y in H with Vy ∈ V r (U ∪ W); let wx wy be an edge of G with wx ∈ Vx and wy ∈ Vy . Let Q = w . . . wx wy be a path in G [ Vx ∪ { wy } ] of whose vertices only w lies on any link, say on Pi (Fig. 8.1.2). Replacing Pi in P by Pi0 := Pi wQ then yields another linkage. If Pi is not the link ending in Vx , then f (Pi0 ) 6 f (Pi ). The choice of P then implies that f (Pi0 ) = f (Pi ), i.e. that Pi ends in the branch set W it enters immediately after Vx . Since Vx is a counterexample to (1) we have W ∈/ U, i.e. W ∈ W. Let P 6= Pi be another link meeting W . Then P does not end in W (because Pi ends there); let P 0 ⊆ P be the (minimal) initial segment of P that ends in W . If we now replace Pi and P by Pi0 and P 0 in P, we obtain a linkage contradicting the choice of P.
Vy Vx ∈ W Pi0
V r (U ∪ W)
w Pi P
∈W
Fig. 8.1.2. If Pi does not end in Vx , we replace Pi and P by Pi0 and P 0
We now assume that Pi does end in Vx ; then f (Pi0 ) = f (Pi ) + 1. As Vx ∈ W, there exists a link Pj that meets Vx and leaves it again; let Pj0 be the initial segment of Pj ending in Vx (Fig 8.1.3). Then f (Pj0 ) 6 f (Pj ) − 1. In fact, since replacing Pi and Pj with Pi0 and Pj0 in P yields another linkage, the choice of P implies that f (Pj0 ) = f (Pj ) − 1, so Pj ends in the branch set W it enters immediately after Vx . Then W ∈ W as before, so we may define P and P 0 as before. Replacing Pi , Pj and P by Pi0 , Pj0 and P 0 in P, we finally obtain a linkage that contradicts the choice of P. This completes the proof of (1). Vy
Vx ∈ W
Pi0 Pi
Pj P
P W
Fig. 8.1.3. If Pi ends in Vx , we replace Pi , Pj , P by Pi0 , Pj0 , P 0
With the help of (1) we may define an injection W → U as follows: given W ∈ W, choose a link that passes through W and next meets a set U ∈ U, and map W 7→ U . (This is indeed an injection, because different links end in different branch sets.) Thus |U| > |W|, and hence |U| > dk/2e. Let us assume the enumeration of v1 , . . . , vk to be such that the first u := |U| of the links P1 , . . . , Pk end in sets from U. Since 2δ(H) >
|H| + 32 k, we can find for any two sets Vx , Vy ∈ U at least 32 k sets Vz such that xz, yz ∈ E(H). At least k/2 of these sets Vz do not lie in U ∪ W. Thus whenever U1 , . . . , U2h are distinct sets in U (so h 6 u/2 6 k/2), we may find inductively h distinct sets V i ∈ V r (U ∪ W) (i = 1, . . . , h) such that V i is joined in G to both U2i−1 and U2i . For each i, any vertex of U2i−1 can be linked by a path through V i to any desired vertex of U2i , and these paths will be disjoint for different i. Joining up the appropriate pairs of paths from P in this way, we see that the set { v1 , . . . , vu } is linked in G, and the lemma is proved. ¤ Lemma 8.1.3. Let k > 6 be an integer. Then every graph G with ε(G) > k has a minor H such that 2δ(H) > |H| + 16 k. G0
Proof . We begin by choosing a (4-)minimal minor G0 of G with ε(G0 ) > k. The minimality of G0 implies that δ(G0 ) > k and ε(G0 ) = k (otherwise we could delete a vertex or an edge of G0 ), and hence k + 1 6 δ(G0 ) 6 d(G0 ) = 2k .
Let x0 ∈ G0 be a vertex of minimum degree. If k is odd, let m := (k + 1)/2 and G1 := G0 [ { x0 } ∪ NG0 (x0 ) ] . Then |G1 | = δ(G0 ) + 1 6 2k + 1 6 2(k + 1) = 4m. By the minimality of G0 , contracting any edge x0 y of G0 will result in the loss of at least k + 1 edges. The vertices x0 and y thus have at least k common neighbours, so δ(G1 ) > k + 1 = 2m (Fig. 8.1.4). y
( >k
x0 NG0 (x0 ) Fig. 8.1.4. The graph G1 4 G: a first approximation to the desired minor H
If k is even, we let m := k/2 and G1 := G0 [ NG0 (x0 ) ] . Then |G1 | = δ(G0 ) 6 2k = 4m, and δ(G1 ) > k = 2m as before.
Thus in either case we have found an integer m > k/2 and a graph G1 4 G such that |G1 | 6 4m (1)
m G1
and δ(G1 ) > 2m, so ε(G1 ) > m > k/2 > 3 .
As 2δ(G1 ) > 4m > |G1 |, our graph G1 is already quite a good candidate for the desired minor H of G. In order to jack up its value of 2δ by another 16 k (as required for H), we shall reapply the above contraction process to G1 , and a little more rigorously than before: step by step, we shall contract edges as long as this results in a loss of no more than 76 m edges per vertex. In other words, we permit a loss of edges slightly greater than maintaining ε > m seems to allow. (Recall that, when we contracted G to G0 , we put this threshold at ε(G) = k.) If this second contraction process terminates with a non-empty graph H0 , then ε(H0 ) will be at least 76 m, higher than for G1 ! The 16 m thus gained will suffice to give the graph H1 , obtained from H0 just as G1 was obtained from G0 , the desired high minimum degree. But how can we be sure that this second contraction process will indeed end with a non-empty graph? Paradoxical though it may seem, the reason is that even a permitted loss of up to 76 m edges (and one vertex) per contraction step cannot destroy the m |G1 | or more edges of G1 in the |G1 | steps possible: the graphs with fewer than m vertices towards the end of the process would simply be too small to be able to shed their allowance of 76 m edges—and, by (1), these small graphs would account for about a quarter of the process! Formally, we shall control the graphs H in the contraction process not by specifying an upper bound on the number of edges to be discarded at each step, but by fixing a lower bound for kHk¡in¢terms of |H|. This bound grows linearly from a value of just above m 2 for |H| = m to a value of less than 4m2 for |H| = 4m. By (1) and (2), H = G1 will satisfy this bound, but clearly it cannot be satisfied by any H with |H| = m; so the contraction process must stop somewhere earlier with |H| > m. To implement this approach, let f (n) := 16 m(n − m − 5) and H :=
H 4 G1 : kHk > m |H| + f (|H|) −
By (1), f (|G1 |) 6 f (4m) = 12 m2 − 56 m < so G1
H by (2).
¡m¢o
¡m¢ 2
For every H ∈ H, any graph obtained from H by one of the following three operations will again be in H: ¡ ¢ (i) deletion of an edge, if kHk > m |H| + f (|H|) − m 2 + 1; (ii) deletion of a vertex of degree at most 76 m; (iii) contraction of an edge xy ∈ H such that x and y have at most 7 6 m − 1 common neighbours in H. H0
Starting with G1 , let us apply these operations as often as possible, and let H0 ∈ H be the graph obtained eventually. Since kK m k = m |K m | − m −
and f (m) = − 56 m > −m , x1
K m does not have enough edges to be in H; thus, H contains no graph on m vertices. Hence |H0 | > m, and in particular H0 6= ∅. Let x1 ∈ H0 be a vertex of minimum degree, and put
H1 := H0 [ { x1 } ∪ NH0 (x1 ) ] . We shall prove that the minimum degree of H := H1 is as large as claimed in the lemma. Note first that δ(H1 ) > 76 m .
Indeed, since H0 is minimal with respect to (ii) and (iii), we have d(x1 ) > 7 6 m in H0 (and hence in H1 ), and every vertex y 6= x1 of H1 has more than 76 m − 1 common neighbours with x1 (and hence more than 76 m neighbours in H1 altogether). In order to convert (3) into the desired inequality of the form 2δ(H1 ) > |H1 | + αm , we need an upper bound for |H1 | in terms of m. Since H0 lies in H but is minimal with respect to (i), we have kH0 k < m |H0 | +
1 1 2 6 m |H0 | − 6 m
´ ¡ ¢ − 56 m − m 2 +1
= 76 m |H0 | − 46 m2 − 13 m + 1 6 76 m |H0 | − 46 m2 .
By the choice of x1 and definition of H1 , therefore, |H1 | − 1 = δ(H0 ) 6 2 ε(H0 ) < 73 m − 43 m2 /|H0 |
6 73 m − 13 m
= 2m , so |H1 | 6 2m. Hence, 2δ(H1 ) > 2m + 13 m (3)
> |H1 | + 13 m > |H1 | + 16 k
Proof of Theorem 8.1.1. We prove the assertion for c := 1116. Let G be a graph with d(G) > 1116r2 . By Theorem 1.4.2, G has a subgraph G0 such that
(1.4.2) G0
κ(G0 ) > 279r > 276r + 3r . 2
Pick a set X := { x1 , . . . , x3r } of 3r vertices in G0 , and let G1 := G0 − X. For each i = 1, . . . , 3r choose a set Yi of 5r neighbours of xi in G1 ; let these sets Yi be disjoint for different i. (This is possible since δ(G0 ) > κ(G0 ) > 15r2 + |X|.) As
X G1 , Yi
δ(G1 ) > κ(G1 ) > κ(G0 ) − |X| > 276r2 , we have ε(G1 ) > 138r2 . By Lemma 8.1.3, G1 has a minor H with 2δ(H) >S|H| + 23r2 and is therefore (15r2 , 7r2 )-linked by Lemma 8.1.2; 3r let Z ⊆ i=1 Yi be a set of 7r2 vertices that is linked in G1 . For all i = 1, . . . , 3r let Zi := Z ∩ Yi . Since Z is linked, it suffices to find r indices i with |Zi | > r − 1: then the corresponding xi will be the branch vertices of a T K r in G0 . If r such i cannot be found, then |Zi | 6 r − 2 for all but at most r − 1 indices i. But then |Z| =
3r X
|Zi | 6 (r − 1) 5r + (2r + 1)(r − 2) < 7r2 = |Z| ,
a contradiction.
Z Zi
Although Theorem 8.1.1 already gives a good estimate, it seems very difficult to determine the exact average degree needed to force a T K r subgraph, even for small r. We shall come back to the case of r = 5 in Section 8.3; more results and conjectures are given in the notes. The following almost counter-intuitive result of Mader implies that the existence of a topological K r minor can be forced essentially by large girth. In the next section, we shall prove the analogue of this for ordinary minors. Theorem 8.1.4. (Mader 1997) For every graph H of maximum degree d > 3 there exists an integer k such that every graph G of minimum degree at least d and girth at least k contains H as a topological minor. As discussed already in Chapter 5.2 and the introduction to Chapter 7, no constant average degree, however large, will force an arbitrary graph to contain a given graph H as a subgraph—as long as H contains at least one cycle. By Proposition 1.2.2 and Corollary 1.5.4, on the other hand, any graph G contains all trees on up to ε(G) + 2 vertices. Large average degree therefore does ensure the occurrence of any fixed tree T as a subgraph. What can we say, however, if we would like T to occur as an induced subgraph? Here, a large average degree appears to do as much harm as good, even for graphs of bounded clique number. (Consider, for example, complete bipartite graphs.) It is all the more remarkable, then, that the assumption of a large chromatic number rather than a large average degree seems to make a difference here: according to a conjecture of Gy´arf´ as, any graph of large enough chromatic number contains either a large complete graph or any given tree as an induced subgraph. (Formally: for every integer r and every tree T , there exists an integer k such that every graph G with χ(G) > k and ω(G) < r contains an induced copy of T .) The weaker topological version of this is indeed true: Theorem 8.1.5. (Scott 1997) For every integer r and every tree T there exists an integer k such that every graph with χ(G) > k and ω(G) < r contains an induced copy of some subdivision of T .
8.2 Minors
8.2 Minors According to Theorem 8.1.1, an average degree of cr2 suffices to force the existence of a topological K r minor in a given graph. If we are content with any minor, topological or not, an even smaller average degree will do: in a pioneering paper of 1968, Mader proved that every graph with an average degree of at least cr log r has a K r minor. The following result, the analogue to Theorems 7.1.1 and 8.1.1 for general minors, determines the precise average degree needed as a function of r, up to a constant c: Theorem 8.2.1. (Kostochka 1982; Thomason 1984) There exists a c ∈ R√such that, for every r ∈ N, every graph G of average degree d(G) > c r log r has a K r minor. Up to the value of c, this bound is best possible as a function of r. The easier implication of the theorem, the fact that in general an average √ degree of c r log r is needed to force a K r minor, follows from considering random graphs, to be introduced in Chapter 11. The converse implication, the fact that this average degree suffices, is proved by methods similar to those described in Section 8.1. Rather than proving Theorem 8.2.1, we therefore devote the remainder of this section to another striking result on forcing minors. At first glance, this result is so surprising that it seems almost paradoxical: as long as we do not merely subdivide edges, we can force a K r minor in a graph simply by raising its girth (Corollary 8.2.3)! Theorem 8.2.2. (Thomassen 1983) Given an integer k, every graph G with girth g(G) > 4k − 3 and δ(G) > 3 has a minor H with δ(H) > k. Proof . As δ(G) > 3, every component of G contains a cycle. In particular, the assertion is trivial for k 6 2; so let k > 3. Consider the vertex set V of a component of G, together with a partition { V1 , . . . , Vm } of V into as many connected sets Vi with at least 2k − 2 vertices each as possible. (Such a partition exists, since |V | > g(G) > 2k − 2 and V is connected in G.) We first show that every G [ Vi ] is a tree. To this end, let Ti be a spanning tree of G [ Vi ]. If G [ Vi ] has an edge e ∈/ Ti , then Ti + e contains a cycle C; by assumption, C has length at least 4k − 3. The edge (about) opposite e on C therefore separates the path C − e, and hence also Ti , into two components with at least 2k − 2 vertices each. Together with the sets Vj for j 6= i, these two components form a partition of V into m + 1 sets that contradicts the maximality of m. So each G [ Vi ] is indeed a tree, i.e. G [ Vi ] = Ti . As δ(G) > 3, the degrees in G of the vertices in Vi sum to at least 3 |Vi |, while the edges of Ti account for only 2 |Vi | − 2 in this sum. Hence for each i, G has
(1.5.3) V, Vi m
at least |Vi | + 2 > 2k edges joining Vi to V r Vi . We shall prove that every Vi sends at most two edges to each of the other Vj ; then Vi must send edges to at least k of those Vj , so the Vi are the branch sets of an M H ⊆ G with δ(H) > k. Suppose, without loss of generality, that G has three V1 –V2 edges. Then there are vertices v1 ∈ V1 and v2 ∈ V2 such that G [ V1 ∪ V2 ] contains three independent v1 –v2 paths P1 , P2 , P3 (Fig. 8.2.1). At most one of
P1 P10 v1
P2 v2
Fig. 8.2.1. Three edges between V1 and V2
these paths can be shorter than 12 g(G). We assume that P1 has length ˚1 ; then |P 0 | > 2k − 2. Since at least d 12 g(G)e > 2k − 1 and let P10 := P 1 P2 ∪ P3 is a cycle of length at least 4k − 3, we can further find disjoint paths P20 , P30 ⊆ P2 ∪ P3 with 2k − 2 vertices each. Since G [ V1 ∪ V2 ] is connected, there exists a partition of V1 ∪ V2 into three connected sets V10 , V20 , V30 such that V (Pi0 ) ⊆ Vi0 for i = 1, 2, 3. Replacing the two sets V1 , V2 in our partition of V with the three sets V10 , V20 , V30 , we obtain a partition of V that contradicts the maximality of m. ¤ The following combination of Theorems 8.2.1 and 8.2.2 brings out the paradoxical character of the latter particularly well: Corollary 8.2.3. There exists√a c ∈ R such that, for every r ∈ N, every graph G with girth g(G) > c r log r and δ(G) > 3 has a K r minor. Proof . We prove the corollary for c := 4c0 , where c0 is the constant from Theorem 8.2.1. Let G be √ given as stated. By Theorem 8.2.2, G has a minor H with δ(H) > c0 r log r. By Theorem 8.2.1, H (and hence G) has a K r minor. ¤
8.3 Hadwiger’s conjecture
8.3 Hadwiger’s conjecture √ As we saw in the preceding two sections, an average degree of c r log r suffices to force an arbitrary graph to have a K r minor, and an average degree of cr2 forces it to have a topological K r minor. If we replace ‘average degree’ above with ‘chromatic number’ then, with almost the same constants c, the two assertions remain true: this is because every graph with chromatic number k has a subgraph of average degree at least k − 1 (Corollary 5.2.3). √ Although both functions above, c r log r and cr2 , are best possible (up to the constant c) for the said implications with ‘average degree’, the question arises whether they are still best possible with ‘chromatic number’—or whether some slower-growing function would do in that case. What is lurking behind this problem about growth rates, of course, is a fundamental question about the nature of the invariant χ: can this invariant have some direct structural effect on a graph in terms of forcing concrete substructures, or is its effect no greater than that of the ‘unstructural’ property of having lots of edges somewhere, which it implies trivially? Neither for general nor for topological minors is the answer to this question known. For general minors, however, the following conjecture of Hadwiger suggests a positive answer; the conjecture is considered by many as one of the deepest open problems in graph theory. Conjecture. (Hadwiger 1943) The following implication holds for every integer r > 0 and every graph G: χ(G) > r ⇒ G < K r . Hadwiger’s conjecture is trivial for r 6 2, easy for r = 3 and r = 4 (exercises), and equivalent to the four colour theorem for r = 5 and r = 6. For r > 7, the conjecture is open. Rephrased as G < K χ(G) , it is true for almost all graphs.3 In general, the conjecture for r + 1 implies it for r (exercise). The Hadwiger conjecture for any fixed r is equivalent to the assertion that every graph without a K r minor has an (r − 1)-colouring. In this reformulation, the conjecture raises the question of what the graphs without a K r minor look like: any sufficiently detailed structural description of those graphs should enable us to decide whether or not they can be (r − 1)-coloured. For r = 3, for example, the graphs without a K r minor are precisely the forests (why?), and these are indeed 2-colourable. For r = 4, there 3
See Chapter 11 for the notion of ‘almost all’.
is also a simple structural characterization of the graphs without a K r minor: [ 12.4.2 ]
Proposition 8.3.1. A graph with at least three vertices is edge-maximal without a K 4 minor if and only if it can be constructed recursively from triangles by pasting 4 along K 2 s.
Proof . Recall first that every M K 4 contains a T K 4 , because ∆(K 4 ) = 3 (Proposition 1.7.2); the graphs without a K 4 minor thus coincide with those without a topological K 4 minor. The proof that any graph constructible as described is edge-maximal without a K 4 minor is left as an easy exercise; in order to deduce Hadwiger’s conjecture for r = 4, we only need the converse implication anyhow. We prove this by induction on |G|. Let G be given, edge-maximal without a K 4 minor. If |G| = 3 then G is itself a triangle, so let |G| > 4 for the induction step. Then G is not complete; let S ⊆ V (G) be a separating set with |S| = κ(G), and let C1 , C2 be distinct components of G − S. Since S is a minimal separator, every vertex in S has a neighbour in C1 and another in C2 . If |S| > 3, this implies that G contains three independent paths P1 , P2 , P3 between a vertex v1 ∈ C1 and a vertex v2 ∈ C2 . Since κ(G) = |S| > 3, the graph G − { v1 , v2 } is connected and contains a (shortest) path P between two different Pi . Then P ∪ P1 ∪ P2 ∪ P3 = T K 4 , a contradiction. Hence κ(G) 6 2, and the assertion follows from Lemma 4.4.45 and the induction hypothesis. ¤ One of the interesting consequences of Proposition 8.3.1 is that all the edge-maximal graphs without a K 4 minor have the same number of edges, and are thus all ‘extremal’: Corollary 8.3.2. Every edge-maximal graph G without a K 4 minor has 2 |G| − 3 edges. Proof . Induction on |G|.
Corollary 8.3.3. Hadwiger’s conjecture holds for r = 4. Proof . If G arises from G1 and G2 by pasting along a complete graph, then χ(G) = max { χ(G1 ), χ(G2 ) } (see the proof of Proposition 5.5.2). Hence, Proposition 8.3.1 implies by induction on |G| that all edge-maximal (and hence all) graphs without a K 4 minor can be 3-coloured. ¤ 4 5
This was defined formally in Chapter 5.5.
The proof of this lemma is elementary and can be read independently of the rest of Chapter 4.
It is also possible to prove Corollary 8.3.3 by a simple direct argument (Exercise 13). By the four colour theorem, Hadwiger’s conjecture for r = 5 follows from the following structure theorem for the graphs without a K 5 minor, just as it follows from Proposition 8.3.1 for r = 4. The proof of Theorem 8.3.4 is similar to that of Proposition 8.3.1, but considerably longer. We therefore state the theorem without proof: Theorem 8.3.4. (Wagner 1937) Let G be an edge-maximal graph without a K 5 minor. If |G| > 4 then G can be constructed recursively, by pasting along triangles and K 2 s, from plane triangulations and copies of the graph W (Fig. 8.3.1).
Fig. 8.3.1. Three representations of the Wagner graph W
Using Corollary 4.2.8, one can easily compute which of the graphs constructed as in Theorem 8.3.4 have the most edges. It turns out that these extremal graphs without a K 5 minor have no more edges than those that are extremal with respect to { M K 5 , M K3,3 }, i.e. the maximal planar graphs: Corollary 8.3.5. A graph with n vertices and no K 5 minor has at most 3n − 6 edges. ¤ Since χ(W ) = 3, Theorem 8.3.4 and the four colour theorem imply Hadwiger’s conjecture for r = 5: Corollary 8.3.6. Hadwiger’s conjecture holds for r = 5.
The Hadwiger conjecture for r = 6 is again substantially more difficult than the case r = 5, and again it relies on the four colour theorem. The proof shows (without using the four colour theorem) that any minimal-order counterexample arises from a planar graph by adding one vertex—so by the four colour theorem it is not a counterexample after all. Theorem 8.3.7. (Robertson, Seymour & Thomas 1993) Hadwiger’s conjecture holds for r = 6.
By Corollary 8.3.5, any graph with n vertices and more than 3n − 6 edges contains an M K 5 . In fact, it even contains a T K 5 . This inconspicuous improvement is another deep result that had been conjectured for over 30 years: Theorem 8.3.8. (Mader 1998) Every graph with n vertices and more than 3n − 6 edges contains K 5 as a topological minor. No structure theorem for the graphs without a T K 5 , analogous to Proposition 8.3.1 and Theorem 8.3.4, is known. However, Mader has characterized those with the greatest possible number of edges: Theorem 8.3.9. (Mader 1997) A graph is extremal without a T K 5 if and only if it can be constructed recursively from maximal planar graphs by pasting along triangles.
Prove, from first principles, the theorem of Wagner (1964) that every graph of chromatic number at least 2r contains K r as a minor. (Hint. Apply induction on r.)
Prove, from first principles, the result of Mader (1967) that every graph of average degree at least 2r−2 contains K r as a minor. (Hint. Induction on r.)
3.− Derive Wagner’s theorem (Ex. 1) from Mader’s theorem (Ex. 2). 4.+ Given an integer r > 0, find an integer k such that every grid with k additional edges has a K r minor, provided that all the ends of the new edges have distance at least k in the grid both from each other and from the grid boundary. (Grids are defined in Chapter 12.3.) 5.+ Show that any function h as in Theorem 3.6.1 satisfies the inequality h(r) > 18 r2 for all even r, and hence that Theorem 8.1.1 is best possible up to the value of the constant c. 6.
Prove the statement of Lemma 8.1.3 for k < 6.
Explain how exactly the term of 16 k in the statement of Lemma 8.1.3 is used in the proof of Theorem 8.1.1. Could it be replaced by k/1000, or by zero?
Explain how exactly the number 76 in the proof of Lemma 8.1.3 was arrived at. Could it be replaced by 32 ?
9.+ For which trees T is there a function f : N → N tending to infinity, such that every graph G with χ(G) < f (d(G)) contains an induced copy of T ? (In other words: can we force the chromatic number up by raising the average degree, as long as T does not occur as an induced subgraph? Or, as in Gy´ arf´ as’s conjecture: will a large average degree force an induced copy of T if the chromatic number is kept small?) 10.− Derive the four colour theorem from Hadwiger’s conjecture for r = 5. 11.− Show that Hadwiger’s conjecture for r + 1 implies the conjecture for r. 12.− Using the results from this chapter, prove the following weakening of Hadwiger’s conjecture: given any ² > 0, every graph of chromatic number at least r1+² has a K r minor, provided that r is large enough. 13.+ Prove Hadwiger’s conjecture for r = 4 from first principles. 14.+ Prove Hadwiger’s conjecture for line graphs. 15.
(i)− Show that Hadwiger’s conjecture is equivalent to the statement that G < K χ(G) for all graphs G. (ii) Show that any minimum-order counterexample G to Hadwiger’s conjecture (as rephrased above) satisfies K χ(G)−1 6⊆ G and has a connected complement.
Show that any graph constructed as in Theorem 8.3.1 is edge-maximal without a K 4 minor.
Prove the implication δ(G) > 3 ⇒ G ⊇ T K 4 . (Hint. Theorem 8.3.1.)
A multigraph is called series-parallel if it can be constructed recursively from a K 2 by the operations of subdividing and of doubling edges. Show that a 2-connected multigraph is series-parallel if and only if it has no (topological) K 4 minor.
Prove Corollary 8.3.5.
Characterize the graphs with n vertices and more than 3n − 6 edges that contain no T K3,3 . In particular, determine ex(n, T K3,3 ). (Hint. By a theorem of Wagner, every edge-maximal graph without a K3,3 minor can be constructed recursively from maximal planar graphs and copies of K 5 by pasting along K 2 s.)
By a theorem of Pelik´ an, every graph of minimum degree at least 4 5 contains a subdivision of K− , a K 5 minus an edge. Using this theorem, prove Thomassen’s 1974 result that every graph with n > 5 vertices and at least 4n − 10 edges contains a T K 5 . (Hint. Show by induction on |G| that if kGk > 4n − 10 then for every vertex x ∈ G there is a T K 5 ⊆ G in which x is not a branch vertex.)
Notes The investigation of graphs not containing a given graph as a minor, or topological minor, has a long history. It probably started with Wagner’s 1935 PhD thesis, in which he sought to ‘detopologize’ the four colour problem by classifying the graphs without a K 5 minor. His hope was to be able to show abstractly that all those graphs were 4-colourable; since the graphs without a K 5 minor include the planar graphs, this would amount to a proof of the four colour conjecture involving no topology whatsoever. The result of Wagner’s efforts, Theorem 8.3.4, falls tantalizingly short of this goal: although it succeeds in classifying the graphs without a K 5 minor in structural terms, planarity re-emerges as one of the criteria used in the classification. From this point of view, it is instructive to compare Wagner’s K 5 theorem with similar classification theorems, such as his analogue for K 4 (Proposition 8.3.1), where the graphs are decomposed into parts from a finite set of irreducible graphs. See R. Diestel, Graph Decompositions, Oxford University Press 1990, for more such classification theorems. Despite its failure to resolve the four colour problem, Wagner’s K 5 structure theorem had consequences for the development of graph theory like few others. To mention just two: it prompted Hadwiger to make his famous conjecture; and it inspired the notion of a tree-decomposition, which is fundamental to the work of Robertson and Seymour on minors (see Chapter 12). Wagner himself responded to Hadwiger’s conjecture with a proof that, in order to force a K r minor, it does suffice to raise the chromatic number of a graph to some value depending only on r (Exercise 1). This theorem then, along with its analogue for topological minors proved independently by Dirac and by Jung, prompted the question of which average degree suffices to force the desired minor. The deepest contribution in this field of research was no doubt made by Mader, in a series of papers from the late sixties. Our proof of Lemma 8.1.3 is presented intentionally in a step-by-step fashion, to bring out some of Mader’s ideas. Mader’s own proof—not to mention that of Thomason’s best possible version of the lemma, as used in the original proof of Theorem 8.1.1— is wrapped up so elegantly that it becomes hard to see the ideas behind it. Except for this lemma, our proof of Theorem 8.1.1 follows B. Bollob´ as & A.G. Thomason, Proof of a conjecture of Mader, Erd˝ os and Hajnal on topological complete subgraphs, Europ. J. Combinatorics 19 (1998), 883–887. The constant c from the theorem was shown by J. Koml´ os & E. Szemer´edi, Topological cliques in graphs II, Combinatorics, Probability and Computing 5 (1996), 79–90, to be no greater than about 12 , which is not far from the lower bound of 18 given in Exercise 5. Theorem 8.1.4 is from W. Mader, Topological subgraphs in graphs of large girth, Combinatorica 18 (1998), 405–412. For H = K r , the theorem says that every graph G with δ(G) > r − 1 and g(G) large contains a T K r . For r = 5, Mader conjectured that g(G) > 5 should be enough, and that the requirement of δ(G) > 4 could be weakened further: he conjectured that any graph of girth at least 5, large enough order n, and 2n − 4 or more edges has a topological K 5 minor. (To see that this implies the minimum degree version of the conjecture even for small order, consider enough disjoint copies of the given graph.) For
general H, Mader improved Theorem 8.1.4 by weakening the requirement of δ(G) > d to d(G) > d − 1 + ² for arbitrary ² > 0 (where now the girth k required to force a T H in such graphs G depends on ² as well as on H); see W. Mader, Subdivisions of a graph of maximal degree n + 1 in graphs of average degree n + ² and large girth, manuscript 1999. Theorem 8.1.5 is due to A.D. Scott, Induced trees in graphs of large chromatic number, J. Graph Theory 24 (1997), 297–311. Theorem 8.2.1 was proved independently by Kostochka (1982; English translation: A.V. Kostochka, Lower bounds of the Hadwiger number of graphs by their average degree, Combinatorica 4 (1984), 307–316) and by A.G. Thomason, An extremal function for contractions of graphs, Math. Proc. Camb. Phil. Soc. 95 (1984), 261– 265. Theorem 8.2.2 was taken from Thomassen’s survey, Paths, Circuits and Subdivisions, in (L.W. Beineke & R.J. Wilson, eds.) Selected Topics in Graph Theory 3, Academic Press 1988. The proof of Hadwiger’s conjecture for r = 4, hinted at in Exercise 13, is given by Hadwiger himself in the 1943 paper containing his conjecture. For a while, there was a counterpart to Hadwiger’s conjecture for topological minors, the conjecture of Haj´ os that χ(G) > r even implies G ⊇ T K r . A counterexample to this conjecture was found in 1979 by Catlin; a little later, Erd˝ os and Fajtlowicz even proved that Haj´ os’s conjecture is false for almost all graphs (see Chapter 11). Mader’s Theorem 8.3.8 that 3n − 5 edges force a topological K 5 minor had been conjectured by Dirac in 1964. Its proof comprises two papers: W. Mader, 3n − 5 edges do force a subdivision of K5 , Combinatorica 18 (1998), 569–595; and W. Mader, An extremal problem for subdivisions of K5− , J. Graph Theory 30 (1999), 261–276. His proof of Theorem 8.3.9 has not been published yet. Dirac’s conjecture has been extended by Seymour, who conjectures that every 5-connected non-planar graph should contain a T K 5 (unpublished).
Ramsey Theory for Graphs
In this chapter we set out from a type of problem which, on the face of it, appears to be similar to the theme of the last two chapters: what kind of substructures are necessarily present in every large enough graph? The regularity lemma of Chapter 7.2 provides one possible answer to this question, saying as it does that every (large) graph G contains large random-like bipartite subgraphs. If we are looking for more definite substructures, however, such as subgraphs isomorphic to some given graphs H, then these H will have to be sufficiently complementary in kind to cater for the variety allowed for G. For example: given an integer r, does every large enough graph contain either a K r or an induced K r ? Does every large enough connected graph contain either a K r or else a large induced path or star? Despite its similarity to extremal problems in that we are looking for local implications of global assumptions, the above type of question leads to a kind of mathematics with a distinctive flavour of its own. Indeed, the theorems and proofs in this chapter have more in common with similar results in algebra or geometry, say, than with most other areas of graph theory. The study of their underlying methods, therefore, is generally regarded as a combinatorial subject in its own right: the discipline of Ramsey theory. In line with the subject of this book, we shall focus on results that are naturally expressed in terms of graphs. Even from the viewpoint of general Ramsey theory, however, this is not as much of a limitation as it might seem: graphs are a natural setting for Ramsey problems, and the material in this chapter brings out a sufficient variety of ideas and methods to convey some of the fascination of the theory as a whole.
9. Ramsey Theory
9.1 Ramsey’s original theorems In its simplest version, Ramsey’s theorem says that, given an integer r > 0, every large enough graph G contains either K r or K r as an induced subgraph. At first glance, this may seem surprising: after all, we need about (r − 2)/(r − 1) of all possible edges to force a K r subgraph in G (Cor. 7.1.3), but neither G nor G can be expected to have more than half the total number of edges. However, as the Tur´ an graphs illustrate well, squeezing many edges into G without creating a K r imposes additional structure on G, which may help us find an induced K r . So how could we go about proving Ramsey’s theorem? Let us try to build a K r or K r in G inductively, starting with an arbitrary vertex v1 ∈ V1 := V (G). If |G| is large, there will be a large set V2 ⊆ V1 r { v1 } of vertices that are either all adjacent to v1 or all non-adjacent to v1 . Accordingly, we may think of v1 as the first vertex of a K r or K r whose other vertices all lie in V2 . Let us then choose another vertex v2 ∈ V2 for our K r or K r . Since V2 is large, it will have a subset V3 , still fairly large, of vertices that are all ‘of the same type’ with respect to v2 as well: either all adjacent or all non-adjacent to it. We then continue our search for vertices inside V3 , and so on (Fig. 9.1.1).
Fig. 9.1.1. Choosing the sequence v1 , v2 , . . .
How long can we go on in this way? This depends on the size of our initial set V1 : each set Vi has at least half the size of its predecessor Vi−1 , so we shall be able to complete s construction steps if G has order about 2s . As the following proof shows, the choice of s = 2r − 3 vertices vi suffices in order to find among them the vertices of a K r or K r .
Theorem 9.1.1. (Ramsey 1930) For every r ∈ N there exists an n ∈ N such that every graph of order at least n contains either K r or K r as an induced subgraph. Proof . The assertion is trivial for r 6 1; we assume that r > 2. Let n := 22r−3 , and let G be a graph of order at least n. We shall define a sequence V1 , . . . , V2r−2 of sets and choose vertices vi ∈ Vi with the following properties: (i) |Vi | = 22r−2−i (i = 1, . . . , 2r − 2);
9.1 Ramsey’s original theorems
(ii) Vi ⊆ Vi−1 r { vi−1 } (i = 2, . . . , 2r − 2); (iii) vi−1 is adjacent either to all vertices in Vi or to no vertex in Vi (i = 2, . . . , 2r − 2). Let V1 ⊆ V (G) be any set of 22r−3 vertices, and pick v1 ∈ V1 arbitrarily. Then (i) holds for i = 1, while (ii) and (iii) hold trivially. Suppose now that Vi−1 and vi−1 ∈ Vi−1 have been chosen so as to satisfy (i)–(iii) for i − 1, where 1 < i 6 2r − 2. Since |Vi−1 r { vi−1 }| = 22r−1−i − 1 is odd, Vi−1 has a subset Vi satisfying (i)–(iii); we pick vi ∈ Vi arbitrarily. Among the 2r − 3 vertices v1 , . . . , v2r−3 , there are r − 1 vertices that show the same behaviour when viewed as vi−1 in (iii), being adjacent either to all the vertices in Vi or to none. Accordingly, these r − 1 vertices and v2r−2 induce either a K r or a K r in G, because vi , . . . , v2r−2 ∈ Vi for all i. ¤ The least integer n associated with r as in Theorem 9.1.1 is the Ramsey number R(r) of r; our proof shows that R(r) 6 22r−3 . In Chapter 11 we shall use a simple probabilistic argument to show that R(r) is bounded below by 2r/2 (Theorem 11.1.3). It is customary in Ramsey theory to think of partitions as colourings: a colouring of (the elements of) a set X with c colours, or c-colouring for short, is simply a partition of X into c classes (indexed by the ‘colours’). In particular, these colourings need not satisfy any non-adjacency requirements as in Chapter 5. Given a c-colouring of [X]k , the set of all k-subsets of X, we call a set Y ⊆ X monochromatic if all the elements of [Y ]k have the same colour,1 i.e. belong to the same of the c partition classes of [X]k . Similarly, if G = (V, E) is a graph and and all the edges of H ⊆ G have the same colour in some colouring of E, we call H a monochromatic subgraph of G, speak of a red (green, etc.) H in G, and so on. In the above terminology, Ramsey’s theorem can be expressed as follows: for every r there exists an n such that, given any n-set X, every 2-colouring of [X]2 yields a monochromatic r-set Y ⊆ X. Interestingly, this assertion remains true for c-colourings of [X]k with arbitrary c and k—with almost exactly the same proof! To avoid repetition, we shall use this opportunity to demonstrate a common alternative proof technique: we first prove an infinite version of the general Ramsey theorem (which is easier, because we need not worry about numbers), and then deduce the finite version by a so-called compactness argument. 1 Note that Y is called monochromatic, but it is the elements of [Y ]k , not of Y , that are (equally) coloured.
Ramsey number R(r)
c-colouring
[X]k monochromatic
192 [ 12.1.1 ]
Theorem 9.1.2. Let k, c be positive integers, and X an infinite set. If [X]k is coloured with c colours, then X has an infinite monochromatic subset. Proof . We prove the theorem by induction on k, with c fixed. For k = 1 the assertion holds, so let k > 1 and assume the assertion for smaller values of k. Let [X]k be coloured with c colours. We shall construct an infinite sequence X0 , X1 , . . . of infinite subsets of X and choose elements xi ∈ Xi with the following properties (for all i): (i) Xi+1 ⊆ Xi r { xi }; (ii) all k-sets { xi } ∪ Z with Z which we associate with xi .
[Xi+1 ]k−1 have the same colour,
We start with X0 := X and pick x0 ∈ X0 arbitrarily. By assumption, X0 is infinite. Having chosen an infinite set Xi and xi ∈ Xi for some i, we c-colour [Xi r { xi }]k−1 by giving each set Z the colour of { xi } ∪ Z from our c-colouring of [X]k . By the induction hypothesis, Xi r { xi } has an infinite monochromatic subset, which we choose as Xi+1 . Clearly, this choice satisfies (i) and (ii). Finally, we pick xi+1 ∈ Xi+1 arbitrarily. Since c is finite, one of the c colours is associated with infinitely many xi . These xi form an infinite monochromatic subset of X. ¤ To deduce the finite version of Theorem 9.1.2, we make use of a standard graph-theoretical tool in combinatorics: Lemma 9.1.3. (K¨ onig’s Infinity Lemma) Let V0 , V1 , . . . be an infinite sequence of disjoint non-empty finite sets, and let G be a graph on their union. Assume that every vertex v in a set Vn with n > 1 has a neighbour f (v) in Vn−1 . Then G contains an infinite path v0 v1 . . . with vn ∈ Vn for all n. f ( f (v))
f (v)
Fig. 9.1.2. K¨ onig’s infinity lemma
Proof . Let P be the set of all paths of the form v f (v) f (f (v)) . . . ending in V0 . Since V0 is finite but P is infinite, infinitely many of the paths in P end at the same vertex v0 ∈ V0 . Of these paths, infinitely many also agree on their penultimate vertex v1 ∈ V1 , because V1 is finite. Of those
paths, infinitely many agree even on their vertex v2 in V2 —and so on. Although the set of paths considered decreases from step to step, it is still infinite after any finite number of steps, so vn gets defined for every n ∈ N. By definition, each vertex vn is adjacent to vn−1 on one of those paths, so v0 v1 . . . is indeed an infinite path. ¤ Theorem 9.1.4. For all k, c, r > 1 there exists an n > k such that every n-set X has a monochromatic r-subset with respect to any c-colouring of [X]k . Proof . As is customary in set theory, we denote by n ∈ N (also) the set { 0, . . . , n − 1 }. Suppose the assertion fails for some k, c, r. Then for every n > k there exist an n-set, without loss of generality the set n, and a c-colouring [n]k → c such that n contains no monochromatic r-set. Let us call such colourings bad ; we are thus assuming that for every n > k there exists a bad colouring of [n]k . Our aim is to combine these into a bad colouring of [N]k , which will contradict Theorem 9.1.2. For every n > k let Vn 6= ∅ be the set of bad colourings of [n]k . For n > k, the restriction f (g) of any g ∈ Vn to [n − 1]k is still bad, and hence lies in Vn−1 . By the infinity lemma, there is an infinite sequence gk , gk+1 , . . . of bad colourings gn ∈ Vn such that f (gn ) = gn−1 for all n > k. For every m > k, all colourings gn with n > m agree on [m]k , so for each Y ∈ [N]k the value of gn (Y ) coincides for all n > max Y . Let us define g(Y ) as this common value gn (Y ). Then g is a bad colouring of [N]k : every r-set S ⊆ N is contained in some sufficiently large n, so S cannot be monochromatic since g coincides on [n]k with the bad colouring gn . ¤ The least integer n associated with k, c, r as in Theorem 9.1.4 is the Ramsey number for these parameters; we denote it by R(k, c, r).
k, c, r
bad colouring
Ramsey number R(k, c, r)
9.2 Ramsey numbers Ramsey’s theorem may be rephrased as follows: if H = K r and G is a graph with sufficiently many vertices, then either G itself or its complement G contains a copy of H as a subgraph. Clearly, the same is true for any graph H, simply because H ⊆ K h for h := |H|. However, if we ask for the least n such that every graph G with n vertices has the above property—this is the Ramsey number R(H) of H—then the above question makes sense: if H has only few edges, it should embed more easily in G or G, and we would expect R(H) to be smaller than the Ramsey number R(h) = R(K h ). A little more generally, let R(H1 , H2 ) denote the least n ∈ N such that H1 ⊆ G or H2 ⊆ G for every graph G of order n. For most graphs
Ramsey number R(H)
R(H1 , H2 )
H1 , H2 , only very rough estimates are known for R(H1 , H2 ). Interestingly, lower bounds given by random graphs (as in Theorem 11.1.3) are often sharper than even the best bounds provided by explicit constructions. The following proposition describes one of the few cases where exact Ramsey numbers are known for a relatively large class of graphs: Proposition 9.2.1. Let s, t be positive integers, and let T be a tree of order t. Then R(T, K s ) = (s − 1)(t − 1) + 1. (5.2.3) (1.5.4)
Proof . The disjoint union of s − 1 graphs K t−1 contains no copy of T , while the complement of this graph, the complete (s − 1)-partite graph s−1 , does not contain K s . This proves R(T, K s ) > (s − 1)(t − 1) + 1. Kt−1 Conversely, let G be any graph of order n = (s − 1)(t − 1) + 1 whose complement contains no K s . Then s > 1, and in any vertex colouring of G (in the sense of Chapter 5) at most s − 1 vertices can have the same colour. Hence, χ(G) > dn/(s − 1)e = t. By Corollary 5.2.3, G has a subgraph H with δ(H) > t − 1, which by Corollary 1.5.4 contains a copy of T . ¤ As the main result of this section, we shall now prove one of those rare general theorems providing a relatively good upper bound for the Ramsey numbers of a large class of graphs, a class defined in terms of a standard graph invariant. The theorem deals with the Ramsey numbers of sparse graphs: it says that the Ramsey number of graphs H with bounded maximum degree grows only linearly in |H|—an enormous improvement on the exponential bound from the proof of Theorem 9.1.1. Theorem 9.2.2. (Chv´ atal, R¨ odl, Szemer´edi & Trotter 1983) For every positive integer ∆ there is a constant c such that R(H) 6 c |H|
for all graphs H with ∆(H) 6 ∆. Proof . The basic idea of the proof is as follows. We wish to show that H ⊆ G or H ⊆ G if |G| is large enough (though not too large). Consider an ²-regular partition of G, as provided by the regularity lemma. If enough of the ²-regular pairs in this partition have positive density, we may hope to find a copy of H in G. If most pairs have zero or low density, we try to find H in G. Let R, R0 and R00 be the ‘regularity graphs’2 of G whose edges correspond to the pairs of density > 0; > 1/2; < 1/2; respectively. Then R is the edge-disjoint union of R0 and R00 . Now to obtain H ⊆ G or H ⊆ G, it suffices by Lemma 7.3.2 to ensure that H is contained in a suitable ‘inflated regularity graph’ Rs0 2 Later, we shall define R00 a little differently, so that it complies with our formal definition of a regularity graph.
9.2 Ramsey numbers
or Rs00 . Since χ(H) 6 ∆(H) + 1 6 ∆ + 1, this will be the case if s > α(H) and we can find a K ∆+1 in R0 or in R00 . But that is easy to ensure: we just need that K r ⊆ R, where r is the Ramsey number of ∆ + 1, which will follow from Tur´ an’s theorem because R is dense. For the formal proof let now ∆ > 1 be given. On input d := 1/2 and ∆, Lemma 7.3.2 returns an ²0 ; since the lemma’s assertion about ²0 becomes weaker if ²0 is made smaller, we may assume that ²0 < 1. Let m := R(∆ + 1) be the Ramsey number of ∆ + 1. Let ² 6 ²0 be positive but small enough that, for k = m (and hence for all k > m), 2² <
1 1 − . m−1 k
So let H with ∆(H) 6 ∆ be given, and let s := |H|. Let G be an arbitrary graph of order n > c |H|; we show that H ⊆ G or H ⊆ G. By Lemma 7.2.1, G has an ²-regular partition { V0 , V1 , . . . , Vk } with exceptional set V0 and |V1 | = . . . = |Vk | =: `, where m 6 k 6 M . Then n − ²n 1−² 1−² s n − |V0 | > =n > cs = . k M M M ²0
²0 m, ²
Finally, let M be the integer returned by the regularity lemma (7.2.1) on input ² and m. All the quantities defined so far depend only on ∆. We shall prove the theorem with M . c := ²0 (1 − ²)
`=
∆, d
s G, n k `
Let R be the regularity graph with parameters ², `, 0 corresponding to this partition. By definition, R has k vertices and µ ¶ k kRk > − ²k 2 2 ´ ³ 1 = 12 k 2 1 − − 2² k ³ 1 1´ 1 1 2 + > 2k 1 − − k m−1 k (1) m−2 = 12 k 2 m−1
> tm−1 (k) edges. By Theorem 7.1.1, therefore, R has a subgraph K = K m . We now colour the edges of R with two colours: red if the edge corresponds to a pair (Vi , Vj ) of density at least 1/2, and green otherwise. Let R0 be the spanning subgraph of R formed by the red edges, and R00
Ramseyminimal
the spanning subgraph of R formed by the green edges and those whose corresponding pair has density exactly 1/2. Then R0 is a regularity graph of G with parameters ², ` and 1/2. And R00 is a regularity graph of G, with the same parameters: as one easily checks, every pair (Vi , Vj ) that is ²-regular for G is also ²-regular for G. By definition of m, our graph K contains a red or a green K r , for r := χ(H) 6 ∆ + 1. Correspondingly, H ⊆ Rs0 or H ⊆ Rs00 . Since ² 6 ²0 and ` > s/²0 by (2), both R0 and R00 satisfy the requirements of Lemma ¤ 7.3.2, so H ⊆ G or H ⊆ G as desired. So far in this section, we have been asking what is the least order of a graph G such that every 2-colouring of its edges yields a monochromatic copy of some given graph H. Rather than focusing on the order of G, we might alternatively try to minimize G itself, with respect to the subgraph relation. Given a graph H, let us call a graph G Ramsey-minimal for H if G is minimal with the property that every 2-colouring of its edges yields a monochromatic copy of H. What do such Ramsey-minimal graphs look like? Are they unique? The following result, which we include for its pretty proof, answers the second question for some H: Proposition 9.2.3. If T is a tree but not a star, then infinitely many graphs are Ramsey-minimal for T .
(1.5.4) (5.2.3) (11.2.2)
Proof . Let |T | =: r. We show that for every n ∈ N there is a graph of order at least n that is Ramsey-minimal for T . Let us borrow the assertion of Theorem 11.2.2 from Chapter 11: by that theorem, there exists a graph G with chromatic number χ(G) > r2 and girth g(G) > n. If we colour the edges of G red and green, then the red and the green subgraph cannot both have an r-(vertex-)colouring in the sense of Chapter 5: otherwise we could colour the vertices of G with the pairs of colours from those colourings and obtain a contradiction to χ(G) > r2 . So let G0 ⊆ G be monochromatic with χ(G0 ) > r. By Corollary 5.2.3, G0 has a subgraph of minimum degree at least r, which contains a copy of T by Corollary 1.5.4. Let G∗ ⊆ G be Ramsey-minimal for T . Clearly, G∗ is not a forest: the edges of any forest can be 2-coloured (partitioned) so that no monochromatic subforest contains a path of length 3, let alone a copy of T . (Here we use that T is not a star, and hence contains a P 3 .) So G∗ contains a cycle, which has length g(G) > n since G∗ ⊆ G. In particular, |G∗ | > n as desired. ¤
9.3 Induced Ramsey theorems
9.3 Induced Ramsey theorems Ramsey’s theorem can be rephrased as follows. For every graph H = K r there exists a graph G such that every 2-colouring of the edges of G yields a monochromatic H ⊆ G; as it turns out, this is witnessed by any large enough complete graph as G. Let us now change the problem slightly and ask for a graph G in which every 2-edge-colouring yields a monochromatic induced H ⊆ G, where H is now an arbitrary given graph. This slight modification changes the character of the problem dramatically. What is needed now is no longer a simple proof that G is ‘big enough’ (as for Theorem 9.1.1), but a careful construction: the construction of a graph that, however we bipartition its edges, contains an induced copy of H with all edges in one partition class. We shall call such a graph a Ramsey graph for H. The fact that such a Ramsey graph exists for every choice of H is one of the fundamental results of graph Ramsey theory. It was proved around 1973, independently by Deuber, by Erd˝ os, Hajnal & P´ osa, and by R¨odl.
Ramsey graph
Theorem 9.3.1. Every graph has a Ramsey graph. In other words, for every graph H there exists a graph G that, for every partition { E1 , E2 } of E(G), has an induced subgraph H with E(H) ⊆ E1 or E(H) ⊆ E2 . We give two proofs. Each of these is highly individual, yet each offers a glimpse of true Ramsey theory: the graphs involved are used as hardly more than bricks in the construction, but the edifice is impressive. First proof. In our construction of the desired Ramsey graph we shall repeatedly replace vertices of a graph G = (V, E) already constructed by copies of another graph H. For a vertex set U ⊆ V let G [ U → H ] denote the graph obtained from G by replacing the vertices u ∈ U with copies H(u) of H and joining each H(u) completely to all H(u0 ) with uu0 ∈ E and to all vertices v ∈ V r U with uv ∈ E (Fig. 9.3.1). Formally,
G U
Fig. 9.3.1. A graph G [ U → H ] with H = K 3
G[U →H ] H(u)
G [ U → H ] is the graph on (U × V (H)) ∪ ((V r U ) × { ∅ }) in which two vertices (v, w) and (v 0 , w0 ) are adjacent if and only if either vv 0 ∈ E, or else v = v 0 ∈ U and ww0 ∈ E(H).3 We prove the following formal strengthening of Theorem 9.3.1: For any two graphs H1 , H2 there exists a graph G = G(H1 , H2 ) such that every edge colouring of G with the colours 1 and 2 yields either an induced H1 ⊆ G with all its edges coloured 1 or an induced H2 ⊆ G with all its edges coloured 2.
G(H1 , H2 )
xi Hi0 , Hi00
This formal strengthening makes it possible to apply induction on |H1 | + |H2 |, as follows. If either H1 or H2 has no edges (in particular, if |H1 | + |H2 | 6 1), then (∗) holds with G = K n for large enough n. For the induction step, we now assume that both H1 and H2 have at least one edge, and that (∗) holds for all pairs (H10 , H20 ) with smaller |H10 | + |H20 |. For each i = 1, 2, pick a vertex xi ∈ Hi that is incident with an edge. Let Hi0 := Hi − xi , and let Hi00 be the subgraph of Hi0 induced by the neighbours of xi . We shall construct a sequence G0 , . . . , Gn of disjoint graphs; Gn will be the desired Ramsey graph G(H1 , H2 ). Along with the graphs Gi , we shall define subsets V i ⊆ V (Gi ) and a map f : V 1 ∪ . . . ∪ V n → V 0 ∪ . . . ∪ V n−1 such that f (V i ) = V i−1
fi origin
for all i > 1. Writing f i := f ◦ . . . ◦ f for the i-fold composition of f whenever it is defined, and f 0 for the identity map on V 0 = V (G0 ), we thus have f i (v) ∈ V 0 for all v ∈ V i . We call f i (v) the origin of v. The subgraphs Gi [ V i ] will reflect the structure of G0 as follows: Vertices in V i with different origins are adjacent in Gi if and only if their origins are adjacent in G0 .
Assertion (2) will not be used formally in the proof below. However, it can help us to visualize the graphs Gi : every Gi (more precisely, every Gi [ V i ]—there will also be some vertices x ∈ Gi − V i ) is essentially an inflated copy of G0 in which every vertexw ∈ G0 has been replaced by 3
The replacement of V r U by (V r U ) × { ∅ } is just a formal device to ensure that all vertices of G [ U → H ] have the same form (v, w), and that G [ U → H ] is formally disjoint from G.
the set of all vertices in V i with origin w, and the map f links vertices with the same origin across the various Gi . By the induction hypothesis, there are Ramsey graphs G1 := G(H1 , H20 )
and G2 := G(H10 , H2 ) .
G1 , G2
0 Let G0 be a copy of G1 , and set V 0 := V (G0 ). Let W00 , . . . , Wn−1 be the 0 0 0 subsets of V spanning an H2 in G . Thus, n is defined as the number of induced copies of H20 in G0 , and we shall construct a graph Gi for 0 every set Wi−1 , i = 1, . . . , n. Since H1 has an edge, n > 1: otherwise 0 G could not be a G(H1 , H20 ). For i = 0, . . . , n − 1, let Wi00 be the image of V (H200 ) under some isomorphism H20 → G0 [ Wi0 ]. Assume now that G0 , . . . , Gi−1 and V 0 , . . . , V i−1 have been defined for some i > 1, and that f has been defined on V 1 ∪ . . . ∪ V i−1 and satisfies (1) for all j 6 i. We expand Gi−1 to Gi in two steps. For the first step, consider the set U i−1 of all the vertices v ∈ V i−1 whose origin 00 f i−1 (v) lies in Wi−1 . (For i = 1, this gives U 0 = W000 .) Expand Gi−1 i−1 ˜ to a graph G by replacing every vertex u ∈ U i−1 with a copy G2 (u) of G2 , i.e. let ˜ i−1 := Gi−1 [ U i−1 → G2 ] G
(see Figures 9.3.2 and 9.3.3). Set f (u0 ) := u for all u G1
G0 , V 0 Wi0 n Wi00
U i−1 G2 (u) ˜ i−1 G
U i−1 and
x(F )
H10 (u)
H100 (u) v0
G2 (u) u0
G0 W00
Fig. 9.3.2. The construction of G1
u0 ∈ G2 (u), and f (v 0 ) := v for all v 0 = (v, ∅) with v ∈ V i−1 r U i−1 . (Recall that (v, ∅) is simply the unexpanded copy of a vertex v ∈ Gi−1 ˜ i−1 .) Let V i be the set of those vertices v 0 or u0 of G ˜ i−1 for which in G f has thus been defined, i.e. the vertices that either correspond directly to a vertex v in V i−1 or else belong to an expansion G2 (u) of such a vertex u. Then (1) holds for i. Also, if we assume (2) inductively for
H10 (u) x(F ) H100 (u) Gi
˜ i−1 ). The graph G ˜ i−1 is already i − 1, then (2) holds again for i (in G i the ‘essential part’ of G : the part that looks like an inflated copy of G0 . ˜ i−1 to the desired graph Gi by In the second step we now extend G i adding some further vertices x ∈/ V . Let F denote the set of all families F of the form ¡ ¢ F = H10 (u) | u ∈ U i−1 , where each H10 (u) is an induced subgraph of G2 (u) isomorphic to H10 . (Less formally: F is the collection of ways to select from each G2 (u) exactly one induced copy of H10 .) For each F ∈ F, add a vertex x(F ) ˜ i−1 and join it to all the vertices of H 00 (u) for every u ∈ U i−1 , to G 1 where H100 (u) is the image of H100 under some isomorphism H10 → H10 (u) (Fig. 9.3.2). Denote the resulting graph by Gi . This completes the inductive definition of the graphs G0 , . . . , Gn . Let us now show that G := Gn satisfies (∗). To this end, we prove the following assertion (∗∗) about Gi for i = 0, . . . , n: For every edge colouring with the colours 1 and 2, Gi contains either an induced H1 coloured 1, or an induced H2 coloured 2, or an induced subgraph H coloured 2 such that V (H) ⊆ V i and the restriction of f i to V (H) is an isomorphism between H and G0 [ Wk0 ] for some k ∈ { i, . . . , n − 1 }.
(∗∗)
Note that the third of the above cases cannot arise for i = n, so (∗∗) for n is equivalent to (∗) with G := Gn . For i = 0, (∗∗) follows from the choice of G0 as a copy of G1 = G(H1 , H20 ) and the definition of the sets Wk0 . Now let 1 6 i 6 n, and assume (∗∗) for smaller values of i. Let an edge colouring of Gi be given. For each u ∈ U i−1 there is a copy of G2 in Gi : Gi ⊇ G2 (u) ' G(H10 , H2 ) .
yu ˆ i−1 U
ˆ i−1 G
If G2 (u) contains an induced H2 coloured 2 for some u ∈ U i−1 , we are done. If not, then every G2 (u) has an induced subgraph H10 (u) ' H10 coloured 1. Let F be the family of these graphs H10 (u), one for each u ∈ U i−1 , and let x := x(F ). If, for some u ∈ U i−1 , all the x–H100 (u) edges in Gi are also coloured 1, we have an induced copy of H1 in Gi and are again done. We may therefore assume that each H100 (u) has a vertex yu for which the edge xyu is coloured 2. Let ˆ i−1 := { yu | u U
U i−1 } ⊆ V i .
Then f defines an isomorphism from h © ˆ i−1 ∪ (v, ∅) | v ˆ i−1 := Gi U G
V (Gi−1 ) r U i−1
ªi
to Gi−1 : just map every yu to u and every (v, ∅) to v. Our edge colouring of Gi thus induces an edge colouring of Gi−1 . If this colouring yields an induced H1 ⊆ Gi−1 coloured 1 or an induced H2 ⊆ Gi−1 coloured 2, we ˆ i−1 ⊆ Gi and are again home. have these also in G By (∗∗) for i − 1 we may therefore assume that Gi−1 has an induced subgraph H 0 coloured 2, with V (H 0 ) ⊆ V i−1 , and such that the restriction of f i−1 to V (H 0 ) is an isomorphism from H 0 to G0 [ Wk0 ] ' H20 ˆ 0 be the corresponding induced for some k ∈ { i − 1, . . . , n − 1 }. Let H i−1 i ˆ ˆ 0) ⊆ V i, subgraph of G ⊆ G (also coloured 2); then V (H ˆ 0 )) = f i−1 (V (H 0 )) = W 0 , f i (V (H k ˆ 0 → G0 [ W 0 ] is an isomorphism. and f i : H k x Gi
H ˆ0
G2 y ˆ0 H
G2 (u) yu
yu0
U i−1
V i−1
G0 0 Wi−1
00 Wi−1
Fig. 9.3.3. A monochromatic copy of H2 in Gi
ˆ 0 ; we therefore If k > i, this completes the proof of (∗∗) with H := H assume that k < i, and hence k = i − 1 (Fig. 9.3.3). By definition ˆ i−1 , the inverse image of W 00 under the isomorphism of U i−1 and G i−1 i ˆ0 0 0 ˆ i−1 . Since x is joined to precisely ] is a subset of U f : H → G [ Wi−1 ˆ i−1 , and all these edges xyu have colour 2, ˆ 0 that lie in U those vertices of H 0 ˆ and x together induce in Gi a copy of H2 coloured 2, and the graph H the proof of (∗∗) is complete. ¤
H0 ˆ0 H
bipartite
embedding P →P0
Let us return once more to the reformulation of Ramsey’s theorem considered at the beginning of this section: for every graph H there exists a graph G such that every 2-colouring of the edges of G yields a monochromatic H ⊆ G. The graph G for which this follows at once from Ramsey’s theorem is a sufficiently large complete graph. If we ask, however, that G shall not contain any complete subgraphs larger than those in H, i.e. that ω(G) = ω(H), the problem again becomes difficult—even if we do not require H to be induced in G. Our second proof of Theorem 9.3.1 solves both problems at once: given H, we shall construct a Ramsey graph for H with the same clique number as H. For this proof, i.e. for the remainder of this section, let us view bipartite graphs P as triples (V1 , V2 , E), where V1 and V2 are the two vertex classes and E ⊆ V1 × V2 is the set of edges. The reason for this more explicit notation is that we want embeddings between bipartite graphs to respect their bipartitions: given another bipartite graph P 0 = (V10 , V20 , E 0 ), an injective map ϕ: V1 ∪ V2 → V10 ∪ V20 will be called an embedding of P in P 0 if ϕ(Vi ) ⊆ Vi0 for i = 1, 2 and ϕ(v1 )ϕ(v2 ) is an edge of P 0 if and only if v1 v2 is an edge of P . (Note that such embeddings are ‘induced’.) Instead of ϕ: V1 ∪ V2 → V10 ∪ V20 we may simply write ϕ: P → P 0 . We need two lemmas. Lemma 9.3.2. Every bipartite graph can be embedded in a bipartite graph of the form (X, [X]k , E) with E = { xY | x ∈ Y }. Proof . Let P be any bipartite graph, with vertex classes { a1 , . . . , an } and { b1 , . . . , bm }, say. Let X be a set with 2n + m elements, say X = { x1 , . . . , xn , y1 , . . . , yn , z1 , . . . , zm } ; we shall define an embedding ϕ: P → (X, [X]n+1 , E). Let us start by setting ϕ(ai ) := xi for all i = 1, . . . , n. Which (n + 1)-sets Y ⊆ X are suitable candidates for the choice of ϕ(bi ) for a given vertex bi ? Clearly those adjacent exactly to the images of the neighbours of bi , i.e. those satisfying Y ∩ { x1 , . . . , xn } = ϕ(NP (bi )) .
Since d(bi ) 6 n, the requirement of (1) leaves at least one of the n + 1 elements of Y unspecified. In addition to ϕ(NP (bi )), we may therefore include in each Y = ϕ(bi ) the vertex zi as an ‘index’; this ensures that ϕ(bi ) 6= ϕ(bj ) for i 6= j, even when bi and bj have the same neighbours in P . To specify the sets Y = ϕ(bi ) completely, we finally fill them up with ‘dummy’ elements yj until |Y | = n + 1. ¤
Our second lemma already covers the bipartite case of the theorem: it says that every bipartite graph has a Ramsey graph—even a bipartite one. Lemma 9.3.3. For every bipartite graph P there exists a bipartite graph P 0 such that for every 2-colouring of the edges of P 0 there is an embedding ϕ: P → P 0 for which all the edges of ϕ(P ) have the same colour. Proof . We may assume by Lemma 9.3.2 that P has the form (X, [X]k , E) with E = { xY | x ∈ Y }. We show the assertion for the graph P 0 := 0 (X 0 , [X 0 ]k , E 0 ), where k 0 := 2k − 1, X 0 is any set of cardinality
(9.1.4) P, X, k, E P 0 , X 0 , k0
³ ´ ¡ 0¢ |X 0 | = R k 0 , 2 kk , k |X| + k − 1 , (this is the Ramsey number defined after Theorem 9.1.4), and E 0 := { x0 Y 0 | x0
Y 0}.
Let us then colour the edges of P 0 with two colours α and β. Of the 0 |Y | = 2k − 1 edges incident with a vertex Y 0 ∈ [X 0 ]k , at least k must have the same colour. For each Y 0 we may therefore choose a fixed k-set Z 0 ⊆ Y 0 such that all the edges x0 Y 0 with x0 ∈ Z 0 have the same colour; we shall call this colour associated with Y 0 . ¡ 0¢ The sets Z 0 can lie within their supersets Y 0 in kk ways, as follows. 0 Let X 0 be linearly ordered. Then for every Y 0 ∈ [X 0 ]k there is a unique order-preserving bijection σY 0 : Y 0 → { 1, . . . , k0 }, which maps Z 0 to one ¡k 0 ¢ of k possible images. ¡ 0¢ 0 We now colour [X 0 ]k with the 2 kk elements of the set 0
E0 α, β
Z0 associated
σY 0
[{ 1, . . . , k0 }]k × { α, β } 0
as colours, giving each Y 0 ∈ [X 0 ]k as its colour the pair (σY 0 (Z 0 ), γ), where γ is the colour α or β associated with Y¡ 00.¢ Since |X 0 | was chosen as the Ramsey number with parameters k 0 , 2 kk and k |X| + k − 1, we know that X 0 has a monochromatic subset W of cardinality k |X| + k − 1. All Z 0 with Y 0 ⊆ W thus lie within their Y 0 in the same way, i.e. there 0 exists an S ∈ [{ 1, . . . , k0 }]k such that σY 0 (Z 0 ) = S for all Y 0 ∈ [W ]k , 0 ∈ k0 [W ] are associated with the same colour, say with α. and all Y We now construct the desired embedding ϕ of P in P 0 . We first define ϕ on X =: { x1 , . . . , xn }, choosing images ϕ(xi ) =: wi ∈ W so that wi < wj in our ordering of X 0 whenever i < j. Moreover, we choose the wi so that exactly k − 1 elements of W are smaller than w1 , exactly k − 1 lie between wi and wi+1 for i = 1, . . . , n − 1, and exactly k − 1 are bigger than wn . Since |W | = kn + k − 1, this can indeed be done (Fig. 9.3.4).
α ϕ|X xi , w i , n
k−1 w1 Y0 w2
k−1
Z˜0
Y˜ 0
k−1 wnn
Fig. 9.3.4. The graph of Lemma 9.3.3 ϕ|[X]k
We now define ϕ on [X]k . Given Y ∈ [X]k , we wish to choose 0 ϕ(Y ) =: Y 0 ∈ [X 0 ]k so that the neighbours of Y 0 among the vertices in ϕ(X) are precisely the images of the neighbours of Y in P , i.e. the vertices ϕ(x) with x ∈ Y , and so that all these edges at Y 0 are coloured α. To find such a set Y 0 , we first fix its subset Z 0 as { ϕ(x) | x ∈ Y } (these are k vertices of type wi ) and then extend Z 0 by k 0 − k further 0 vertices u ∈ W r ϕ(X) to a set Y 0 ∈ [W ]k , in such a way that Z 0 lies correctly within Y 0 , i.e. so that σY 0 (Z 0 ) = S. This can be done, because k − 1 = k 0 − k other vertices of W lie between any two wi . Then Y 0 ∩ ϕ(X) = Z 0 = { ϕ(x) | x
Y },
so Y 0 has the correct neighbours in ϕ(X), and all the edges between Y 0 and these neighbours are coloured α (because those neighbours lie in Z 0 and Y 0 is associated with α). Finally, ϕ is injective on [X]k : the images Y 0 of different vertices Y are distinct, because their intersections with ¤ ϕ(X) differ. Hence, our map ϕ is indeed an embedding of P in P 0 .
Second proof of Theorem 9.3.1. Let H be given as in the theorem, and let n := R(r) be the Ramsey number of r := |H|. Then, for every 2-colouring of its edges, the graph K = K n contains a monochromatic copy of H—although not necessarily induced. We start by constructing a graph G0 , as follows. Imagine the vertices ¡n¢ and replace every vertex by a row ¡ ¢of K to be arranged in a column, each of the of nr vertices. Then r columns arising can be associated ¡ ¢ with one of the nr ways of embedding V (H) in V (K); let us furnish this column with G0 thus aris¢ ¡n¢the edges of such a copy of H. The¡graph n ing consists of r disjoint copies of H and (n − r) r isolated vertices (Fig. 9.3.5). ¡n¢ r {z
r, n
n−r Fig. 9.3.5. The graph G0
In order to define G0 formally, we assume that V (K) = { 1, . . . , n } and choose copies H1 , . . . , H(n) of H in K with pairwise distinct vertex r sets. (Thus, on each r-set in V (K) we have one fixed copy Hj of H.) We then define © ¡ ¢ª V (G0 ) := (i, j) | i = 1, . . . , n; j = 1, . . . , nr 0
E(G ) :=
n ([ r) ©
(i, j)(i0 , j) | ii0
ª E(Hj ) .
j=1
The idea of the proof now is as follows. Our aim is to reduce the general case of the theorem to the bipartite case dealt with in Lemma 9.3.3. Applying the lemma iteratively to all the pairs of rows of G0 , we construct a very large graph G such that for every edge colouring of G there is an induced copy of G0 in G that is monochromatic on all the bipartite subgraphs induced by its pairs of rows, i.e. in which edges between the same two rows always have the same colour. The projection of this G0 ⊆ G to { 1, . . . , n } (by contracting its rows) then defines an edge colouring of K. By the choice of |K|, one of the Hj ⊆ K will be monochromatic. But this Hj occurs with the same colouring in the jth column of our G0 , where it is an induced subgraph of G0 , and hence of G.
Formally, we shall define a sequence G0 , . . . , Gm of n-partite graphs G , with n-partition { V1k , . . . , Vnk } say, and then let G := Gm . The graph G0 has been defined above; let V10 , . . . , Vn0 be its rows: © ¡ ¢ª Vi0 := (i, j) | j = 1, . . . , nr . k
Vi0 ek , m i1 , i2 P P0 W1 , W 2 ϕp , q
Now let e1 , . . . , em be an enumeration of the edges of K. For k = 0, . . . , m − 1, construct Gk+1 from Gk as follows. If ek+1 = i1 i2 , say, let P = (Vik1 , Vik2 , E) be the bipartite subgraph of Gk induced by its i1 th and i2 th row. By Lemma 9.3.3, P has a bipartite Ramsey graph P 0 = (W1 , W2 , E 0 ). We wish to define Gk+1 ⊇ P 0 in such a way that every (monochromatic) embedding P → P 0 can be extended to an embedding Gk → Gk+1 . Let { ϕ1 , . . . , ϕq } be the set of all embeddings of P in P 0 , and let V (Gk+1 ) := V1k+1 ∪ . . . ∪ Vnk+1 , where Vik+1
W1 W2 := Sq
for i = i1 for i = i2 k ∈ p=1 (Vi × { p }) for i / { i1 , i2 }.
(Thus for i 6= i1 , i2 , we take as Vik+1 just q disjoint copies of Vik .) We now define the edge set of Gk+1 so that the obvious extensions of ϕp to all of V (Gk ) become embeddings of Gk in Gk+1 : for p = 1, . . . , q, let ψp : V (Gk ) → V (Gk+1 ) be defined by ½ ϕp (v) for v ∈ P ψp (v) := (v, p) for v ∈/ P and let q [ { ψp (v)ψp (v 0 ) | vv 0 ∈ E(Gk ) } . E(Gk+1 ) := p=1
Now for every 2-colouring of its edges, Gk+1 contains an induced copy ψp (Gk ) of Gk whose edges in P , i.e. those between its i1 th and i2 th row, have the same colour: just choose p so that ϕp (P ) is the monochromatic induced copy of P in P 0 that exists by Lemma 9.3.3. We claim that G := Gm satisfies the assertion of the theorem. So let a 2-colouring of the edges of G be given. By the construction of Gm from Gm−1 , we can find in Gm an induced copy of Gm−1 such that for em = ii0 all edges between the ith and the i0 th row have the same colour. In the same way, we find inside this copy of Gm−1 an induced copy of Gm−2 whose edges between the ith and the i0 th row have the same colour also for ii0 = em−1 . Continuing in this way, we finally arrive at an induced copy of G0 in G such that, for each pair (i, i0 ), all the edges between Vi0 and Vi00 have the same colour. As shown earlier, this ¤ G0 contains a monochromatic induced copy Hj of H.
9.4. Ramsey properties and connectivity
9.4 Ramsey properties and connectivity According to Ramsey’s theorem, every large enough graph G has a very dense or a very sparse induced subgraph of given order, a K r or K r . If we assume that G is connected, we can say a little more: Proposition 9.4.1. For every r ∈ N there is an n ∈ N such that every connected graph of order at least n contains K r , K1,r or P r as an induced subgraph. Proof . Let d + 1 be the Ramsey number of r, let n > 1 + rd r , and let G be a graph of order at least n. If G has a vertex v of degree at least d + 1 then, by Theorem 9.1.1 and the choice of d, either N (v) induces a K r in G or { v } ∪ N (v) induces a K1,r . On the other hand, if ∆(G) 6 d, then by Proposition 1.3.3 G has radius > r, and hence contains two vertices at a distance > r. Any shortest path in G between these two vertices ¤ contains a P r . The collection of ‘typical’ induced subgraphs in Proposition 9.4.1 is smallest possible in the following sense. If G is any set of connected graphs with the same property, i.e. such that, given r ∈ N, every large enough connected graph G contains an induced copy of a graph of order > r from G, then G contains arbitrarily large complete graphs, stars and paths. (Note that if we take a complete graph, a star or a path as G, and then all its subgraphs are again of that type.) But Proposition 9.4.1 tells us that we need no more than these. In principle, we could look for a set like G for any assumed connectivity k. We could try to find a ‘minimal’ set (in the above sense) of typical k-connected graphs, one such that every large k-connected graph has a large subgraph in this set. Unfortunately, G seems to grow very quickly with k: already for k = 2 it becomes thoroughly messy if (as for k = 1) we insist that those subgraphs be induced. By relaxing our specification of containment from ‘induced subgraph’ to ‘topological minor’ and on to ‘minor’, however, we can give some neat characterizations up to k = 4. Proposition 9.4.2. For every r ∈ N there is an n ∈ N such that every 2-connected graph of order at least n contains C r or K2,r as a topological minor. Proof . Let d be the n associated with r in Proposition 9.4.1, and let G be a 2-connected graph with more than 1 + rd r vertices. By Proposition 1.3.3, either G has a vertex of degree > d or diam(G) > rad(G) > r. In the latter case let a, b ∈ G be two vertices at distance > r. By Menger’s theorem (3.3.5), G contains two independent a–b paths. These form a cycle of length > r.
Assume now that G has a vertex v of degree > d. Since G is 2connected, G − v is connected and thus has a spanning tree; let T be a minimal tree in G − v that contains all the neighbours of v. Then every leaf of T is a neighbour of v. By the choice of d, either T has a vertex of degree > r or T contains a path of length > r, without loss of generality linking two leaves. Together with v, such a path forms a cycle of length > r. A vertex u of degree > r in T can be joined to v by r ¤ independent paths through T , to form a T K2,r . Theorem 9.4.3. (Oporowski, Oxley & Thomas 1993) For every r ∈ N there is an n ∈ N such that every 3-connected graph of order at least n contains a wheel of order r or a K3,r as a minor. Let us call a graph of the form C n ∗ K 2 (n > 4) a double wheel , the 1-skeleton of a triangulation of the cylinder as in Fig. 9.4.1 a crown, and the 1-skeleton of a triangulation of the M¨obius strip a M¨obius crown.
Fig. 9.4.1. A crown and a M¨ obius crown
Theorem 9.4.4. (Oporowski, Oxley & Thomas 1993) For every r ∈ N there is an n ∈ N such that every 4-connected graph with at least n vertices has a minor of order > r that is a double wheel, a crown, a M¨obius crown, or a K4,s . Note that the minors occurring in Theorems 9.4.3 and 9.4.4 are themselves 3- and 4-connected, respectively, and are not minors of one another. Thus in each case, the collection of minors is minimal in the sense discussed earlier.
Exercises 1.− Determine the Ramsey number R(3). 2.
Deduce the case k = 2 (but c arbitrary) of Theorem 9.1.4 directly from Theorem 9.1.1.
3.+ Construct a graph on R that has neither a complete nor an edgeless induced subgraph on |R| = 2ℵ0 vertices. (So Ramsey’s theorem does not extend to uncountable sets.) 4.+ Use Ramsey’s theorem to show that for any k, ` ∈ N there is an n ∈ N such that every sequence of n distinct integers contains an increasing subsequence of length k + 1 or a decreasing subsequence of length ` + 1. Find an example showing that n > k`. Then prove the theorem of Erd˝ os and Szekeres that n = k` + 1 will do.
Sketch a proof of the following theorem of Erd˝ os and Szekeres: for every k ∈ N there is an n ∈ N such that among any n points in the plane, no three of them collinear, there are k points spanning a convex k-gon, i.e. such that none of them lies in the convex hull of the others.
Prove the following result of Schur: for every k ∈ N there is an n ∈ N such that, for every partition of { 1, . . . , n } into k sets, at least one of the subsets contains numbers x, y, z such that x + y = z.
Let (X, 6) be a totally ordered set, and let G = (V, E) be the graph on V := [X]2 with E := {(x, y)(x0 , y 0 ) | x < y = x0 < y 0 }. (i) Show that G contains no triangle. (ii) Show that χ(G) will get arbitrarily large if |X| is chosen large enough.
A family of sets is called a ∆-system if every two of the sets have the same intersection. Show that every infinite family of sets of the same finite cardinality contains an infinite ∆-system.
Prove the following weakening of Scott’s Theorem 8.1.5: for every r ∈ N and every tree T there exists a k ∈ N such that every graph G with χ(G) > k and ω(G) < r contains a subdivision of T in which no two branch vertices are adjacent in G (unless they are adjacent in T ).
Use the infinity lemma to show that, given k ∈ N, a countably infinite graph is k-colourable (in the sense of Chapter 5) if all its finite subgraphs are k-colourable.
Let m, n ∈ N, and assume that m − 1 divides n − 1. Show that every tree T of order m satisfies R(T, K1,n ) = m + n − 1.
Prove that 2c < R(2, c, 3) 6 3c! for every c
(Hint. Induction on c.) 13.− Derive the statement (∗) in the first proof of Theorem 9.3.1 from the theorem itself, i.e. show that (∗) is only formally stronger than the theorem. 14.
Show that the Ramsey graph G for H constructed in the second proof of Theorem 9.3.1 does indeed satisfy ω(G) = ω(H).
Show that, given any two graphs H1 and H2 , there exists a graph G = G(H1 , H2 ) such that, for every vertex-colouring of G with colours 1 and 2, there is either an induced copy of H1 coloured 1 or an induced copy of H2 coloured 2 in G. (Hint. Apply induction as in the first proof of Theorem 9.3.1.)
Show that every infinite connected graph contains an infinite path or an infinite star.
17.− The K r from Ramsey’s theorem, last sighted in Proposition 9.4.1, conspicuously fails to make an appearance from Proposition 9.4.2 onwards. Can it be excused?
Notes Due to increased interaction with research on random and pseudo-random4 structures (the latter being provided, for example, by the regularity lemma), the Ramsey theory of graphs has recently seen a period of major activity and advance. Theorem 9.2.2 is an early example of this development. For the more classical approach, the introductory text by R.L. Graham, B.L. Rothschild & J.H. Spencer, Ramsey Theory (2nd edn.), Wiley 1990, makes stimulating reading. This book includes a chapter on graph Ramsey theory, but is not confined to it. A more recent general survey is given by J. Neˇsetˇril in the Handbook of Combinatorics (R.L. Graham, M. Gr¨ otschel & L. Lov´ asz, eds.), North-Holland 1995. The Ramsey theory of infinite sets forms a substantial part of combinatorial set theory, and is treated in depth in P. Erd˝ os, A. Hajnal, A. M´ at´e & R. Rado, Combinatorial Set Theory, NorthHolland 1984. An attractive collection of highlights from various branches of Ramsey theory, including applications in algebra, geometry and point-set topology, is offered in B. Bollob´ as, Graph Theory, Springer GTM 63, 1979. K¨ onig’s infinity lemma, or K¨ onig’s lemma for short, is contained in the first-ever book on the subject of graph theory: D. K¨ onig, Theorie der endlichen und unendlichen Graphen, Akademische Verlagsgesellschaft, Leipzig 1936. The compactness technique for deducing finite results from infinite (or vice versa), hinted at in Section 9.1, is less mysterious than it sounds. As long as ‘infinite’ means ‘countably infinite’, it is precisely the art of applying the infinity lemma (as in the proof of Theorem 9.1.4), no more no less. For larger infinite sets, the same argument becomes equivalent to the well-known theorem of Tychonov that arbitrary products of compact spaces are compact— which has earned the compactness argument its name. Details can be found in Ch. 6, Thm. 10 of Bollob´ as, and in Graham, Rothschild & Spencer, Ch. 1, Thm. 4. Another frequently used version of the general compactness argument is Rado’s selection lemma; see A. Hajnal’s chapter on infinite combinatorics in the Handbook cited above. Theorem 9.2.2 is due to V. Chv´ atal, V. R¨ odl, E. Szemer´edi & W.T. Trotter, The Ramsey number of a graph with bounded maximum degree, J. Combin. Theory B 34 (1983), 239–243. Our proof follows the sketch in J. Koml´ os & M. Simonovits, Szemer´edi’s Regularity Lemma and its applications in graph theory, in (D. Mikl´ os, V.T. S´ os & T. Sz˝ onyi, eds.) Paul Erd˝ os is 80, Vol. 2, Proc. Colloq. Math. Soc. J´ anos Bolyai (1996). The theorem marks a breakthrough towards a conjecture of Burr and Erd˝ os (1975), which asserts that the Ramsey numbers of graphs with bounded average degree in every subgraph are linear: for every d ∈ N, the conjecture says, there exists a constant c such that R(H) 6 c |H| for all graphs H with d(H 0 ) 6 d for all H 0 ⊆ H. This conjecture has been verified also for the class of planar graphs (Chen & Schelp 1993) and, more generally, for the class of graphs not containing K r (for any fixed r) as a topological minor (R¨ odl & Thomas 1996). See Neˇsetˇril’s Handbook chapter for references. 4
Concrete graphs whose structure resembles the structure expected of a random graph are called pseudo-random. For example, the bipartite graphs spanned by an ²-regular pair of vertex sets in a graph are pseudo-random.
Our first proof of Theorem 9.3.1 is based on W. Deuber, A generalization of Ramsey’s theorem, in (A. Hajnal, R. Rado & V.T. S´ os, eds.) Infinite and finite sets, North-Holland 1975. The same volume contains the alternative proof of this theorem by Erd˝ os, Hajnal and P´ osa. R¨ odl proved the same result in his MSc thesis at the Charles University, Prague, in 1973. Our second proof of Theorem 9.3.1, which preserves the clique number of H for G, is due to J. Neˇsetˇril & V. R¨ odl, A short proof of the existence of restricted Ramsey graphs by means of a partite construction, Combinatorica 1 (1981), 199–202. The two theorems in Section 9.4 are due to B. Oporowski, J. Oxley & R. Thomas, Typical subgraphs of 3- and 4-connected graphs, J. Combin. Theory B 57 (1993), 239–257.
Hamilton Cycles
In Chapter 1.8 we briefly discussed the problem of when a graph contains an Euler tour, a closed walk traversing every edge exactly once. The simple Theorem 1.8.1 solved that problem quite satisfactorily. Let us now ask the analogous question for vertices: when does a graph G contain a closed walk that contains every vertex of G exactly once? If |G| > 3, then any such walk is a cycle: a Hamilton cycle of G. If G has a Hamilton cycle, it is called hamiltonian. Similarly, a path in G containing every vertex of G is a Hamilton path. To determine whether or not a given graph has a Hamilton cycle is much harder than deciding whether it is Eulerian, and no good characterization1 is known of the graphs that do. We shall begin this chapter by presenting the standard sufficient conditions for the existence of a Hamilton cycle (Sections 10.1 and 10.2). The rest of the chapter is then devoted to the beautiful theorem of Fleischner that the ‘square’ of every 2-connected graph has a Hamilton cycle. This is one of the main results ˇ ıha) in the field of Hamilton cycles. The simple proof we present (due to R´ is still a little longer than other proofs in this book, but not difficult.
10.1 Simple sufficient conditions What kind of condition might be sufficient for the existence of a Hamilton cycle in a graph G? Purely global assumptions, like high edge density, will not be enough: we cannot do without the local property that every vertex has at least two neighbours. But neither is any large (but constant) minimum degree sufficient: it is easy to find graphs without a Hamilton cycle whose minimum degree exceeds any given constant bound. 1 The notion of a ‘good characterization’ can be made precise; see the introduction to Chapter 12.5 and the notes for Chapter 12.
Hamilton cycle Hamilton path
10. Hamilton Cycles
The following classic result derives its significance from this background: Theorem 10.1.1. (Dirac 1952) Every graph with n > 3 vertices and minimum degree at least n/2 has a Hamilton cycle. Proof . Let G = (V, E) be a graph with |G| = n > 3 and δ(G) > n/2. Then G is connected: otherwise, the degree of any vertex in the smallest component C of G would be less than |C| 6 n/2. Let P = x0 . . . xk be a longest path in G. By the maximality of P , all the neighbours of x0 and all the neighbours of xk lie on P . Hence at least n/2 of the vertices x0 , . . . , xk−1 are adjacent to xk , and at least n/2 of these same k < n vertices xi are such that x0 xi+1 ∈ E. By the pigeon hole principle, there is a vertex xi that has both properties, so we have x0 xi+1 ∈ E and xi xk ∈ E for some i < k (Fig. 10.1.1).
xi+1 xi
Fig. 10.1.1. Finding a Hamilton cycle in the proof Theorem 10.1.1
We claim that the cycle C := x0 xi+1 P xk xi P x0 is a Hamilton cycle of G. Indeed, since G is connected, C would otherwise have a neighbour in G − C, which could be combined with a spanning path of C into a path longer than P . ¤ Theorem 10.1.1 is best possible in that we cannot replace the bound of n/2 with bn/2c: if n is odd and G is the union of two copies of K dn/2e meeting in one vertex, then δ(G) = bn/2c but κ(G) = 1, so G cannot have a Hamilton cycle. In other words, the high level of the bound of δ > n/2 is needed to ensure, if nothing else, that G is 2-connected: a condition just as trivially necessary for hamiltonicity as a minimum degree of at least 2. It would seem, therefore, that prescribing some high (constant) value for κ rather than for δ stands a better chance of implying hamiltonicity. However, this is not so: although k-connected graphs contain long cycles in terms of k (Ex. 14, Ch. 3), the graphs Kn,k show that their circumference need not grow with n. There is another invariant with a similar property: a low independence number α(G) ensures that G has long cycles (Ex. 13, Ch. 5), though not necessarily a Hamilton cycle. Put together, however, the two assumptions of high connectivity and low independence number surprisingly complement each other to produce a sufficient condition for hamiltonicity:
10.1 Simple sufficient conditions
Proposition 10.1.2. Every graph G with |G| > 3 and κ(G) > α(G) has a Hamilton cycle. Proof . Put κ(G) =: k, and let C be a longest cycle in G. Enumerate the vertices of C cyclically, say as V (C) = { vi | i ∈ Zn } with vi vi+1 ∈ E(C) for all i ∈ Zn . If C is not a Hamilton cycle, pick a vertex v ∈ G − C and a v–C fan F = { Pi | i ∈ I } in G, where I ⊆ Zn and each Pi ends in vi . Let F be chosen with maximum cardinality; then vvj ∈/ E(G) for any j ∈/ I, and |F| > min { k, |C| } (1) by Menger’s theorem (3.3.3). For every i ∈ I, we have i + 1 ∈/ I: otherwise, (C ∪ Pi ∪ Pi+1 ) − vi vi+1 would be a cycle longer than C (Fig. 10.1.2, left). Thus |F| < |C|, and hence |I| = |F| > k by (1). Furthermore, vi+1 vj+1 ∈/ E(G) for all i, j ∈ I, as otherwise (C ∪ Pi ∪ Pj ) + vi+1 vj+1 − vi vi+1 − vj vj+1 would be a cycle longer than C (Fig. 10.1.2, right). Hence { vi+1 | i ∈ I } ∪ { v } is a set of k + 1 or more independent vertices in G, contradicting α(G) 6 k. ¤ v F
vi+1
Pi+1 vj+1
vj vi +1
C Fig. 10.1.2. Two cycles longer than C
It may come as a surprise to learn that hamiltonicity for planar graphs is related to the four colour problem. As we noted in Chapter 6.6, the four colour theorem is equivalent to the non-existence of a planar snark, i.e. to the assertion that every bridgeless planar cubic graph has a 4-flow. It is easily checked that ‘bridgeless’ can be replaced with ‘3connected’ in this assertion, and that every hamiltonian graph has a 4-flow (Ex. 12, Ch. 6). For a proof of the four colour theorem, therefore, it would suffice to show that every 3-connected planar cubic graph has a Hamilton cycle! Unfortunately, this is not the case: the first counterexample was found by Tutte in 1946. Ten years later, Tutte proved the following deep theorem as a best possible weakening: Theorem 10.1.3. (Tutte 1956) Every 4-connected planar graph has a Hamilton cycle.
(3.3.3) k
10.2 Hamilton cycles and degree sequences
degree sequence hamiltonian sequence pointwise greater
Historically, Dirac’s theorem formed the point of departure for the discovery of a series of weaker and weaker degree conditions, all sufficient for hamiltonicity. The development culminated in a single theorem that encompasses all the earlier results: the theorem we shall prove in this section. If G is a graph with n vertices and degrees d1 6 . . . 6 dn , then the n-tuple (d1 , . . . , dn ) is called the degree sequence of G. Note that this sequence is unique, even though G has several vertex enumerations giving rise to its degree sequence. Let us call an arbitrary integer sequence (a1 , . . . , an ) hamiltonian if every graph with n vertices and a degree sequence pointwise greater than (a1 , . . . , an ) is hamiltonian. (A sequence (d1 , . . . , dn ) is pointwise greater than (a1 , . . . , an ) if di > ai for all i.) The following theorem characterizes all hamiltonian sequences: Theorem 10.2.1. (Chv´atal 1972) An integer sequence (a1 , . . . , an ) such that 0 6 a1 6 . . . 6 an < n and n > 3 is hamiltonian if and only if the following holds for every i < n/2: ai 6 i ⇒ an−i > n − i .
(a1 , . . . , an )
(d1 , . . . , dn )
Proof . Let (a1 , . . . , an ) be an arbitrary integer sequence such that 0 6 a1 6 . . . 6 an < n and n > 3. We first assume that this sequence satisfies the condition of the theorem and prove that it is hamiltonian. Suppose not; then there exists a graph G = (V, E) with a degree sequence (d1 , . . . , dn ) such that di > ai
G = (V, E) v1 , . . . , v n
for all i
but G has no Hamilton cycle. Let G be chosen with the maximum number of edges, and let (v1 , . . . , vn ) be an enumeration of V with d(vi ) = di for all i. By (1), our assumptions for (a1 , . . . , an ) transfer to (d1 , . . . , dn ), i.e., di 6 i ⇒ dn−i > n − i
x1 , . . . , xn
for all i < n/2.
Let x, y be distinct and non-adjacent vertices in G, with d(x) 6 d(y) and d(x) + d(y) as large as possible. One easily checks that the degree sequence of G + xy is pointwise greater than (d1 , . . . , dn ), and hence than (a1 , . . . , an ). Hence, by the maximality of G, the new edge xy lies on a Hamilton cycle H of G + xy. Then H − xy is a Hamilton path x1 , . . . , xn in G, with x1 = x and xn = y say. As in the proof of Dirac’s theorem, we now consider the index sets I := { i | xxi+1
E}
and J := { j | xj y
E }.
Then I ∪ J ⊆ { 1, . . . , n − 1 }, and I ∩ J = ∅ because G has no Hamilton cycle. Hence d(x) + d(y) = |I| + |J| < n , (3) so h := d(x) < n/2 by the choice of x. Since xi y ∈/ E for all i ∈ I, all these xi were candidates for the choice of x (together with y). Our choice of { x, y } with d(x) + d(y) maximum thus implies that d(xi ) 6 d(x) for all i ∈ I. Hence G has at least |I| = h vertices of degree at most h, so dh 6 h. By (2), this implies that dn−h > n − h, i.e. the h + 1 vertices vn−h , . . . , vn all have degree at least n − h. Since d(x) = h, one of these vertices, z say, is not adjacent to x. Since d(x) + d(z) > h + (n − h) = n ,
this contradicts the choice of x and y by (3). Let us now show that, conversely, for every sequence (a1 , . . . , an ) of the theorem with ah 6 h
and an−h 6 n − h − 1
for some h < n/2, there exists a graph that has a pointwise greater degree sequence than (a1 , . . . , an ) but no Hamilton cycle. Clearly it suffices, given h, to show this for the greatest such sequence (a1 , . . . , an ), the sequence (h, . . . , h , n − h − 1, . . . , n − h − 1 , n − 1, . . . , n − 1) . | {z } | {z } | {z } h times
n−2h times
h times
vh ...
K n−h vn−h+1
Kh,h vh+1 Fig. 10.2.1. Any cycle containing v1 , . . . , vh misses vh+1
As Figure 10.2.1 shows, there is indeed a graph with degree sequence (4) but no Hamilton cycle: the graph with vertices v1 , . . . , vn and edge set { vi vj | i, j > h } ∪ { vi vj | i 6 h; j > n − h } ,
i.e. the union of a K n−h on the vertices vh+1 , . . . , vn and a Kh,h with ¤ partition sets { v1 , . . . , vh } and { vn−h+1 , . . . , vn }. By applying Theorem 10.2.1 to G ∗ K 1 , one can easily prove the following adaptation of the theorem to Hamilton paths. Let an integer sequence be called path-hamiltonian if every graph with a pointwise greater degree sequence has a Hamilton path. Corollary 10.2.2. An integer sequence (a1 , . . . , an ) such that n > 2 and 0 6 a1 6 . . . 6 an < n is path-hamiltonian if and only if every i 6 n/2 ¤ is such that ai < i ⇒ an+1−i > n − i.
10.3 Hamilton cycles in the square of a graph Gd
Given a graph G and a positive integer d, we denote by Gd the graph on V (G) in which two vertices are adjacent if and only if they have distance at most d in G. Clearly, G = G1 ⊆ G2 ⊆ . . . Our goal in this section is to prove the following fundamental result: Theorem 10.3.1. (Fleischner 1974) If G is a 2-connected graph, then G2 has a Hamilton cycle.
We begin with three simple lemmas. Let us say that an edge e ∈ G2 bridges a vertex v ∈ G if its ends are neighbours of v in G. Lemma 10.3.2. Let P = v0 . . . vk be a path (k > 1), and let G be the graph obtained from P by adding two vertices u, w, together with the edges uv1 and wvk (Fig. 10.3.1). (i) P 2 contains a path Q from v0 to v1 with V (Q) = V (P ) and vk−1 vk ∈ E(Q), such that each of the vertices v1 , . . . , vk−1 is bridged by an edge of Q. (ii) G2 contains disjoint paths Q from v0 to vk and Q0 from u to w, such that V (Q) ∪ V (Q0 ) = V (G) and each of the vertices v1 , . . . , vk is bridged by an edge of Q or Q0 . w
u P v0
Fig. 10.3.1. The graph G in Lemma 10.3.2
10.3 Hamilton cycles in the square of a graph
Proof . (i) If k is even, let Q := v0 v2 . . . vk−2 vk vk−1 vk−3 . . . v3 v1 . If k is odd, let Q := v0 v2 . . . vk−1 vk vk−2 . . . v3 v1 . (ii) If k is even, let Q := v0 v2 . . . vk−2 vk ; if k is odd, let Q := v0 v1 v3 . . . vk−2 vk . In both cases, let Q0 be the u–w path on the remaining ¤ vertices of G2 . Lemma 10.3.3. Let G = (V, E) be a cubic multigraph with a Hamilton cycle C. Let e ∈ E(C) and f ∈ E r E(C) be edges with a common end v (Fig. 10.3.2). Then there exists a closed walk in G that traverses e once, every other edge of C once or twice, and every edge in E r E(C) once. This walk can be chosen to contain the triple (e, v, f ), that is, it traverses e in the direction of v and then leaves v by the edge f . e
e v
v0 v 00
Fig. 10.3.2. The multigraphs G and G0 in Lemma 10.3.3
Proof . By Proposition 1.2.1, C has even length. Replace every other edge of C by a double edge, in such a way that e does not get replaced. In the arising 4-regular multigraph G0 , split v into two vertices v 0 , v 00 , making v 0 incident with e and f , and v 00 incident with the other two edges at v (Fig. 10.3.2). By Theorem 1.8.1 this multigraph has an Euler tour, which induces the desired walk in G. ¤ Lemma 10.3.4. For every 2-connected graph G and x ∈ V (G), there is a cycle C ⊆ G that contains x as well as a vertex y 6= x with NG (y) ⊆ V (C). Proof . If G has a Hamilton cycle, there is nothing more to show. If not, let C 0 ⊆ G be any cycle containing x; such a cycle exists, since G is 2-connected. Let D be a component of G − C 0 . Assume that C 0 and D are chosen so that |D| is minimal. Since G is 2-connected, D has at least two neighbours on C 0 . Then C 0 contains a path P between ˚ does not contain x and two such neighbours u and v, whose interior P has no neighbour in D (Fig. 10.3.3). Replacing P in C 0 by a u–v path through D, we obtain a cycle C that contains x and a vertex y ∈ D. If y had a neighbour z in G − C, then z would lie in a component D0 $ D of G − C, contradicting the choice of C 0 and D. Hence all the neighbours of y lie on C, and C satisfies the assertion of the lemma. ¤
u P x
C Fig. 10.3.3. The proof of Lemma 10.3.4
Proof of Theorem 10.3.1. We show by induction on |G| that, given any vertex x∗ ∈ G, there is a Hamilton cycle H in G2 with the following property: Both edges of H at x∗ lie in G.
x∗ C y∗
P(D) ˜ C
P(D)
For |G| = 3, we have G = K 3 and the assertion is trivial. So let |G| > 4, assume the assertion for graphs of smaller order, and let x∗ ∈ V (G) be given. By Lemma 10.3.4, there is a cycle C ⊆ G that contains both x∗ and a vertex y ∗ 6= x∗ whose neighbours in G all lie on C. If C is a Hamilton cycle of G, there is nothing to show; so assume ˜ denote that G − C 6= ∅. Consider a component D of G − C. Let D the graph G/(G − D) obtained from G by contracting G − D into a new ˜ is again vertex x ˜. If |D| = 1, set P(D) := { D }. If |D| > 1, then D 2 ˜ 2-connected. Hence, by the induction hypothesis, D has a Hamilton ˜ Note that the path C˜ − x cycle C˜ whose edges at x ˜ both lie in D. ˜ may 2 have some edges that do not lie in G : edges joining two neighbours of x ˜ that have no common neighbour in G (and are themselves non-adjacent ˜ denote the set of these edges, and let P(D) denote the set in G). Let E ˜ this is a set of paths in G2 whose ends of components of (C˜ − x ˜) − E; ˜ are adjacent to x ˜ in D (Fig. 10.3.4). P(D)
D x ˜ Fig. 10.3.4. P(D) consists of three paths, one of which is trivial P
Let P denote the union of the sets P(D) over all components D of G − C. Clearly, P has the following properties:
10.3 Hamilton cycles in the square of a graph 2 The elements of P are pairwise S disjoint paths in G avoiding C, and V (G) = V (C) ∪ P ∈ P V (P ). Every end y of a path P ∈ P has a neighbour on C in G; we choose such a neighbour and call it the foot of P at y.
(1) foot
If P ∈ P is trivial, then P has exactly one foot. If P is non-trivial, then P has a foot at each of its ends. These two feet need not be distinct, however; so any non-trivial P has either one or two feet. We shall now modify P a little, preserving the properties summarized under (1); no properties of P other than those will be used later in the proof. If a vertex of C is a foot of two distinct paths P, P 0 ∈ P, say at y ∈ P and at y 0 ∈ P 0 , then yy 0 is an edge and P yy 0 P 0 is a path in G2 ; we replace P and P 0 in P by this path. We repeat this modification of P until the following holds: No vertex of C is a foot of two distinct paths in P.
For i = 1, 2 let Pi ⊆ P denote the set of all paths in P with exactly i feet, and let Xi ⊆ V (C) denote the set of all feet of paths in Pi . Then X1 ∩ X2 = ∅ by (2), and y ∗ ∈/ X1 ∪ X2 . Let us also simplify G a little; again, these changes will affect neither the paths in P nor the validity of (1) and (2). First, we shall assume from now on that all elements of P are paths in G itself, not just in G2 . This assumption may give us some additional edges for G2 , but we shall not use these in our construction of the desired Hamilton cycle H. (Indeed, H will contain all the paths from P whole, as subpaths.) Thus if H lies in G2 and satisfies (∗) for the modified version of G, it will do so also for the original. For every P ∈ P, we further delete all P –C edges in G except those between the ends of P and its corresponding feet. Finally, we delete all chords of C in G. We are thus assuming without loss of generality: The only edges of G between C and a path P ∈ P are the two edges between the ends of P and its corresponding feet. (If |P | = 1, these two edges coincide.) The only edges of G with both ends on C are the edges of C itself.
P1 , P 2 X1 , X 2
Our goal is to construct the desired Hamilton cycle H of G2 from the paths in P and suitable paths in C 2 . As a first approximation, we shall construct a closed walk W in the graph [ ˜ := G − P1 , G a walk that will already satisfy a (∗)-type condition and traverse every path in P2 exactly once. Later, we shall modify W so that it passes through every vertex of C exactly once and, finally, so as to include the
˜ G
v + , right v − , left interval [ v, w ] etc.
I∗, P ∗ Q∗
e(v)
paths from P1 . For the construction of W we assume that P2 6= ∅; the case of P2 = ∅ is much simpler and will be treated later. We start by choosing a fixed cyclic orientation of C, a bijection i 7→ vi from Z|C| to V (C) with vi vi+1 ∈ E(C) for all i ∈ Z|C| . Let us think of this orientation as clockwise; then every vertex vi ∈ C has a right neighbour vi+ := vi+1 and a left neighbour vi− := vi−1 . Accordingly, the edge v − v lies to the left of v, the edge vv + lies on its right, and so on. A non-trivial path P = vi vi+1 . . . vj−1 vj in C such that V (P ) ∩ X2 = { vi , vj } will be called an interval , with left end vi and right end vj . Thus, C is the union of |X2 | = 2 |P2 | intervals. As usual, we write P =: ˚ as well as [ vi , vj ) := P˚ vj and (vi , vj ] := ˚ vi P . [ vi , vj ] and set (vi , vj ) := P For intervals [ u, v ] and [ v, w ] with a common end v we say that [ u, v ] lies to the left of [ v, w ], and [ v, w ] lies to the right of [ u, v ]. We denote the unique interval [ v, w ] with x∗ ∈ (v, w ] as I ∗ , the path in P2 with foot w as P ∗ , and the path I ∗ wP ∗ as Q∗ . ˜ as a multigraph M For the construction of W , we may think of G on X2 whose edges are the intervals on C and the paths in P2 (with their feet as ends). By (2), M is cubic, so we may apply Lemma 10.3.3 with ˜ e := I ∗ and f := P ∗ . The lemma provides us with a closed walk W in G ∗ which traverses I once, every other interval of C once or twice, and every path in P2 once. Moreover, W contains Q∗ as a subpath. The two edges at x∗ of this path lie in G; in this sense, W already satisfies (∗). Let us now modify W so that W passes through every vertex of C exactly once. Simultaneously, we shall prepare for the later inclusion of the paths from P1 by defining a map v 7→ e(v) that is injective on X1 and assigns to every v ∈ X1 an edge e(v) of the modified W with the following property: The edge e(v) either bridges v or is incident with it. In the latter case, e(v) ∈ C and e(v) 6= vx∗ .
For simplicity, we shall define the map v 7→ e(v) on all of V (C) r X2 , a set that includes X1 by (2). To ensure injectivity on X1 , we only have to make sure that no edge vw ∈ C is chosen both as e(v) and as e(w). Indeed, since |X1 | > 2 if injectivity is a problem, and P2 6= ∅ by assumption, we have |C − y ∗ | > |X1 | + 2 |P2 | > 4 and hence |C| > 5; thus, no edge of G2 can bridge more than one vertex of C, or bridge a vertex of C and lie on C at the same time. For our intended adjustments of W at the vertices of C, we consider the intervals of C one at a time. By definition of W , every interval is of one of the following three types: Type 1 : W traverses I once; Type 2 : W traverses I twice, in one direction and back immediately afterwards (formally: W contains a triple (e, x, e) with x ∈ X2 and e ∈ E(I));
Type 3 : W traverses I twice, on separate occasions (i.e., there is no triple as above). By definition of W , the interval I ∗ is of type 1. The vertex x in the definition of a type 2 interval will be called the dead end of that interval. Finally, since Q∗ is a subpath of W and W traverses both I ∗ and P ∗ only once, we have: The interval to the right of I ∗ is of type 2 and has its dead end on the left.
Consider a fixed interval I = [ x1 , x2 ]. Let y1 be the neighbour of x1 , and y2 the neighbour of x2 on a path in P2 . Let I − denote the interval to the left of I. Suppose first that I is of type 1. We then leave W unchanged on I. If I 6= I ∗ we choose as e(v), for each v ∈ ˚ I, the edge to the left of v. As I − 6= I ∗ by (4), and hence x1 6= x∗ , these choices of e(v) satisfy (∗∗). If I, and as the I = I ∗ , we define e(v) as the edge left of v if v ∈ (x1 , x∗ ] ∩ ˚ edge right of v if v ∈ (x∗ , x2 ). These choices of e(v) are again compatible with (∗∗). Suppose now that I is of type 2. Assume first that x2 is the dead end of I. Then W contains the walk y1 x1 Ix2 Ix1 I − (possibly in reverse x2 , and replace order). We now apply Lemma 10.3.2 (i) with P := y1 x1 I˚ in W the subwalk y1 x1 Ix2 Ix1 by the y1 –x1 path Q ⊆ G2 of the lemma ˚ = V (P ) r { y1 , x1 } = V (˚ I). The vertices (Fig. 10.3.5). Then V (Q) y1
W I − x1
Q e(x− 2 )
Fig. 10.3.5. How to modify W on an interval of type 2
v ∈ (x1 , x− 2 ) are each bridged by an edge of Q, which we choose as e(v). − − ) As e(x− 2 we choose the edge to the left of x2 (unless x2 = x1 ). This edge, too, lies on Q, by the lemma. Moreover, by (4) it is not incident with x∗ (since x2 is the dead end of I, by assumption) and hence satisfies (∗∗). The case that x1 is the dead end of I can be treated in the same way: using Lemma 10.3.2 (i), we replace in W the subwalk ˚ = V (˚ I), choose as e(v) y2 x2 Ix1 Ix2 by a y2 –x2 path Q ⊆ G2 with V (Q) + , x ) an edge of Q bridging v, and define e(x for v ∈ (x+ 2 1 1 ) as the edge + + to the right of x1 (unless x1 = x2 ). Suppose finally that I is of type 3. Since W traverses the edge y1 x1 only once and the interval I − no more than twice, W contains y1 x1 I and I − ∪ I as subpaths, and I − is of type 1. By (4), however, I − 6= I ∗ . Hence, when e(v) was defined for the vertices v ∈ ˚ I − , the rightmost edge − − x1 x1 of I was not chosen as e(v) for any v, so we may now replace this
I, x1 , x2 y1 , y 2 I−
edge. Since W traverses I + no more than twice, it must traverse the edge x2 y2 immediately after one of its two subpaths y1 x1 I and x− 1 x1 I. ) as the vertex u in Take the starting vertex of this subpath (y1 or x− 1 Lemma 10.3.2 (ii), and the other vertex in { y1 , x− } as v ; moreover, set 0 1 vk := x2 and w := y2 . Then the lemma enables us to replace these two 2 subpaths of W between { y1 , x− 1 } and { x2 , y2 } by disjoint paths in G (Fig. 10.3.6), and furthermore assigns to every vertex v ∈ ˚ I an edge e(v) of one of those paths, bridging v. y1
y2 x1
y1 v0 x1
y2 x2 = vk
Fig. 10.3.6. A type 3 modification for the case u = y1 and k odd
˜ H
˜2. Following the above modifications, W is now a closed walk in G ˜ exactly once. Let us check that, moreover, W contains every vertex of G For vertices of the paths in P2 this is clear, because W still traverses every such path once and avoids it otherwise. For the vertices of C − X2 , it follows from the above modifications by Lemma 10.3.2. So how about the vertices in X2 ? Let x ∈ X2 be given, and let y be its neighbour on a path in P2 . Let I1 denote the interval I that satisfied yxI ⊆ W before the modification of W , and let I2 denote the other interval ending in x. If I1 is of type 1, then I2 is of type 2 with dead end x. In this case, x was retained in W when W was modified on I1 but skipped when W was modified on I2 , and is thus contained exactly once in W now. If I1 is of type 2, then x is not its dead end, and I2 is of type 1. The subwalk of W that started with yx and then went along I1 and back, was replaced with a y–x path. This path is now followed on W by the unchanged interval I2 , so in this case too the vertex x is now contained in W exactly once. Finally, if I1 is of type 3, then x was contained in one of the replacement paths Q, Q0 from Lemma 10.3.2 (ii); as these paths were disjoint by the assertion of the lemma, x is once more left on W exactly once. We have thus shown that W , after the modifications, is a closed walk ˜ exactly once, so W defines a Hamilton ˜ 2 containing every vertex of G in G 2 ˜ ˜ ˜ satisfies (∗). cycle H of G . Since W still contains the path Q∗ , H Up until now, we have assumed that P2 is non-empty. If P2 = ∅, ˜ := G ˜ = C; then, again, H ˜ satisfies (∗). It remains to turn let us set H 2 ˜ H into a Hamilton cycle H of G by incorporating the paths from P1 . In order to be able to treat the case of P2 = ∅ along with the case of P2 6= ∅, we define a map v 7→ e(v) also when P2 = ∅, as follows: for
every v
C − y ∗ , set ½ e(v) :=
vv + vv −
if v if v
∈ ∈
[ x∗ , y ∗ ) (y ∗ , x∗ ).
(Here, [ x∗ , y ∗ ) and (y ∗ , x∗ ) denote the obvious paths in C defined analogously to intervals.) As before, this map v 7→ e(v) is injective, satisfies (∗∗), and is defined on a superset of X1 ; recall that y ∗ cannot lie in X1 by definition. ˜ say with foot Let P ∈ P1 be a path to be incorporated into H, v ∈ X1 and ends y1 , y2 . (If |P | = 1, then y1 = y2 .) Our aim is to replace ˜ by P ; we thus have to show that the ends of P the edge e := e(v) in H are joined to those of e by suitable edges of G2 . ˜ its neighbours By (2) and (3), v has only two neighbours in G, x1 , x2 on C. If v is incident with e, i.e. if e = vxi with i ∈ { 1, 2 }, we replace e by the path vy1 P y2 xi ⊆ G2 (Fig. 10.3.7). If v is not incident y1
P, v y1 , y 2
˜ Fig. 10.3.7. Replacing the edge e in H
with e then e bridges v, by (∗∗). Then e = x1 x2 , and we replace e by the path x1 y1 P y2 x2 ⊆ G2 (Fig. 10.3.8). Since v 7→ e(v) is injective ˜ (one for on X1 , assertion (2) implies that all these modifications of H every P ∈ P1 ) can be performed independently, and hence produce a Hamilton cycle H of G2 . y1
Let us finally check that H satisfies (∗), i.e. that both edges of H ˜ it suffices to show that any edge at x∗ lie in G. Since (∗) holds for H, ˜ that is not in H (and hence has the form e = e(v) for some e = x∗ z of H v ∈ X1 ) was replaced by an x∗ –z path whose first edge lies in G. Where can the vertex v lie? Let us show that v must be incident with e. If not then P2 6= ∅, and e bridges v. Now P2 6= ∅ and v ∈ X1 together imply that |C − y ∗ | > |X1 | + 2 |P2 | > 3, so |C| > 4. As e ∈ G ˜ the fact that e bridges v thus contradicts (3). (by (∗) for H),
e, z v
So v is indeed incident with e. Hence v ∈ { x∗ , z } by definition of e, while e 6= vx∗ by (∗∗). Thus v = x∗ , and e was replaced by a path of the form x∗ y1 P y2 z. Since x∗ y1 is an edge of G, this replacement again preserves (∗). Therefore H does indeed satisfy (∗), and our induction is complete. ¤ We close the chapter with a far-reaching conjecture generalizing Dirac’s theorem: Conjecture. (Seymour 1974) Let G be a graph of order n > 3, and let k be a positive integer. If G has minimum degree k n, δ(G) > k+1 then G has a Hamilton cycle H such that H k ⊆ G. For k = 1, this is precisely Dirac’s theorem. The case k = 2 had already been conjectured by P´ osa in 1963 and was proved for large n by Koml´os, S´ ark¨ozy & Szemer´edi (1996).
Show that every uniquely 3-edge-colourable cubic graph is hamiltonian. (‘Unique’ means that all 3-edge-colourings induce the same edge partition.)
Prove or disprove the following strengthening of Proposition 10.1.2: ‘Every k-connected graph G with |G| > 3 and χ(G) > |G|/k has a Hamilton cycle.’
Given a graph G, consider a maximal sequence G0 , . . . , Gk such that G0 = G and Gi+1 = Gi + xi yi for i = 0, . . . , k − 1, where xi , yi are two non-adjacent vertices of Gi satisfying dGi (xi ) + dGi (yi ) > |G|. The last graph of the sequence, Gk , is called the Hamilton closure of G. Show that this graph depends only on G, not on the choice of the sequence G0 , . . . , Gk .
Let x, y be two nonadjacent vertices of a connected graph G, with d(x) + d(y) > |G|. Show that G has a Hamilton cycle if and only if G + xy has one. Using the previous exercise, deduce the following strengthening of Dirac’s theorem: if d(x) + d(y) > |G| for every two non-adjacent vertices x, y ∈ G, then G has a Hamilton cycle.
Given an even positive integer k, construct for every n > k a k-regular graph of order 2n + 1.
6.− Find a hamiltonian graph whose degree sequence is not hamiltonian.
7.− Let G be a graph with fewer than i vertices of degree at most i, for every i < |G|/2. Use Chv´ atal’s theorem to show that G is hamiltonian. (Thus in particular, Chv´ atal’s theorem implies Dirac’s theorem.) 8.
Find a connected graph G whose square G2 has no Hamilton cycle.
9.+ Show by induction on |G| that the third power G3 of a connected graph G contains a Hamilton path between any two vertices. Deduce that G3 is hamiltonian. 10.
Show that the square of a 2-connected graph contains a Hamilton path between any two vertices.
An oriented complete graph is called a tournament. Show that every tournament contains a (directed) Hamilton path.
12.+ Let G be a graph in which every vertex has odd degree. Show that every edge of G lies on an even number of Hamilton cycles. (Hint. Let xy ∈ E(G) be given. The Hamilton cycles through xy correspond to the Hamilton paths in G − xy from x to y. Consider the set H of all Hamilton paths in G − xy starting at x, and show that an even number of these end in y. To show this, define a graph on H so that the desired assertion follows from Proposition 1.2.1.)
Notes The problem of finding a Hamilton cycle in a graph has the same kind of origin as its Euler tour counterpart and the four colour problem: all three problems come from mathematical puzzles older than graph theory itself. What began as a game invented by W.R. Hamilton in 1857—in which ‘Hamilton cycles’ had to be found on the graph of the dodecahedron—reemerged over a hundred years later as a combinatorial optimization problem of prime importance: the travelling salesman problem. Here, a salesman has to visit a number of customers, and his problem is to arrange these in a suitable circular route. (For reasons not included in the mathematical brief, the route has to be such that after visiting a customer the salesman does not pass through that town again.) Much of the motivation for considering Hamilton cycles comes from variations of this algorithmic problem. A detailed discussion of the various degree conditions for hamiltonicity referred to at the beginning of Section 10.2 can be found in R. Halin, Graphentheorie, Wissenschaftliche Buchgesellschaft 1980. All the relevant references for Sections 10.1 and 10.2 can be found there, or in B. Bollob´ as, Extremal Graph Theory, Academic Press 1978. The ‘proof’ of the four colour theorem indicated at the end of Section 10.1, which is based on the (false) premise that every 3-connected cubic planar graph is hamiltonian, is usually attributed to the Scottish mathematician P.G. Tait. Following Kempe’s flawed proof of 1879 (see the notes for Chapter 5), it seems that Tait believed to be in possession of at least one ‘new proof of Kempe’s theorem’. However, when he addressed the Edinburgh Mathematical Society on
this subject in 1883, he seems to have been aware that he could not—really— prove the above statement about Hamilton cycles. His account in P.G. Tait, Listing’s topologie, Phil. Mag. 17 (1884), 30–46, makes some entertaining reading. A shorter proof of Tutte’s theorem that 4-connected planar graphs are hamiltonian was given by C. Thomassen, A theorem on paths in planar graphs, J. Graph Theory 7 (1983), 169–176. Tutte’s counterexample to Tait’s assumption that even 3-connectedness suffices (at least for cubic graphs) is shown in Bollob´ as, and in J.A. Bondy & U.S.R. Murty, Graph Theory with Applications, Macmillan 1976 (where Tait’s attempted proof is discussed in some detail). Proposition 10.1.2 is due to Chv´ atal & Erd˝ os (1972). Our proof of Fleischˇ ıha, A new proof of the theorem by Fleischner’s theorem is based on S. R´ ner, J. Combin. Theory B 52 (1991), 117–123. Seymour’s conjecture is from P.D. Seymour, Problem 3, in (T.P. McDonough and V.C. Mavron, eds.) Combinatorics, Cambridge University Press 1974. P´ osa’s conjecture was proved for large n by J. Koml´ os, G.N. S´ ark¨ ozy & E. Szemer´edi, On the square of a Hamiltonian cycle in dense graphs, Random Structures and Algorithms 9 (1996), 193–211.
Random Graphs
At various points in this book, we already encountered the following fundamental theorem of Erd˝ os: for every integer k there is a graph G with g(G) > k and χ(G) > k. In plain English: there exist graphs combining arbitrarily large girth with arbitrarily high chromatic number. How could one prove such a theorem? The standard approach would be to construct a graph with those two properties, possibly in steps by induction on k. However, this is anything but straightforward: the global nature of the second property forced by the first, namely, that the graph should have high chromatic number ‘overall’ but be acyclic (and hence 2-colourable) locally, flies in the face of any attempt to build it up, constructively, from smaller pieces that have the same or similar properties. In his pioneering paper of 1959, Erd˝ os took a radically different approach: for each n he defined a probability space on the set of graphs with n vertices, and showed that, for some carefully chosen probability measures, the probability that an n-vertex graph has both of the above properties is positive for all large enough n. This approach, now called the probabilistic method , has since unfolded into a sophisticated and versatile proof technique, in graph theory as much as in other branches of discrete mathematics. The theory of random graphs is now a subject in its own right. The aim of this chapter is to offer an elementary but rigorous introduction to random graphs: no more than is necessary to understand its basic concepts, ideas and techniques, but enough to give an inkling of the power and elegance hidden behind the calculations. Erd˝ os’s theorem asserts the existence of a graph with certain properties: it is a perfectly ordinary assertion showing no trace of the randomness employed in its proof. There are also results in random graphs that are generically random even in their statement: these are theorems about almost all graphs, a notion we shall meet in Section 11.3. In the
11. Random Graphs
last section, we give a detailed proof of a theorem of Erd˝ os and R´enyi that illustrates a proof technique frequently used in random graphs, the so-called second moment method .
11.1 The notion of a random graph V G
p q
Ωe Pe G(n, p) Ω
Let V be a fixed set of n elements, say V = { 0, . . . , n − 1 }. Our aim is to turn the set G of all graphs on V into a probability space, and then to consider the kind of questions typically asked about random objects: What is the probability that a graph G ∈ G has this or that property? What is the expected value of a given invariant on G, say its expected girth or chromatic number? Intuitively, we should be able to generate G randomly as follows. For each e ∈ [V ]2 we decide by some random experiment whether or not e shall be an edge of G; these experiments are performed independently, and for each the probability of success—i.e. of accepting e as an edge for G—is equal to some fixed1 number p ∈ [ 0, 1 ]. Then if G0 is some fixed graph on V , with m edges say, the elementary event { G0 } has a n probability of pm q ( 2 )−m (where q := 1 − p): with this probability, our randomly generated graph G is this particular graph G0 . (The probability that G is isomorphic to G0 will usually be greater.) But if the probabilities of all the elementary events are thus determined, then so is the entire probability measure of our desired space G. Hence all that remains to be checked is that such a probability measure on G, one for which all individual edges occur independently with probability p, does indeed exist.2 In order to construct such a measure on G formally, we start by defining for every potential edge e ∈ [V ]2 its own little probability space Ωe := { 0e , 1e }, choosing Pe ({ 1e }) := p and Pe ({ 0e }) := q as the probabilities of its two elementary events. As our desired probability space G = G(n, p) we then take the product space Ω :=
Ωe .
e ∈ [V ]2 1 Often, the value of p will depend on the cardinality n of the set V on which our random graphs are generated; thus, p will be the value p = p(n) of some function n 7→ p(n). Note, however, that V (and hence n) is fixed for the definition of G: for each n separately, we are constructing a probability space of the graphs G on V = { 0, . . . , n − 1 }, and within each space the probability that e ∈ [V ]2 is an edge of G has the same value for all e. 2 Any reader ready to believe this may skip ahead now to the end of Proposition 11.1.1, without missing anything.
11.1 The notion of a random graph
Thus, formally, an element of Ω is a map ω assigning to every e ∈ [V ]2 either 0e or 1e , and the probability measure P on Ω is the product measure of all the measures Pe . In practice, of course, we identify ω with the graph G on V whose edge set is
E(G) = { e | ω(e) = 1e } , and call G a random graph on V with edge probability p. Following standard probabilistic terminology, we may now call any set of graphs on V an event in G(n, p). In particular, for every e ∈ [V ]2 the set Ae := { ω | ω(e) = 1e }
random graph event Ae
of all graphs G on V with e ∈ E(G) is an event: the event that e is an edge of G. For these events, we can now prove formally what had been our guiding intuition all along: Proposition 11.1.1. The events Ae are independent and occur with probability p. Proof . By definition, Ae = { 1e } ×
Ω e0 .
e0 6=e
Since P is the product measure of all the measures Pe , this implies Y 1 = p. P (Ae ) = p · e0 6=e
Similarly, if { e1 , . . . , ek } is any subset of [V ]2 , then ´ ³ Y Ωe P (Ae1 ∩ . . . ∩ Aek ) = P { 1e1 } × . . . × { 1ek } × = pk = P (Ae1 ) · · · P (Aek ) .
e∈ / { e1 ,...,ek }
As noted before, P is determined uniquely by the value of p and our assumption that the events Ae are independent. In order to calculate probabilities in G(n, p), it therefore generally suffices to work with these two assumptions: our concrete model for G(n, p) has served its purpose and will not be needed again. As a simple example of such a calculation, consider the event that G contains some fixed graph H on a subset of V as a subgraph; let |H| =: k and kHk =: `. The probability of this event H ⊆ G is the product of the probabilities Ae over all the edges e ∈ H, so P [ H ⊆ G ] = p` . In
k contrast, the probability that H is an induced subgraph of G is p` q (2)−` : now the edges missing from H are required to be missing from G too, and they do so independently with probability q. The probability PH that G has an induced subgraph isomorphic to H is usually more difficult to compute: since the possible instances of H on subsets of V overlap, the events that they occur in G are not independent. However, the sum (over all k-sets U ⊆ V ) of the probabilities P [ H ' G [ U ] ] is always an upper bound for PH , since PH is the measure of the union of all those events. For example, if H = K k , we have the following trivial upper bound on the probability that G contains an induced copy of H:
[ 11.2.1 ] [ 11.3.4 ]
Lemma 11.1.2. For all integers n, k with n > k > 2, the probability that G ∈ G(n, p) has a set of k independent vertices is at most P [ α(G) > k ] 6
µ ¶ n (k2) q . k
Proof . k The probability that a fixed k-set U ⊆ V is independent in (2) G ¡n¢is q . The assertion thus follows from the fact that there are only ¤ k such sets U . Analogously, the probability that G ∈ G(n, p) contains a K k is at most µ ¶ n (k2) P [ ω(G) > k ] 6 p . k Now if k is fixed, and n is small enough that these bounds for the probabilities P [ α(G) > k ] and P [ ω(G) > k ] sum to less than 1, then G contains graphs that have neither property: graphs which contain neither a K k nor a K k induced. But then any such n is a lower bound for the Ramsey number of k ! As the following theorem shows, this lower bound is quite close to the upper bound of 22k−3 implied by the proof of Theorem 9.1.1: Theorem 11.1.3. (Erd˝ os 1947) For every integer k > 3, the Ramsey number of k satisfies R(k) > 2k/2 . Proof . For k = 3 we trivially have R(3) > 3 > 23/2 , so let k > 4. We show that, for all n 6 2k/2 and G ∈ G(n, 12 ), the probabilities P [ α(G) > k ] and P [ ω(G) > k ] are both less than 12 . Since p = q = 12 , Lemma 11.1.2 and the analogous assertion for ω(G) imply the following for all n 6 2k/2 (use that k! > 2k for k > 4):
µ ¶ n ¡ 1 ¢(k2) k 2 ¡ k k ¢ − 1 k(k−1) < n /2 2 2 ¡ 2 ¢ 1 6 2k /2 /2k 2− 2 k(k−1)
P [ α(G) > k ], P [ ω(G) > k ] 6
= 2−k/2 <
. ¤
In the context of random graphs, each of the familiar graph invariants (like average degree, connectivity, girth, chromatic number, and so on) may be interpreted as a non-negative random variable on G(n, p), a function
X: G(n, p) → [ 0, ∞) . The mean or expected value of X is the number E(X) :=
mean expectation
P ({ G }) · X(G) .
G ∈ G(n,p)
E(X)
Note that the operator E, the expectation, is linear: we have E(X + Y ) = E(X) + E(Y ) and E(λX) = λE(X) for any two random variables X, Y on G(n, p) and λ ∈ R. Computing the mean of a random variable X can be a simple and effective way to establish the existence of a graph G such that X(G) < a for some fixed a > 0 and, moreover, G has some desired property P. Indeed, if the expected value of X is small, then X(G) cannot be large for more than a few graphs in G(n, p), because X(G) > 0 for all G ∈ G(n, p). Hence X must be small for many graphs in G(n, p), and it is reasonable to expect that among these we may find one with the desired property P. This simple idea lies at the heart of countless non-constructive existence proofs using random graphs, including the proof of Erd˝ os’s theorem presented in the next section. Quantified, it takes the form of the following lemma, whose proof follows at once from the definition of the expectation and the additivity of P : Lemma 11.1.4. (Markov’s Inequality) Let X > 0 be a random variable on G(n, p) and a > 0. Then P [ X > a ] 6 E(X)/a . Proof . E(X) =
P ({ G }) · X(G)
[ 11.2.2 ] [ 11.4.1 ] [ 11.4.3 ]
G∈G(n,p) X(G)>a
P ({ G }) · a
= P [X > a]·a.
(n)k
Since our probability spaces are finite, the expectation can often be computed by a simple application of double counting, a standard combinatorial technique we met before in the proofs of Corollary 4.2.8 and Theorem 5.5.3. For example, if X is a random variable on G(n, p) that counts the number of subgraphs of G in some fixed set H of graphs on V , then E(X), by definition, counts the number of pairs (G, H) such that H ⊆ G, each weighted with the probability of { G }. Algorithmically, we compute E(X) by going through the graphs G ∈ G(n, p) in an ‘outer loop’ and performing, for each G, an ‘inner loop’ that runs through the graphs H ∈ H and counts ‘P ({ G })’ whenever H ⊆ G. Alternatively, we may count the same set of weighted pairs with H in the outer and G in the inner loop: this amounts to adding up, over all H ⊆ H, the probabilities P [ H ⊆ G ]. To illustrate this once in detail, let us compute the expected number of cycles of some given length k > 3 in a random graph G ∈ G(n, p). So let X: G(n, p) → N be the random variable that assigns to every random graph G its number of k-cycles, the number of subgraphs isomorphic to C k . Let us write (n)k := n (n − 1)(n − 2) · · · (n − k + 1) for the number of sequences of k distinct elements of a given n-set.
Lemma 11.1.5. The expected number of k-cycles in G E(X) =
G(n, p) is
(n)k k p . 2k
Proof . For every k-cycle C with vertices in V = { 0, . . . , n − 1 }, the vertex set of the graphs in G(n, p), let XC : G(n, p) → { 0, 1 } denote the indicator random variable of C: n 1 if C ⊆ G; XC : G 7→ 0 otherwise. Since XC takes only 1 as a positive value, its expectation E(XC ) equals the measure P [ XC = 1 ] of the set of all graphs in G(n, p) that contain C. But this is just the probability that C ⊆ G: E(XC ) = P [ C ⊆ G ] = pk .
How many such cycles C = v0 . . . vk−1 v0 are there? There are (n)k sequences v0 . . . vk−1 of distinct vertices in V , and each cycle is identified by 2k of those sequences—so there are exactly (n)k /2k such cycles. Our random variable X assigns to every graph G its number of kcycles. Clearly, this is the sum of all the values XC (G), where C varies over the (n)k /2k cycles of length k with vertices in V : X XC . X = C
Since the expectation is linear, (1) thus implies E(X) = E
³X C
´ XC
E(XC ) =
(n)k k p 2k ¤
11.2 The probabilistic method Very roughly, the probabilistic method in discrete mathematics has developed from the following idea. In order to prove the existence of an object with some desired property, one defines a probability space on some larger—and certainly non-empty—class of objects, and then shows that an element of this space has the desired property with positive probability. The ‘objects’ inhabiting this probability space may be of any kind: partitions or orderings of the vertices of some fixed graph arise as naturally as mappings, embeddings and, of course, graphs themselves. In this section, we illustrate the probabilistic method by giving a detailed account of one of its earliest results: of Erd˝ os’s classic theorem on large girth and chromatic number. Erd˝ os’s theorem says that, given any positive integer k, there is a graph G with girth g(G) > k and chromatic number χ(G) > k. Let us call cycles of length at most k short, and sets of |G|/k or more vertices big. For a proof of Erd˝ os’s theorem, it suffices to find a graph G without short cycles and without big independent sets of vertices: then the colour classes in any vertex colouring of G are small (not big), so we need more than k colours to colour G. How can we find such a graph G? If we choose p small enough, then a random graph in G(n, p) is unlikely to contain any (short) cycles. If we choose p large enough, then G is unlikely to have big independent vertex sets. So the question is: do these two ranges of p overlap, that is, can we choose p so that, for some n, it is both small enough to give P [ g 6 k ] < 12 and large enough for P [ α > n/k ] < 12 ? If so, then
short big/small
G(n, p) will contain at least one graph without either short cycles or big independent sets. Unfortunately, such a choice of p is impossible: the two ranges of p do not overlap! As we shall see in Section 11.4, we must keep p below n−1 to make the occurrence of short cycles in G unlikely—but for any such p there will most likely be no cycles in G at all (Exercise 19), so G will be bipartite and hence have at least n/2 independent vertices. But all is not lost. In order to make big independent sets unlikely, we shall fix p above n−1 , at n²−1 for some ² > 0. Fortunately, though, if ² is small enough then this will produce only few short cycles in G, even compared with n (rather than, more typically, with nk ). If we then delete a vertex in each of those cycles, the graph H obtained will have no short cycles, and its independence number α(H) will be at most that of G. Since H is not much smaller than G, its chromatic number will thus still be large, so we have found a graph with both large girth and large chromatic number. To prepare for the formal proof of Erd˝ os’s theorem, we first show that an edge probability of p = n²−1 is indeed always large enough to ensure that G ∈ G(n, p) ‘almost surely’ has no big independent set of vertices. More precisely, we prove the following slightly stronger assertion: Lemma 11.2.1. Let k > 0 be an integer, and let p = p(n) be a function of n such that p > (6k ln n)n−1 for n large. Then lim P [ α > 12 n/k ] = 0 .
(11.1.2)
Proof . For all integers n, r with n > r > 2, and all G 11.1.2 implies µ ¶ n (r2) P [α > r] 6 q r r 6 nr q ( 2 ) ´r ³ = nq (r−1)/2 ´r ³ 6 ne−p(r−1)/2 ;
G(n, p), Lemma
here, the last inequality follows from the fact that 1 − p 6 e−p for all p. (Compare the functions x 7→ ex and x 7→ x + 1 for x = −p.) Now if p > (6k ln n)n−1 and r > 12 n/k, then the term under the exponent satisfies ne−p(r−1)/2 = ne−pr/2 + p/2 6 ne−(3/2) ln n + p/2 6 n n−3/2 e1/2 √ √ = e / n −→ 0 . n→∞
11.2 The probabilistic method
Since p > (6k ln n)n−1 for n large, we thus obtain for r := d 12 n/ke lim P [ α > 12 n/k ] = lim P [ α > r ] = 0 ,
Theorem 11.2.2. (Erd˝ os 1959) For every integer k there exists a graph H with girth g(H) > k and chromatic number χ(H) > k. Proof . Assume that k > 3, fix ² with 0 < ² < 1/k, and let p := n²−1 . Let X(G) denote the number of short cycles in a random graph G ∈ G(n, p), i.e. its number of cycles of length at most k. By Lemma 11.1.5, we have E(X) =
k X (n)i i=3
[ 9.2.3 ] (11.1.4) (11.1.5) p, ², X
ni pi 6 12 (k − 2) nk pk ;
note that (np)i 6 (np)k , because np = n² > 1. By Lemma 11.1.4, ± P [ X > n/2 ] 6 E(X) (n/2) 6 (k − 2) nk−1 pk = (k − 2) nk−1 n(²−1)k = (k − 2) nk²−1 . As k² − 1 < 0 by our choice of ², this implies that lim P [ X > n/2 ] = 0 .
Let n be large enough that P [ X > n/2 ] < 12 and P [ α > 12 n/k ] < 12 ; the latter is possible by our choice of p and Lemma 11.2.1. Then there is a graph G ∈ G(n, p) with fewer than n/2 short cycles and α(G) < 1 2 n/k. From each of those cycles delete a vertex, and let H be the graph obtained. Then |H| > n/2 and H has no short cycles, so g(H) > k. By definition of G, n/2 |H| > > k. χ(H) > α(H) α(G) ¤
Corollary 11.2.3. There are graphs with arbitrarily large girth and arbitrarily large values of the invariants κ, ε and δ. Proof . Apply Corollary 5.2.3 and Theorem 1.4.2.
11.3 Properties of almost all graphs property
almost all etc.
A graph property is a class of graphs that is closed under isomorphism, one that contains with every graph G also the graphs isomorphic to G. If p = p(n) is a fixed function (possibly constant), and P is a graph property, we may ask how the probability P [ G ∈ P ] behaves for G ∈ G(n, p) as n → ∞. If this probability tends to 1, we say that G ∈ P for almost all (or almost every) G ∈ G(n, p), or that G ∈ P almost surely; if it tends to 0, we say that almost no G ∈ G(n, p) has the property P. (For example, in Lemma 11.2.1 we proved that, for a certain p, almost no G ∈ G(n, p) has a set of more than 12 n/k independent vertices.) To illustrate the new concept let us show that, for constant p, every fixed abstract3 graph H is an induced subgraph of almost all graphs: Proposition 11.3.1. For every constant p ∈ (0, 1) and every graph H, almost every G ∈ G(n, p) contains an induced copy of H. Proof . Let H be given, and k := |H|. If n > k and U ⊆ { 0, . . . , n − 1 } is a fixed set of k vertices of G, then G [ U ] is isomorphic to H with a certain probability r > 0. This probability r depends on p, but not on n (why not?). Now G contains a collection of bn/kc disjoint such sets U . The probability that none of the corresponding graphs G [ U ] is isomorphic to H is (1 − r)bn/kc , since these events are independent by the disjointness of the edges sets [U ]2 . Thus P [ H 6⊆ G induced ] 6 (1 − r)bn/kc −→ 0 , n→∞
which implies the assertion.
Pi,j
The following lemma is a simple device enabling us to deduce that quite a number of natural graph properties (including that of Proposition 11.3.1) are shared by almost all graphs. Given i, j ∈ N, let Pi,j denote the property that the graph considered contains, for any disjoint vertex sets U, W with |U | 6 i and |W | 6 j, a vertex v ∈/ U ∪ W that is adjacent to all the vertices in U but to none in W . Lemma 11.3.2. For every constant p ∈ (0, 1) and i, j graph G ∈ G(n, p) has the property Pi,j .
N, almost every
3 The word ‘abstract’ is used to indicate that only the isomorphism type of H is known or relevant, not its actual vertex and edge sets. In our context, it indicates that the word ‘subgraph’ is used in the usual sense of ‘isomorphic to a subgraph’.
11.3 Properties of almost all graphs
Proof . For fixed U, W and v ∈ G − (U ∪ W ), the probability that v is adjacent to all the vertices in U but to none in W , is p|U | q |W | > pi q j . Hence, the probability that no suitable v exists for these U and W , is (1 − p|U | q |W | )n−|U |−|W | 6 (1 − pi q j )n−i−j (for n > i + j), since the corresponding events are independent for different v. As there are no more than ni+j pairs of such sets U, W in V (G) (encode sets U of fewer than i points as non-injective maps { 0, . . . , i − 1 } → { 0, . . . , n − 1 }, etc.), the probability that some such pair has no suitable v is at most ni+j (1 − pi q j )n−i−j , which tends to zero as n → ∞ since 1 − pi q j < 1.
Corollary 11.3.3. For every constant p ∈ (0, 1) and k ∈ N, almost every graph in G(n, p) is k-connected. Proof . By Lemma 11.3.2, it is enough to show that every graph in P2,k−1 is k-connected. But this is easy: any graph in P2,k−1 has order at least k + 2, and if W is a set of fewer than k vertices, then by definition of P2,k−1 any other two vertices x, y have a common neighbour v ∈/ W ; in particular, W does not separate x from y. ¤ In the proof of Corollary 11.3.3, we showed substantially more than was asked for: rather than finding, for any two vertices x, y ∈/ W , some x–y path avoiding W , we showed that x and y have a common neighbour outside W ; thus, all the paths needed to establish the desired connectivity could in fact be chosen of length 2. What seemed like a clever trick in this particular proof is in fact indicative of a more fundamental phenomenon for constant edge probabilities: by an easy result in logic, any statement about graphs expressed by quantifying over vertices only (rather than over sets or sequences of vertices)4 is either almost surely true or almost surely false. All such statements, or their negations, are in fact immediate consequences of an assertion that the graph has property Pi,j , for some suitable i, j. As a last example of an ‘almost all’ result we now show that almost every graph has a surprisingly high chromatic number: 4 In the terminology of logic: any first order sentence in the language of graph theory
Proposition 11.3.4. For every constant p ∈ (0, 1) and every ² > 0, almost every graph G ∈ G(n, p) has chromatic number χ(G) >
n log(1/q) · . 2+² log n
Proof . For any fixed n > k > 2, Lemma 11.1.2 implies µ ¶ n (k2) P [α > k] 6 q k k 6 nk q (2) log n
= q k log q + 2 k(k−1) ¡ 2 log n ¢ k − +k−1 = q 2 log(1/q) . For k := (2 + ²)
log n log(1/q)
the exponent of this expression tends to infinity with n, so the expression itself tends to zero. Hence, almost every G ∈ G(n, p) is such that in any vertex colouring of G no k vertices can have the same colour, so every colouring uses more than log(1/q) n n = · k 2+² log n colours.
By a result of Bollob´ as (1988), Proposition 11.3.4 is sharp in the following sense: if we replace ² by −², then the lower bound given for χ turns into an upper bound. Most of the results of this section have the interesting common feature that the values of p played no role whatsoever: if almost every graph in G(n, 12 ) had the property considered, then the same was true for almost every graph in G(n, 1/1000). How could this happen? Such insensitivity of our random model to changes of p was certainly not intended: after all, among all the graphs with a certain property P it is often those having P ‘only just’ that are the most interesting—for those graphs are most likely to have different properties too, properties to which P might thus be set in relation. (The proof of Erd˝ os’s theorem is a good example.) For most properties, however—and this explains the above phenomenon—the critical order of magnitude of p around which the property will ‘just’ occur or not occur lies far below any constant value of p: it is typically a function of n tending to zero as n → ∞.
Let us then see what happens if p is allowed to vary with n. Almost immediately, a fascinating picture unfolds. For edge probabilities p whose order of magnitude lies below n−2 , a random graph G ∈ G(n, p) almost surely has no edges at all. √ As p grows, G acquires more and more structure: from about p = n n−2 onwards, it almost surely has a component with more than two vertices, these components grow into trees, and around p = n−1 the first cycles are born. Soon, some of these will have several crossing chords, making the graph non-planar. At the same time, one component outgrows the others, until it devours them around p = (log n)n−1 , making the graph connected. Hardly later, at p = (1 + ²)(log n)n−1 , our graph almost surely has a Hamilton cycle! It has become customary to compare this development of random graphs as p grows to the evolution of an organism: for each p = p(n), one thinks of the properties shared by almost all graphs in G(n, p) as properties of ‘the’ typical random graph G ∈ G(n, p), and studies how G changes its features with the growth rate of p. As with other species, the evolution of random graphs happens in relatively sudden jumps: the critical edge probabilities mentioned above are thresholds below which almost no graph and above which almost every graph has the property considered. More precisely, we call a real function t = t(n) with t(n) 6= 0 for all n a threshold function for a graph property P if the following holds for all p = p(n), and G ∈ G(n, p): ½ lim P [ G
P] =
0 if p/t → 0 as n → ∞ 1 if p/t → ∞ as n → ∞.
If P has a threshold function t, then clearly any positive multiple ct of t is also a threshold function for P; thus, threshold functions in the above sense are only ever unique up to a multiplicative constant.5 Which graph properties have threshold functions? Natural candidates for such properties are increasing ones, properties closed under the addition of edges. (Graph properties of the form { G | G ⊇ H }, with H fixed, are common increasing properties; connectedness is another.) And indeed, Bollob´ as & Thomason (1987) have shown that all increasing properties, trivial exceptions aside, have threshold functions. In the next section we shall study a general method to compute threshold functions.
5 Our notion of threshold reflects only the crudest interesting level of screening: for some properties, such as connectedness, one can define sharper thresholds where the constant factor is crucial. Note also the role of the constant factor in our comparison of connectedness with hamiltonicity in the previous paragraph.
11.4 Threshold functions and second moments Consider a graph property of the form P = { G | X(G) > 0 } , X >0
where X > 0 is a random variable on G(n, p). Countless properties can be expressed naturally in this way; if X denotes the number of spanning trees, for example, then P corresponds to connectedness. How could we prove that P has a threshold function t? Any such proof will consist of two parts: a proof that almost no G ∈ G(n, p) has P when p is small compared with t, and one showing that almost every G has P when p is large. If X is integral, we may use Markov’s inequality for the first part of the proof and find an upper bound for E(X) instead of P [ X > 0 ]: if E(X) is small then X(G) can be positive—and hence at least 1—only for few G ∈ G(n, p). Besides, the expectation is much easier to calculate than probabilities: without worrying about such things as independence or incompatibility of events, we may compute the expectation of a sum of random variables—for example, of indicator random variables—simply by adding up their individual expected values. For the second part of the proof, things are more complicated. In order to show that P [ X > 0 ] is large, it is not enough to bound E(X) from below: since X is not bounded above, E(X) may be large simply because X is very large on just a few graphs G—so X may still be zero for most G ∈ G(n, p).6 In order to prove that P [ X > 0 ] → 1, we thus have to show that this cannot happen, i.e. that X does not deviate a lot from its mean too often. The following elementary tool from probability theory achieves just that. As is customary, we write µ := E(X)
and define σ > 0 by setting ¡ ¢ σ 2 := E (X − µ)2 .
This quantity σ 2 is called the variance or second moment of X; by definition, it is a (quadratic) measure of how much X deviates from its mean. Since E is linear, the defining term for σ 2 expands to σ 2 = E(X 2 − 2µX + µ2 ) = E(X 2 ) − µ2 . 6
For some p between n−1 and (log n)n−1 , for example, almost every G ∈ G(n, p) has an isolated vertex (and hence no spanning tree), but its expected number of spanning trees tends to infinity with n ! See the Exercise 13 for details.
11.4 Threshold functions and second moments
Note that µ and σ 2 always refer to a random variable on some fixed probability space. In our setting, where we consider the spaces G(n, p), both quantities are functions of n. The following lemma says exactly what we need: that X cannot deviate a lot from its mean too often. Lemma 11.4.1. (Chebyshev’s Inequality) For all real λ > 0, £ ¤ P |X − µ| > λ 6 σ 2 /λ2 .
Proof . By Lemma 11.1.4 and definition of σ 2 ,
P [ |X − µ| > λ ] = P [ (X − µ)2 > λ2 ] 6 σ 2 /λ2 . ¤ For a proof that X(G) > 0 for almost all G inequality can be used as follows:
G(n, p), Chebyshev’s
Lemma 11.4.2. If µ > 0 for n large, and σ 2 /µ2 → 0 as n → ∞, then X(G) > 0 for almost all G ∈ G(n, p). Proof . Any graph G with X(G) = 0 satisfies |X(G) − µ| = µ. Hence Lemma 11.4.1 implies with λ := µ that £ ¤ P [ X = 0 ] 6 P |X − µ| > µ 6 σ 2 /µ2 −→ 0 . n→∞
Since X > 0, this means that X > 0 almost surely, i.e. that X(G) > 0 ¤ for almost all G ∈ G(n, p). As the main result of this section, we now prove a theorem that will at once give us threshold functions for a number of natural properties. Given a graph H, we denote by PH the graph property of containing a copy of H as a subgraph. We shall call H balanced if ε(H 0 ) 6 ε(H) for all subgraphs H 0 of H. Theorem 11.4.3. (Erd˝ os & R´enyi 1960) If H is a balanced graph with k vertices and ` > 1 edges, then t(n) := n−k/` is a threshold function for PH .
k, ` t
244 (11.1.4) (11.1.5) X
Proof . Let X(G) denote the number of subgraphs of G isomorphic to H. Given n ∈ N, let H denote the set of all graphs isomorphic to H whose vertices lie in { 0, . . . , n − 1 }, the vertex set of the graphs G ∈ G(n, p): © ª H := H 0 | H 0 ' H, V (H 0 ) ⊆ { 0, . . . , n − 1 } . Given H 0 ∈ H and G ∈ G(n, p), we shall write H 0 ⊆ G to express that H 0 itself—not just an isomorphic copy of H 0 —is a subgraph of G. By h we denote the number of ¡ ¢isomorphic copies of H on a fixed k-set; clearly, h 6 k! . As there are nk possible vertex sets for the graphs in H, we thus have µ ¶ µ ¶ n n |H| = h6 k! 6 nk . k k
p, γ
Given p = p(n), we set γ := p/t; then p = γn−k/` .
We have to show that almost no G ∈ G(n, p) lies in PH if γ → 0 as n → ∞, and that almost all G ∈ G(n, p) lie in PH if γ → ∞ as n → ∞. For the first part of the proof, we find an upper bound for E(X), the expected number of subgraphs of G isomorphic to H. As in the proof of Lemma 11.1.5, double counting gives E(X) =
P [ H0 ⊆ G ] .
H0 ∈H
For every fixed H 0
H, we have P [ H 0 ⊆ G ] = p` ,
E(X) = |H| p` 6 nk (γn−k/` )` = γ ` .
because kHk = `. Hence,
Thus if γ → 0 as n → ∞, then P [G
PH ] = P [ X > 1 ] 6 E(X) 6 γ ` −→ 0
by Markov’s inequality (11.1.4), so almost no G
G(n, p) lies in PH .
We now come to the second part of the proof: we show that almost all G ∈ G(n, p) lie in PH if γ → ∞ as n → ∞. Note first that, for n > k, µ ¶ µ ¶ 1 n n−k+1 n ··· n−k = k! n n k µ ¶k 1 n−k+1 > k! n µ ¶k 1 k−1 > ; 1− k! k
¡ ¢ thus, nk exceeds nk by no more than a factor independent of n. Our goal¢ is to apply Lemma 11.4.2, and hence to bound σ 2 /µ2 = ¡ E(X 2 ) − µ2 /µ2 from above. As in (3) we have X P [ H 0 ∪ H 00 ⊆ G ] . (7) E(X 2 ) = (H 0 ,H 00 ) ∈ H2
Let us then calculate these probabilities P [ H 0 ∪ H 00 ⊆ G ]. H 0 , H 00 ∈ H, we have P [ H 0 ∪ H 00 ⊆ G ] = p2`−kH
∩H 00 k
Since H is balanced, ε(H 0 ∩ H 00 ) 6 ε(H) = `/k. With |H 0 ∩ H 00 | =: i this yields kH 0 ∩ H 00 k 6 i`/k, so by 0 6 p 6 1, P [ H 0 ∪ H 00 ⊆ G ] 6 p2`−i`/k .
We have now estimated the individual summands in (7); what does this imply for the sum as a whole? Since (8) depends on the parameter i = |H 0 ∩ H 00 |, we partition the range H2 of the sum in (7) into the subsets © ª Hi2 := (H 0 , H 00 ) ∈ H2 : |H 0 ∩ H 00 | = i , i = 0, . . . , k, and calculate for each Hi2 the corresponding sum X P [ H 0 ∪ H 00 ⊆ G ] Ai := i
by itself. (Here, as below, we use i to denote sums over all pairs (H 0 , H 00 ) ∈ Hi2 .) If i = 0 then H 0 and H 00 are disjoint, so the events H 0 ⊆ G and 00 H ⊆ G are independent. Hence, A0 =
P [ H 0 ∪ H 00 ⊆ G ]
P [ H 0 ⊆ G ] · P [ H 00 ⊆ G ] X P [ H 0 ⊆ G ] · P [ H 00 ⊆ G ] 0
(H 0 ,H 00 ) ∈ H2
³ X
´ ³ X ´ P [ H0 ⊆ G ] · P [ H 00 ⊆ G ]
H 00 ∈ H
= µ2 .
P0 P P00 for H 0 ∈ H and Let us now estimate Ai for i > 1. Writing P P P0 P00 for H 00 ∈ H , we note that i can be written as |H 0 ∩H 00 |=i . For P 0 fixed H 0 (corresponding to the first sum ), the second sum ranges over µ ¶µ ¶ k n−k h i k−i summands: the number of graphs H 00 ∈ H with |H 00 ∩ H 0 | = i. Hence, for all i > 1 and suitable constants c1 , c2 independent of n, X
P [ H 0 ∪ H 00 ⊆ G ] X0 µk ¶µn − k ¶ 6 h p2` p−i`/k i k−i (8) ¶ µ ¶µ ¡ ¢−i`/k n−k k h p2` γ n−k/` = |H| k−i i (2)
Ai =
6 |H| p` c1 nk−i h p` γ −i`/k ni = µ c1 nk h p` γ −i`/k µ ¶ n h p` γ −i`/k 6 µ c2 k (6) (5)
= µ2 c2 γ −i`/k
6 µ2 c2 γ −`/k if γ > 1. By definition of the Ai , this implies with c3 := kc2 that E(X 2 )/µ2 =
and hence
A0 /µ2 +
Ai /µ2
6 1 + c3 γ −`/k
E(X 2 ) − µ2 σ2 = 6 c3 γ −`/k −→ 0 . γ→∞ µ2 µ2
By Lemma 11.4.2, therefore, X > 0 almost surely, i.e. almost all G ∈ G(n, p) have a subgraph isomorphic to H and hence lie in PH . ¤ Theorem 11.4.3 allows us to read off threshold functions for a number of natural graph properties. Corollary 11.4.4. If k > 3, then t(n) = n−1 is a threshold function for the property of containing a k-cycle. ¤ Interestingly, the threshold function in Corollary 11.4.4 is independent of the cycle length k considered: in the evolution of random graphs, cycles of all (constant) lengths appear at about the same time! There is a similar phenomenon for trees. Here, the threshold function does depend on the order of the tree considered, but not on its shape: Corollary 11.4.5. If T is a tree of order k > 2, then t(n) = n−k/(k−1) is a threshold function for the property of containing a copy of T . We finally have the following result for complete subgraphs: Corollary 11.4.6. If k > 2, then t(n) = n−2/(k−1) is a threshold function for the property of containing a K k . Proof . K k is balanced, because ε(K i ) = 12 (i − 1) < 12 (k − 1) = ε(K k ) for ¤ i < k. With ` := kK k k = 12 k(k − 1), we obtain n−k/` = n−2/(k−1) . It is not difficult to adapt the proof of Theorem 11.4.3 to the case 0 that H is unbalanced. The threshold then becomes t(n) = n−1/ε (H) , 0 where ε (H) := max { ε(F ) | F ⊆ H }; see Exercise 22.
Exercises 1.− What is the probability ¡ ¢ that a random graph in G(n, p) has exactly m edges, for 0 6 m 6 n2 fixed? 2.
What is the expected number of edges in G r
G(n, p)? G(n, p)?
What is the expected number of K -subgraphs in G
Characterize the graphs that occur as a subgraph in every graph of sufficiently large average degree.
In the usual terminology of measure spaces (and in particular, of probability spaces), the phrase ‘almost all’ is used to refer to a set of points whose complement has measure zero. Rather than considering a limit of probabilities in G(n, p) as n → ∞, would it not be more natural to define a probability space on the set of all finite graphs (one copy of each) and to investigate properties of ‘almost all’ graphs in this space, in the sense above?
Show that if almost all G ∈ G(n, p) have a graph property P1 and almost all G ∈ G(n, p) have a graph property P2 , then almost all G ∈ G(n, p) have both properties, i.e. have the property P1 ∩ P2 .
7.− Show that, for constant p diameter 2.
(0, 1), almost every graph in G(n, p) has
Show that, for constant p ∈ (0, 1), almost no graph in G(n, p) has a separating complete subgraph.
Derive Proposition 11.3.1 from Lemma 11.3.2.
(i) Show that with probability 1 an infinite random graph G has all the properties Pi,j (i, j ∈ N).
G(ℵ0 , p)
(ii) Show that any two (infinite) graphs having all the properties Pi,j are isomorphic. (Thus, up to isomorphism, there is only one countably infinite random graph.) 11.
Let ² > 0 and p = p(n) > 0, and let r > (1 + ²)(2 ln n)/p be an integervalued function of n. Show that almost no graph in G(n, p) contains r independent vertices.
Show that for every graph H there exists a function p = p(n) such that limn→∞ p(n) = 0 but almost every G ∈ G(n, p) contains an induced copy of H.
13.+ (i) Show that, for every 0 < ² 6 1 and p = (1 − ²)(ln n)n−1 , almost every G ∈ G(n, p) has an isolated vertex. (ii) Find a probability p = p(n) such that almost every G ∈ G(n, p) is disconnected but the expected number of spanning trees of G tends to infinity as n → ∞. (Hint for (ii): A theorem of Cayley states that K n has exactly nn−2 spanning trees.) 14.+ Given r ∈ N, find a c > 0 such that, for p = cn−1 , almost every G ∈ G(n, p) has a K r minor. Can c be chosen independently of r? 15.
Find an increasing graph property without a threshold function, and a property that is not increasing but has a threshold function.
16.− Let H be a graph of order k, and let h denote the number of graphs isomorphic to H on some fixed set of k elements. Show that h 6 k!. For which graphs H does equality hold? 17.− For every k > 1, find a threshold function for { G | ∆(G) > k }. 18.− Given d ∈ N, is there a threshold function for the property of containing a d-dimensional cube (see Ex. 2, Ch. 1)? If so, which; if not, why not? 19.
Show that t(n) = n−1 is also a threshold function for the property of containing any cycle.
Does the property of containing any tree of order k (for k > 2 fixed) have a threshold function? If so, which?
21.+ Given a graph H, let P be the property of containing an induced copy of H. If H is complete then, by Corollary 11.4.6, P has a threshold function. Show that P has no threshold function if H is not complete. 22.+ Prove the following version of Theorem 11.4.3 for unbalanced subgraphs. Let H be any graph with at least one edge, and put ε0 (H) := max { ε(F ) | ∅ = 6 F ⊆ H }. Then the threshold function for PH is 0 t(n) = n−1/ε (H) . (Hint. Imitate the proof of Theorem 11.4.3. Instead of the sets Hi , 2 consider the sets HF := { (H 0 , H 00 ) ∈ H2 | H 0 ∩ H 00 = F }. Replace the distinction between the cases of i = 0 and i > 0 by the distinction between the cases of kF k = 0 and kF k > 0.)
Notes There are a number of monographs and texts on the subject of random graphs. The most comprehensive of these is B. Bollob´ as, Random Graphs, Academic Press 1985. Another advanced but very readable monograph is S. Janson, T. L Ã uczak & A. Ruci´ nski, Topics in Random Graphs, in preparation; this concentrates on areas developed since Random Graphs was published. E.M. Palmer, Graphical Evolution, Wiley 1985, covers material similar to parts of Random Graphs but is written in a more elementary way. Compact introductions going beyond what is covered in this chapter are given by B. Bollob´ as, Graph Theory, Springer GTM 63, 1979, and by M. Karo´ nski, Handbook of Combinatorics (R.L. Graham, M. Gr¨ otschel & L. Lov´ asz, eds.), North-Holland 1995. A stimulating advanced introduction to the use of random techniques in discrete mathematics more generally is given by N. Alon & J.H. Spencer, The Probabilistic Method, Wiley 1992. One of the attractions of this book lies in the way it shows probabilistic methods to be relevant in proofs of entirely deterministic theorems, where nobody would suspect it. Another example for this phenomenon is Alon’s proof of Theorem 5.4.1; see the notes for Chapter 5. The probabilistic method had its first origins in the 1940s, one of its earliest results being Erd˝ os’s probabilistic lower bound for Ramsey numbers (Theorem 11.1.3). Lemma 11.3.2 about the properties Pi,j is taken from Bollob´ as’s Springer text cited above. A very readable rendering of the proof that, for constant p, every first order sentence about graphs is either almost surely true or almost surely false, is given by P. Winkler, Random structures and zero-one laws, in (N.W. Sauer et al., eds.) Finite and Infinite Combinatorics in Sets and Logic (NATO ASI Series C 411), Kluwer 1993. The seminal paper on graph evolution is P. Erd˝ os & A. R´enyi, On the evolution of random graphs, Publ. Math. Inst. Hungar. Acad. Sci. 5 (1960), 17–61. This paper also includes Theorem 11.4.3 and its proof. The generalization of this theorem to unbalanced subgraphs was first proved by Bollob´ as in 1981, using advanced methods; a simple adaptation of the original Erd˝ os-Renyi proof was found by Ruci´ nski & Vince (1986), and is presented in Karo´ nski’s Handbook chapter.
There is another way of defining a random graph G, which is just as natural and common as the model we considered. Rather than choosing the edges of G independently, we choose the entire graph G uniformly at random from among all the graphs on { 0, . . . , n − 1 } that have exactly M = M ¡ N(n) ¢ edges: then each of these graphs occurs with the same probability of M , ¡n¢ where N := 2 . Just as we studied the likely properties of the graphs in G(n, p) for different functions p = p(n), we may investigate how the properties of G in the other model depend on the function M (n). If M is close to pN , the expected number of edges of a graph in G(n, p), then the two models behave very similarly. It is then largely a matter of convenience which of them to consider; see Bollob´ as for details. In order to study threshold phenomena in more detail, one often considers the following random graph process: starting with a K n as stage zero, one chooses additional edges one by one (uniformly at random) until the graph is complete. This is a simple example of a Markov chain, whose M th stage corresponds to the ‘uniform’ random graph model described above. A survey about threshold phenomena in this setting is given by T. L Ã uczak, The phase transition in a random graph, in (D. Mikl´ os, V.T. S´ os & T. Sz˝ onyi, eds.) Paul Erd˝ os is 80, Vol. 2, Proc. Colloq. Math. Soc. J´ anos Bolyai (1996).
Minors, Trees, and WQO
Our goal in this last chapter is a single theorem, one which dwarfs any other result in graph theory and may doubtless be counted among the deepest theorems that mathematics has to offer: in every infinite set of graphs there are two such that one is a minor of the other. This graph minor theorem (or minor theorem for short), inconspicuous though it may look at first glance, has made a fundamental impact both outside graph theory and within. Its proof, due to Neil Robertson and Paul Seymour, takes well over 500 pages. So we have to be modest: of the actual proof of the minor theorem, this chapter will convey only a very rough impression. However, as with most truly fundamental results, the proof has sparked off the development of methods of quite independent interest and potential. This is true particularly for the use of tree-decompositions, a technique we shall meet in Sections 12.3 and 12.4. Section 12.1 gives an introduction to wellquasi-ordering, a concept central to the minor theorem. In Section 12.2 we apply this concept to prove the minor theorem for trees. The chapter finishes with an overview in Section 12.5 of the proof of the general graph minor theorem, and of some of its immediate consequences.
12.1 Well-quasi-ordering A reflexive and transitive relation is called a quasi-ordering. A quasiordering 6 on X is a well-quasi-ordering, and the elements of X are well-quasi-ordered by 6, if for every infinite sequence x0 , x1 , . . . in X
well-quasiordering
252 good pair good/bad sequence
12. Minors, Trees, and WQO
there are indices i < j such that xi 6 xj . Then (xi , xj ) is a good pair of this sequence. A sequence containing a good pair is a good sequence; thus, a quasi-ordering on X is a well-quasi-ordering if and only if every infinite sequence in X is good. An infinite sequence is bad if it is not good. Proposition 12.1.1. A quasi-ordering 6 on X is a well-quasi-ordering if and only if X contains neither an infinite antichain nor an infinite strictly decreasing sequence x0 > x1 > . . ..
Proof . The forward implication is trivial. Conversely, let x0 , x1 , . . . be any infinite sequence in X. Let K be the complete graph on N = { 0, 1, . . . }. Colour the edges ij (i < j) of K with three colours: green if xi 6 xj , red if xi > xj , and amber if xi , xj are incomparable. By Ramsey’s theorem (9.1.2), K has an infinite induced subgraph whose edges all have the same colour. If there is neither an infinite antichain nor an infinite strictly decreasing sequence in X, then this colour must be green, i.e. x0 , x1 , . . . has an infinite subsequence in which every pair is good. In particular, the sequence x0 , x1 , . . . is good. ¤ In the proof of Proposition 12.1.1, we showed more than was needed: rather than finding a single good pair in x0 , x1 , . . ., we found an infinite increasing subsequence. We have thus shown the following: Corollary 12.1.2. If X is well-quasi-ordered, then every infinite sequence in X has an infinite increasing subsequence. ¤
The following lemma, and the idea of its proof, are fundamental to the theory of well-quasi-ordering. Let 6 be a quasi-ordering on a set X. For finite subsets A, B ⊆ X, write A 6 B if there is an injective mapping f : A → B such that a 6 f (a) for all a ∈ A. This naturally extends 6 to a quasi-ordering on [X]
Lemma 12.1.3. If X is well-quasi-ordered by 6, then so is [X]
Proof . Suppose that 6 is a well-quasi-ordering on X but not on [X]< n, and that there exists a bad sequence in [X]
12.1 Well-quasi-ordering
By Corollary 12.1.2, the sequence (an )n ∈ N has an infinite increasing subsequence (ani )i ∈ N . By the minimal choice of An0 , the sequence A0 , . . . , An0 −1 , Bn0 , Bn1 , Bn2 , . . . is good; consider a good pair. Since (An )n ∈ N is bad, this pair cannot have the form (Ai , Aj ) or (Ai , Bj ), as Bj 6 Aj . So it has the form (Bi , Bj ). Extending the injection Bi → Bj by ai 7→ aj , we deduce again ¤ that (Ai , Aj ) is good, a contradiction.
12.2 The graph minor theorem for trees The minor theorem can be expressed by saying that the finite graphs are well-quasi-ordered by the minor relation 4. Indeed, by Proposition 12.1.1 and the obvious fact that no strictly descending sequence of minors can be infinite, being well-quasi-ordered is equivalent to the non-existence of an infinite antichain, the formulation used earlier. In this section, we prove a strong version of the graph minor theorem for trees: Theorem 12.2.1. (Kruskal 1960) The finite trees are well-quasi-ordered by the topological minor relation. We shall base the proof of Theorem 12.2.1 on the following notion of an embedding between rooted trees, which strengthens the usual embedding as a topological minor. Consider two trees T and T 0 , with roots r and r0 say. Let us write T 6 T 0 if there exists an isomorphism ϕ, from some subdivision of T to a subtree T 00 of T 0 , that preserves the tree-order on V (T ) associated with T and r. (Thus if x < y in T then ϕ(x) < ϕ(y) in T 0 ; see Fig. 12.2.1.) As one easily checks, this is a quasi-ordering on the class of all rooted trees.
ϕ(r)
ϕ T r
T0 r0
Fig. 12.2.1. An embedding of T in T 0 showing that T 6 T 0
T 6 T0
254 (12.1.3)
Tn rn An
A Tk n(k)
Proof of Theorem 12.2.1. We show that the rooted trees are wellquasi-ordered by the relation 6 defined above; this clearly implies the theorem. Suppose not. To derive a contradiction, we proceed as in the proof of Lemma 12.1.3. Given n ∈ N, assume inductively that we have chosen a sequence T0 , . . . , Tn−1 of rooted trees such that some bad sequence of rooted trees starts with this sequence. Choose as Tn a minimum-order rooted tree such that some bad sequence starts with T0 , . . . , Tn . For each n ∈ N, denote the root of Tn by rn . Clearly, (Tn )n ∈ N is a bad sequence. For each n, let An denote the set of components of Tn − rn , made into rooted trees by choosing the neighbours of rn as their roots. Note that the tree-orderSof these trees is that induced by Tn . Let us prove that the set A := n ∈ N An of all these trees is well-quasi-ordered. Let (T k )k ∈ N be any sequence of trees in A. For every k ∈ N choose an n = n(k) such that T k ∈ An . Pick a k with smallest n(k). Then T0 , . . . , Tn(k)−1 , T k , T k+1 , . . . is a good sequence, by the minimal choice of Tn(k) and T k $ Tn(k) . Let (T, T 0 ) be a good pair of this sequence. Since (Tn )n ∈ N is bad, T cannot be among the first n(k) members T0 , . . . , Tn(k)−1 of our sequence: then T 0 would be some T i with i > k, i.e. T 6 T 0 = T i 6 Tn(i) ;
i, j
since n(k) 6 n(i) by the choice of k, this would make (T, Tn(i) ) a good pair in the bad sequence (Tn )n ∈ N . Hence (T, T 0 ) is a good pair also in (T k )k ∈ N , completing the proof that A is well-quasi-ordered. By Lemma 12.1.3,1 the sequence (An )n ∈ N in [A]
Any readers worried that we might need the lemma for sequences or multisets rather than just sets here, please note that isomorphic elements of An are not identified: we always have |An | = d(rn ).
12.3 Tree-decompositions
12.3 Tree-decompositions Trees are graphs with some very distinctive and fundamental properties; consider Theorem 1.5.1 and Corollary 1.5.2, or the more sophisticated example of Kruskal’s theorem. It is therefore legitimate to ask to what degree those properties can be transferred to more general graphs, graphs that are not themselves trees but tree-like in some sense.2 In this section, we study a concept of tree-likeness that permits generalizations of all the tree properties referred to above (including Kruskal’s theorem), and which plays a crucial role in the proof of the graph minor theorem. Let G be a graph, T a tree, and let V = (Vt )t ∈ T be a family of vertex sets Vt ⊆ V (G) indexed by the vertices t of T . The pair (T, V) is called a tree-decomposition of G if it satisfies the following three conditions: treeS decomposition (T1) V (G) = t ∈ T Vt ; (T2) for every edge e lie in Vt ;
G there exists a t
(T3) Vt1 ∩ Vt3 ⊆ Vt2 whenever t1 , t2 , t3
T such that both ends of e
T satisfy t2
∈ t1 T t3 .
Conditions (T1) and (T2) together say that G is the union of the subgraphs G [ Vt ]; we call these subgraphs and the sets Vt themselves the parts of (T, V) and say that (T, V) is a tree-decomposition of G into these parts. Condition (T3) implies that the parts of (T, V) are organized roughly like a tree (Fig. 12.3.1).
Vt3 ? t3
e?
? t2
G Fig. 12.3.1. Edges and parts ruled out by (T2) and (T3)
Before we discuss the role that tree-decompositions play in the proof of the minor theorem, let us note some of their basic properties. Consider a fixed tree-decomposition (T, V) of G, with V = (Vt )t ∈ T as above. Perhaps the most important feature of a tree-decomposition is that it transfers the separation properties of its tree to the graph decomposed: 2 What exactly this ‘sense’ should be will depend both on the property considered and on its intended application.
(T, V), Vt
Lemma 12.3.1. Let t1 t2 be any edge of T and let T1 , T2 be the com∈ ∈ ponents S of T − t1 t2 , with t1 S T1 and t2 T2 . Then Vt1 ∩ Vt2 separates U1 := t ∈ T1 Vt from U2 := t ∈ T2 Vt in G (Fig. 12.3.2).
T2 T1 U1
t1 Vt1 ∩ Vt2
Fig. 12.3.2. Vt1 ∩ Vt2 separates U1 from U2 in G
Proof . Both t1 and t2 lie on every t–t0 path in T with t ∈ T1 and t0 ∈ T2 . Therefore U1 ∩ U2 ⊆ Vt1 ∩ Vt2 by (T3), so all we have to show is that G has no edge u1 u2 with u1 ∈ U1 r U2 and u2 ∈ U2 r U1 . If u1 u2 is such an edge, then by (T2) there is a t ∈ T with u1 , u2 ∈ Vt . By the choice of u1 and u2 we have neither t ∈ T2 nor t ∈ T1 , a contradiction. ¤ Note that tree-decompositions are passed on to subgraphs: [ 12.4.2 ]
¡ ¢ Lemma 12.3.2. For every H ⊆ G, the pair T, (Vt ∩ V (H))t ∈ T is a tree-decomposition of H. ¤ Similarly for contractions: Lemma 12.3.3. Suppose that G is h ∈ V (H). Let f : V (G) → V (H) be tex of G the index of the branch set Wt := { f (v) | v ∈ Vt }, and put W := decomposition of H.
an M H with branch sets Uh , the map assigning to each vercontaining it. For all t ∈ T let (Wt )t ∈ T . Then (T, W) is a tree-
Proof . The assertions (T1) and (T2) for (T, W) follow immediately from the corresponding assertions for (T, V). Now let t1 , t2 , t3 ∈ T be as in (T3), and consider a vertex h ∈ Wt1 ∩ Wt3 of H; we show that h ∈ Wt2 . By definition of Wt1 and Wt3 , there are vertices v1 ∈ Vt1 ∩ Uh and v3 ∈ Vt3 ∩ Uh . Since Uh is connected in G and Vt2 separates v1 from v3 in G by Lemma 12.3.1, Vt2 has a vertex in Uh . By definition of Wt2 , this implies h ∈ Wt2 . ¤ Here is another useful consequence of Lemma 12.3.1:
Lemma 12.3.4. Given a set W ⊆ V (G), there is either a t ∈ T such that W ⊆ Vt , or there are vertices w1 , w2 ∈ W and an edge t1 t2 ∈ T such that w1 , w2 lie outside the set Vt1 ∩ Vt2 and are separated by it in G. Proof . Let us orient the edges of T as follows. For each edge t1 t2 ∈ T , define U1 , U2 as in Lemma 12.3.1; then Vt1 ∩ Vt2 separates U1 from U2 . If Vt1 ∩ Vt2 does not separate any two vertices of W that lie outside it, we can find an i ∈ { 1, 2 } such that W ⊆ Ui , and orient t1 t2 towards ti . Let t be the last vertex of a maximal directed path in T ; we claim that W ⊆ Vt . Given w ∈ W , let t0 ∈ T be such that w ∈ Vt0 . If t0 6= t, then the edge e at t that separates t0 from t in T is directed towards t, so w also lies in Vt00 for some t00 in the component of T − e containing t. ¤ Therefore w ∈ Vt by (T3). The following special case of Lemma 12.3.4 is used particularly often: Lemma 12.3.5. Any complete subgraph of G is contained in some part of (T, V). ¤ As indicated by Figure 12.3.1, the parts of (T, V) reflect the structure of the tree T , so in this sense the graph G decomposed resembles a tree. However, this is valuable only inasmuch as the structure of G within each part is negligible: the smaller the parts, the closer the resemblance. This observation motivates the following definition. The width of (T, V) is the number © ª max |Vt | − 1 : t ∈ T , and the tree-width tw(G) of G is the least width of any tree-decomposition of G. As one easily checks,3 trees themselves have tree-width 1. By Lemmas 12.3.2 and 12.3.3, the tree-width of a graph will never be increased by deletion or contraction: Proposition 12.3.6. If H 4 G then tw(H) 6 tw(G).
Graphs of bounded tree-width are sufficiently similar to trees that it becomes possible to adapt the proof of Kruskal’s theorem to the class of these graphs; very roughly, one has to iterate the ‘minimal bad sequence’ argument from the proof of Lemma 12.1.3 tw(G) times. This takes us a step further towards a proof of the graph minor theorem: Theorem 12.3.7. (Robertson & Seymour 1990) For every integer k > 0, the graphs of tree-width < k are well-quasiordered by the minor relation. 3 Indeed the ‘−1’ in the definition of width serves no other purpose than to make this statement true.
tree-width tw(G)
touch bramble cover order
In order to make use of Theorem 12.3.7 for a proof of the general minor theorem, we should be able to say something about the graphs it does not cover, i.e. to deduce some information about a graph from the assumption that its tree-width is large. Our next theorem achieves just that: it identifies a canonical obstruction to small tree-width, a structural phenomenon that occurs in a graph if and only if its tree-width is large. Let us say that two subsets of V (G) touch if they have a vertex in common or G contains an edge between them. A set of mutually touching connected vertex sets in G is a bramble. Extending our terminology of Chapter 2.1, we say that a subset of V (G) covers (or is a cover of) a bramble B if it meets every element of B. The least number of vertices covering a bramble is the order of that bramble. The following simple observation will be useful: Lemma 12.3.8. Any set of vertices separating two covers of a bramble also covers that bramble. Proof . Since each set in the bramble is connected and meets both of the covers, it also meets any set separating these covers. ¤
A typical example of a bramble is the set of crosses in a grid. The k × k grid is the graph on { 1, . . . , k }2 with the edge set { (i, j)(i0 , j 0 ) : |i − i0 | + |j − j 0 | = 1 } . The crosses of this grid are the k2 sets Cij := { (i, `) | ` = 1, . . . , k } ∪ { (`, j) | ` = 1, . . . , k } . Thus, the cross Cij is the union of the grid’s ith column and its jth row. Clearly, the crosses of the k × k grid form a bramble of order k: they are covered by any row or column, while any set of fewer than k vertices misses both a row and a column, and hence a cross. The following result is sometimes called the tree-width duality theorem: Theorem 12.3.9. (Seymour & Thomas 1993) Let k > 0 be an integer. A graph has tree-width > k if and only if it contains a bramble of order > k.
Proof . For the backward implication, let B be any bramble in a graph G. We show that every tree-decomposition (T, (Vt )t ∈ T ) of G has a part that meets every set in B. As in the proof of Lemma 12.3.4 we start by orienting the edges t1 t2 of T . If X := Vt1 ∩ Vt2 meets every B ∈ B, we are done. If not, then
for each B disjoint from X there is an i ∈ { 1, 2 } such that B ⊆ Ui r X (defined as in Lemma 12.3.1); recall that B is connected. Moreover, this i is the same for all such B, because they touch. We now orient the edge t1 t2 towards ti . If every edge of T is oriented in this way and t is the last vertex of a maximal directed path in T , then Vt meets every set in B—just as in the proof of Lemma 12.3.4. To prove the forward direction, we now assume that G contains no bramble of order > k. We show that for every bramble B in G there is a B-admissible tree-decomposition of G, one in which any part of order > k fails to cover B. For B = ∅ this implies that tw(G) < k, because every set covers the empty bramble. Let B be given, and assume inductively that for every bramble B 0 with more sets than B there is a B0 -admissible tree-decomposition of G. (The induction starts, since no bramble in G has more than 2|G| sets.) Let X ⊆ V (G) be a cover of B with as few vertices as possible; then ` := |X| 6 k is the order of B. Our aim is to show the following: For every component C of G − X there exists a B-admissible tree-decomposition of G [ X ∪ V (C) ] with X as a part.
X `
Then these tree-decompositions can be combined to a B-admissible treedecomposition of G by identifying their nodes corresponding to X. (If X = V (G), then the tree-decomposition with X as its only part is Badmissible.) So let C be a fixed component of G − X, write H := G [ X ∪ V (C) ], and put B0 := B ∪ { C }. If B0 is not a bramble then C fails to touch some element of B, and hence Y := V (C) ∪ N (C) does not cover B. Then the tree-decomposition of H consisting of the two parts X and Y satisfies (∗). So we may assume that B0 is a bramble. Since X covers B but not B 0 , we have |B0 | > |B|. Our induction hypothesis therefore ensures that G has a B 0 -admissible tree-decomposition (T, (Vt )t ∈ T ). If this decomposition is also B-admissible, there is nothing more to show. If not, then one of its parts of order > k, Vs say, covers B. Since no set of fewer than ` vertices covers B, Lemma 12.3.8 implies with Menger’s theorem (3.3.1) that Vs and X are linked by ` disjoint paths P1 , . . . , P` . As Vs fails to cover B 0 and hence lies in G − C, the paths Pi meet H only in their ends xi ∈ X. For each i = 1, . . . , ` pick a ti ∈ T with xi ∈ Vti , and let Wt := (Vt ∩ (X ∪ V (C))) ∪ { xi | t
Badmissible
sT ti } ;
for all t ∈ T (Fig. 12.3.3). Then (T, (Wt )t ∈ T ) is the tree-decomposition which (T, (Vt )t ∈ T ) induces on H (cf. Lemma 12.3.2), except that a few
C, H B0
T, (Vt )t ∈ T s Pi xi ti
Vt0 x1
Vt2 x2 x3
Vt3 Vt
Vs Fig. 12.3.3. Wt contains x2 and x3 but not x1 ; Wt0 contains no xi
xi have been added to some of the parts. Despite these additions, we still have |Wt | 6 |Vt | for all t: for each xi ∈ Wt r Vt we have t ∈ sT ti , so Vt contains some other vertex of Pi (Lemma 12.3.1); that vertex does not lie in Wt , because Pi meets H only in xi . Moreover, (T, (Wt )t ∈ T ) clearly satisfies (T3), because each xi is added to every part along some path in T , so it is again a tree-decomposition. As Ws = X, all that is left to show for (∗) is that this decomposition is B-admissible. Consider any Wt of order > k. Then Wt meets C, because |X| = ` 6 k. Since (T, (Vt )t ∈ T ) is B 0 -admissible and |Vt | > |Wt | > k, we know that Vt fails to meet some B ∈ B; let us show that Wt does not meet this B either. If it does, it must do so in some xi ∈ Wt r Vt . Then B is a connected set meeting both Vs and Vti but not Vt . As t ∈ sT ti by definition of Wt , this contradicts Lemma 12.3.1. ¤ Often, Theorem 12.3.9 is stated in terms of the bramble number of a graph, the largest order of any bramble in it. The theorem then says that the tree-width of a graph is exactly one less than its bramble number (Exercise 15). How useful even the easy backward direction of Theorem 12.3.9 can be is exemplified once more by our example of the crosses bramble in the k × k grid: this bramble has order k, so by the theorem the k × k grid has tree-width at least k − 1. (Try to show this without the theorem!) In fact, the k × k grid has tree-width k (Exercise 16). But more important than its precise value is the fact that the tree-width of grids tends to infinity with their size. For as we shall see, large grid minors pose another canonical obstruction to small tree-width: not only do large grids (and hence all graphs containing large grids as minors; cf. Proposition 12.3.6) have large tree-width, but conversely every graph of large tree-width has a large grid minor (Theorem 12.4.4). Yet another canonical obstruction to small tree-width is described in Exercise 30.
Given any two vertices t1 , t2 ∈ T , Lemma 12.3.1 implies that every Vt with t ∈ t1 T t2 separates Vt1 from Vt2 in G. Let us call our treedecomposition (T, V) of G linked , or lean,4 if it satisfies the following condition:
linked/lean
(T4) given any s ∈ N and t1 , t2 ∈ T , either G contains s disjoint Vt1 –Vt2 paths or there exists a t ∈ t1 T t2 such that |Vt | < s. The ‘branches’ in a lean tree-decomposition are thus stripped of any bulk not necessary to maintain their connecting qualities: if a branch is thick (the parts along a path in T large), then G is highly connected along this branch. In our quest for tree-decompositions into ‘small’ parts, we now have two criteria to choose between: the global ‘worst case’ criterion of width, which ensures that T is nontrivial (unless G is complete) but says nothing about the tree-likeness of G among parts other than the largest, and the more subtle local criterion of leanness, which ensures tree-likeness everywhere along T but might be difficult to achieve except with trivial or near-trivial T . Surprisingly, though, it is always possible to find a tree-decomposition that is optimal with respect to both criteria at once: Theorem 12.3.10. (Thomas 1990) Every graph G has a lean tree-decomposition of width tw(G). The proof of Theorem 12.3.10 is not too long but technical, and we shall not present it. The fact that this theorem gives us a very useful property of minimum-width tree-decompositions ‘for free’ has made it a valuable tool wherever tree-decompositions are applied. The tree-decomposition (T, V) of G is called simplicial if all the separators Vt1 ∩ Vt2 induce complete subgraphs in G. This assumption can enable us to lift assertions about the parts of the decomposition to G itself. For example, if all the parts in a simplicial tree-decomposition of G are k-colourable, then so is G (proof?). The same applies to the property of not containing a K r minor for some fixed r. Algorithmically, it is easy to obtain a simplicial tree-decomposition of a given graph into irreducible parts. Indeed, all we have to do is split the graph recursively along complete separators; if these are always chosen minimal, then the set of parts obtained will even be unique (Exercise 22). Conversely, if G can be constructed recursively from a set H of graphs by pasting along complete subgraphs, then G has a simplicial tree-decomposition into elements of H. For example, by Wagner’s Theorem 8.3.4, any graph without a K 5 minor has a supergraph with a simplicial tree-decomposition into plane triangulations and copies of the 4
depending on which of the two dual aspects of (T4) we wish to emphasize
simplicial
Wagner graph W , and similarly for graphs without K 4 minors (see Proposition 12.4.2). Tree-decompositions may thus lead to intuitive structural characterizations of graph properties. A particularly simple example is the following characterization of chordal graphs: [ 12.4.2 ]
Proposition 12.3.11. G is chordal if and only if G has a tree-decomposition into complete parts.
Proof . We apply induction on |G|. We first assume that G has a treedecomposition (T, V) such that G [ Vt ] is complete for every t ∈ T ; let us choose (T, V) with |T | minimal. If |T | 6 1, then G is complete and hence chordal. So let t1 t2 ∈ T be an edge, and for i = 1, 2 define Ti and Gi := G [ Ui ] as in Lemma 12.3.1. Then G = G1 ∪ G2 by (T1) and (T2), and V (G1 ∩ G2 ) = Vt1 ∩ Vt2 by the lemma; thus, G1 ∩ G2 is complete. Since (Ti , (Vt )t ∈ Ti ) is a tree-decomposition of Gi into complete parts, both Gi are chordal by the induction hypothesis. (By the choice of (T, V), neither Gi is a subgraph of G [ Vt1 ∩ Vt2 ] = G1 ∩ G2 , so both Gi are indeed smaller than G.) Since G1 ∩ G2 is complete, any induced cycle in G lies in G1 or in G2 and hence has a chord, so G too is chordal. Conversely, assume that G is chordal. If G is complete, there is nothing to show. If not then, by Proposition 5.5.1, G is the union of smaller chordal graphs G1 , G2 with G1 ∩ G2 complete. By the induction hypothesis, G1 and G2 have tree-decompositions (T1 , V1 ) and (T2 , V2 ) into complete parts. By Lemma 12.3.5, G1 ∩ G2 lies inside one of those parts in each case, say with indices t1 ∈ T1 and t2 ∈ T2 . As one easily checks, ((T1 ∪ T2 ) + t1 t2 , V1 ∪ V2 ) is a tree-decomposition of G into complete parts. ¤ © ª Corollary 12.3.12. tw(G) = min ω(H) − 1 | G ⊆ H; H chordal . Proof . By Lemma 12.3.5 and Proposition 12.3.11, each of the graphs H considered for the minimum has a tree-decomposition of width ω(H) − 1. Every such tree-decomposition induced one of G by Lemma 12.3.2, so tw(G) 6 ω(H) − 1 for every H. Conversely, let us construct an H as above with ω(H) − 1 6 tw(G). ∈ Let (T, V) be a tree-decomposition of G of width tw(G). S For every t T let Kt denote the complete graph on Vt , and put H := t ∈ T Kt . Clearly, (T, V) is also a tree-decomposition of H. By Proposition 12.3.11, H is chordal, and by Lemma 12.3.5, ω(H) − 1 is at most the width of (T, V), i.e. at most tw(G). ¤
12.4 Tree-width and forbidden minors
12.4 Tree-width and forbidden minors If H is any set or class of graphs, then the class Forb4 (H) := { G | G 6< H for all H
H}
of all graphs without a minor in H is a graph property, i.e. is closed under isomorphism.5 When it is written as above, we say that this property is expressed by specifying the graphs H ∈ H as forbidden (or excluded ) minors. By Proposition 1.7.3, Forb4 (H) is closed under taking minors: if G0 4 G ∈ Forb4 (H) then G0 ∈ Forb4 (H). Graph properties that are closed under taking minors will be called hereditary in this chapter. Every hereditary property can in turn be expressed by forbidden minors:
Forb4 (H)
forbidden minors (1.7.3) hereditary
Proposition 12.4.1. A graph property P can be expressed by forbidden minors if and only if it is hereditary.
Proof . For the ‘if’ part, note that P = Forb4 (P), where P is the complement of P. ¤
In Section 12.5, we shall return to the general question of how a given hereditary property is best represented by forbidden minors. In this section, we are interested in one particular type of hereditary property: bounded tree-width. Thus, let us consider the property of having tree-width less than some given integer k. By Propositions 12.3.6 and 12.4.1, this property can be expressed by forbidden minors. Choosing their set H as small as possible, we find that H = { K 3 } for k = 2: the graphs of tree-width < 2 are precisely the forests. For k = 3, we have H = { K 4 }: Proposition 12.4.2. A graph has tree-width < 3 if and only if it has no K 4 minor. Proof . By Lemma 12.3.5, we have tw(K 4 ) > 3. By Proposition 12.3.6, therefore, a graph of tree-width < 3 cannot contain K 4 as a minor. Conversely, let G be a graph without a K 4 minor; we assume that |G| > 3. Add edges to G until the graph G0 obtained is edge-maximal without a K 4 minor. By Proposition 8.3.1, G0 can be constructed recursively from triangles by pasting along K 2 s. By induction on the number of recursion steps and Lemma 12.3.5, every graph constructible in this way has a tree-decomposition into triangles (as in the proof of Proposition 12.3.11). Such a tree-decomposition of G0 has width 2, and by Lemma 12.3.2 it is also a tree-decomposition of G. ¤ 5
As usual, we abbreviate Forb4 ({ H }) to Forb4 (H).
(8.3.1) (12.3.2) (12.3.5) (12.3.11)
A question converse to the above is to ask for which H (other than K 3 and K 4 ) the tree-width of the graphs in Forb4 (H) is bounded. Interestingly, it is not difficult to show that any such H must be planar. Indeed, as all grids and their minors are planar (why?), every class Forb4 (H) with non-planar H contains all grids; yet as we saw after Theorem 12.3.9, the grids have unbounded tree-width. The following deep and surprising theorem says that, conversely, the tree-width of the graphs in Forb4 (H) is bounded for every planar H: Theorem 12.4.3. (Robertson & Seymour 1986) Given a graph H, the graphs without an H minor have bounded treewidth if and only if H is planar. The rest of this section is devoted to the proof of Theorem 12.4.3. To prove Theorem 12.4.3 we have to show that forbidding any planar graph H as a minor bounds the tree-width of a graph. In fact, we only have to show this for the special cases when H is a grid, because every planar graph is a minor of some grid. (To see this, take a drawing of the graph, fatten its vertices and edges, and superimpose a sufficiently fine plane grid.) It thus suffices to show the following: Theorem 12.4.4. (Robertson & Seymour 1986) For every integer r there is an integer k such that every graph of treewidth at least k has an r × r grid minor.
externally k-connected
Our proof of Theorem 12.4.4, which is much shorter than the original proof, proceeds as follows. Let r be given, and let G be any graph of large enough tree-width (depending on r). We first show that G contains a large family A = { A1 , . . . , Am } of disjoint connected vertex sets such that each pair Ai , Aj ∈ A can be linked in G by a family Pij of many disjoint Ai –Aj paths avoiding all the other sets in A. We then consider all the pairs (Pij , Pi0 j 0 ) of these path families. If we can find a pair among these such that many of the paths in Pij meet many of the paths in Pi0 j 0 , we shall think of the paths in Pij as horizontal and the paths in Pi0 j 0 as vertical and extract a subdivision of an r × r grid from their union. (This will be the difficult part of the proof, because these paths will in general meet in a less orderly way than they do in a grid.) If not, then for every pair (Pij , Pi0 j 0 ) many of the paths in Pij avoid many of the paths in Pi0 j 0 . We can then select one path Pij ∈ Pij from each family so that these selected paths are pairwise disjoint. Contracting each of the connected sets A ∈ A will then give us a K m minor in G, which contains the desired r × r grid if m > r2 . To implement these ideas formally, we need a few definitions. Let us call a set X ⊆ V (G) externally k-connected in G if |X| ≥ k and for all disjoint subsets Y, Z ⊆ X with |Y | = |Z| ≤ k there are |Y | disjoint
Y –Z paths in G that have no inner vertex or edge in G [ X ]. Note that the vertex set of a k-connected subgraph of G need not be externally k-connected in G. On the other hand, any horizontal path in the r × r grid is externally k-connected in that grid for every k 6 r. (How?) One of the first things we shall prove below is that any graph of large enough tree-width—not just grids—contains a large externally kconnected set of vertices (Lemma 12.4.5). Conversely, it is easy to show that large externally k-connected sets (with k large) can exist only in graphs of large tree-width (Exercise 30). So, like large grid minors, these sets form a canonical obstruction to small tree-width: they can be found in a graph if and only if its tree-width is large. An ordered pair (A, B) of subgraphs of G will be called a premesh in G if G = A ∪ B and A contains a tree T such that
premesh
(i) T has maximum degree ≤ 3; (ii) every vertex of A ∩ B lies in T and has degree ≤ 2 in T ; (iii) T has a leaf in A ∩ B, or |T | = 1 and T ⊆ A ∩ B. The order of such a premesh is the number |A ∩ B|, and if V (A ∩ B) is externally k-connected in B then this premesh is a k-mesh in G.
order k-mesh
Lemma 12.4.5. Let G be a graph and let h ≥ k ≥ 1 be integers. If G contains no k-mesh of order h then G has tree-width < h + k − 1. Proof . We may assume that G is connected. Let U ⊆ V (G) be maximal such that G [ U ] has a tree-decomposition D of width < h + k − 1 with the additional property that, for every component C of G − U , the ˜ is a premesh neighbours of C in U lie in one part of D and (G − C, C) ˜ of order ≤ h, where C := G [ V (C) ∪ N (C) ]. Clearly, U 6= ∅. We claim that U = V (G). Suppose not. Let C be a component of G − U , put X := N (C), and let T be a tree associated with the premesh ˜ (G − C, C). By assumption, |X| ≤ h; let us show that equality holds here. If not, let u ∈ X be a leaf of T (respectively { u } := V (T )) as in (iii), and let v ∈ C be a neighbour of u. Put U 0 := U ∪ { v } and X 0 := X ∪ { v }, let T 0 be the tree obtained from T by joining v to u, and let D0 be the tree-decomposition of G [ U 0 ] obtained from D by adding X 0 as a new part (joined to a part of D containing X, which exists by our choice of U ; see Fig. 12.4.1). Clearly D0 still has width < h + k − 1. Consider a component C 0 of G − U 0 . If C 0 ∩ C = ∅ then C 0 is also a component of G − U , so N (C 0 ) lies inside a part of D (and hence of D0 ), and (G − C 0 , C˜ 0 ) is a premesh of order ≤ h by assumption. If C 0 ∩ C 6= ∅, then C 0 ⊆ C and N (C 0 ) ⊆ X 0 . Moreover, v ∈ N (C 0 ): otherwise N (C 0 ) ⊆ X would separate C 0 from v, contradicting the fact that C 0 and v lie in the same component C of G − X. Since v is a leaf of T 0 , it is straightforward to
U D
˜ C C X T
C C0
U u T
Fig. 12.4.1. Extending U and D when |X| < h
k0 S Ps
check that (G − C 0 , C˜ 0 ) is again a premesh of order ≤ h, contrary to the maximality of U . ˜ cannot Thus |X| = h, so by assumption our premesh (G − C, C) be a k-mesh; let Y, Z ⊆ X be sets to witness this. Let P be a set of as many disjoint Y –Z paths in H := G [ V (C) ∪ Y ∪ Z ] − E(G [ Y ∪ Z ]) ˜ we have as possible. Since all these paths are ‘external’ to X in C, 0 k := |P| < |Y | = |Z| 6 k by the choice of Y and Z. By Menger’s theorem (3.3.1), Y and Z are separated in H by a set S of k 0 vertices. Clearly, S has exactly one vertex on each path in P; we denote the path containing the vertex s ∈ S by Ps (Fig. 12.4.2). H Ps Y
T0 s
U C0 X Fig. 12.4.2. S separates Y from Z in H
Let X 0 := X ∪ S and U 0 := U ∪ S, and let D0 be the treedecomposition of G [ U 0 ] obtained from D by adding X 0 as a new part. Clearly, |X 0 | ≤ |X| + |S| ≤ h + k − 1. We show that U 0 contradicts the maximality of U . Since Y ∪ Z ⊆ N (C) and |S| < |Y | = |Z| we have S ∩ C 6= ∅, so U 0 is larger than U . Let C 0 be a component of G − U 0 . If C 0 ∩ C = ∅, we argue as earlier. So C 0 ⊆ C and N (C 0 ) ⊆ X 0 . As before, C 0 has at least one neighbour v in S ∩ C, since X cannot separate C 0 ⊆ C from S ∩ C. By definition of S, C 0 cannot have neighbours in both Y \ S
and Z \ S; we assume it has none in Y \ S. Let T 0 be the union of T and all the Y –S subpaths of paths Ps with s ∈ N (C 0 ) ∩ C; since these subpaths start in Y \ S and have no inner vertices in X 0 , they cannot meet C 0 . Therefore (G − C 0 , C˜ 0 ) is a premesh with tree T 0 and leaf v; the degree conditions on T 0 are easily checked. Its order is |N (C 0 )| ≤ |X| − |Y | + |S| = h − |Y | + k 0 < h, a contradiction to the maximality of U . ¤ Lemma 12.4.6. Let k ≥ 2 be an integer. Let T be a tree of maximum degree 6 3 and X ⊆ V (T ). Then T has a set F of edges such that every component of T − F has between k and 2k − 1 vertices in X, except that one such component may have fewer vertices in X. Proof . We apply induction on |X|. If |X| ≤ 2k − 1 we put F = ∅. So assume that |X| ≥ 2k. Let e be an edge of T such that some component T 0 of T − e has at least k vertices in X and |T 0 | is as small as possible. As ∆(T ) ≤ 3, the end of e in T 0 has degree at most two in T 0 , so the minimality of T 0 implies that |X ∩ V (T 0 )| ≤ 2k − 1. Applying the ¤ induction hypothesis to T − T 0 we complete the proof. Lemma 12.4.7. Let G be a bipartite graph with bipartition (A, B), |A| = a, |B| = b, and let c ≤ a and d ≤ b be positive integers. Assume that G has at most (a − c)(b − d)/d edges. Then there exist C ⊆ A and D ⊆ B such that |C| = c and |D| = d and C ∪ D is independent in G. Proof . As ||G|| ≤ (a − c)(b − d)/d, fewer than b − d vertices in B have more than (a − c)/d neighbours in A. Choose D ⊆ B so that |D| = d and each vertex in D has at most (a − c)/d neighbours in A. Then D sends a total of at most a − c edges to A, so A has a subset C of c vertices without a neighbour in D. ¤ Given a tree T , call an r-tuple (x1 , . . . , xr ) of distinct vertices of T good if, for every j = 1, . . . , r − 1, the xj –xj+1 path in T contains none of the other vertices in this r-tuple. Lemma 12.4.8. Every tree T of order at least r(r − 1) contains a good r-tuple of vertices. Proof . Pick a vertex x ∈ T . Then T is the union of its subpaths xT y, where y ranges over its leaves. Hence unless one of these paths has at least r vertices, T has at least |T |/(r − 1) > r leaves. Since any path of r vertices and any set of r leaves gives rise to a good r-tuple in T , this proves the assertion. ¤ Our next lemma shows how to obtain a grid from two large systems of paths that intersect in a particularly orderly way.
good r-tuple
Lemma 12.4.9. Let d, r ≥ 2 be integers such that d ≥ r2r+2 . Let G be a graph containing a set H of r2 − 1 disjoint paths and a set V = { V1 , . . . , Vd } of d disjoint paths. Assume that every path in V meets every path in H, and that each path H ∈ H consists of d consecutive (vertex-disjoint) segments such that Vi meets H only in its ith segment, for every i = 1, . . . , d (Fig. 12.4.3). Then G has an r × r grid minor. ... ...
... V1
Fig. 12.4.3. Paths intersecting as in Lemma 12.4.9
H1, . . . , Hr I, ik H0
Proof . For each i = 1, . . . , d, consider the graph with vertex set H in which two paths are adjacent whenever Vi contains a subpath between them that meets no other path in H. Since Vi meets every path in H, this is a connected graph; let Ti be a spanning tree in it. Since |H| ≥ r(r − 1), Lemma 12.4.8 implies that each of these d ≥ r2 (r2 )r trees Ti has a good r-tuple of vertices. Since there are no more than (r2 )r distinct r-tuples on H, some r2 of the trees Ti have a common good r-tuple (H 1 , . . . , H r ). Let I = { i1 , . . . , ir2 } be the index set of these trees (with ij < ik for j < k) and put H0 := { H 1 , . . . , H r }. Here is an informal description of how we construct our r × r grid. Its ‘horizontal’ paths will be the paths H 1 , . . . , H r . Its ‘vertical’ paths will be pieced together edge by edge, as follows. The r − 1 edges of the first vertical path will come from the first r − 1 trees Ti , trees with their index i among the first r elements of I. More precisely, its ‘edge’ between H j and H j+1 will be the sequence of subpaths of Vij (together with some connecting horizontal bits taken from paths in H \ H0 ) induced by the edges of an H j –H j+1 path in Tij that has no inner vertices in H0 ; see Fig. 12.4.4. (This is why we need (H 1 , . . . , H r ) to be a good r-tuple in every tree Ti .) Similarly, the jth edge of the second vertical path will come from an H j –H j+1 path in Tir+j , and so on.6 To merge these individual edges into r vertical paths, we then contract in each horizontal 6
Although we need only r − 1 edges for each vertical path, we reserve r rather than just r − 1 of the paths Vi for each vertical path to make the indexing more lucid. The paths Vir , Vi2r , . . . are left unused.
H j+1 H0
H P
The H j –H j+1 path P in Tij
Vij ij th segment P0
H Hj
H 00 H j+1
The H j –H j+1 path P 0 in G
Vi1 H
Vij
Vir+1
Vi2r+1
Hj H j+1 Hr
{z contract
} |
{z contract ...
P 0 viewed as a (subdivided) H j –H j+1 edge Fig. 12.4.4. An H j –H j+1 path in Tij inducing segments of Vij for the jth edge of the grid’s first vertical path
Hkj ˆj H vkj
path the initial segment that meets the first r paths Vi with i ∈ I, then contract the segment that meets the following r paths Vi with i ∈ I, and so on. Formally, we proceed as follows. Consider all j, k ∈ { 1, . . . , r }. (We shall think of the index j as counting the horizontal paths, and of the index k as counting the vertical paths of the grid to be constructed.) Let Hkj be the minimal subpath of H j that contains the ith segment of H j ˆ j be obtained from for all i with i(k−1)r < i ≤ ikr (put i0 := 0). Let H j H by first deleting any vertices following its ir2 th segment and then ˆ j = vj . . . vj . contracting every subpath Hkj to one vertex vkj . Thus, H r 1 Given j ∈ { 1, . . . , r − 1 } and k ∈ { 1, . . . , r }, we have to define a path Vkj that will form the subdivided ‘vertical edge’ vkj vkj+1 . This path will consist of segments of the path Vi together with some otherwise unused segments of paths from H \ H0 , for i := i(k−1)r+j ; recall that, ˆ j+1 , this Vi does indeed meet H j and H j+1 ˆ j and H by definition of H precisely in vertices that were contracted into vkj and vkj+1 , respectively. To define Vkj , consider an H j –H j+1 path P = H1 . . . Ht in Ti that has no inner vertices in H0 . (Thus, H1 = H j and Ht = H j+1 .) Every edge Hs Hs+1 of P corresponds to an Hs –Hs+1 subpath of Vi that has no inner vertex on any path in H. Together with (parts of) the ith segments of H2 , . . . , Ht−1 , these subpaths of Vi form an H j –H j+1 path P 0 in G that has no inner vertices on any of the paths H 1 , . . . , H r and meets no path from H outside its ith segment. Replacing the ends of P 0 on H j and H j+1 with vkj and vkj+1 , respectively, we obtain our desired path Vkj forming the jth (subdivided) edge of the kth ‘vertical’ path of our grid. Since the paths P 0 are disjoint for different i and different pairs (j, k) give rise to different i, the paths Vkj are disjoint except for possible common ends vkj . Moreover, they have no inner vertices on any of the paths H 1 , . . . , H r , because none of these H j is an inner vertex of any of the paths P ⊆ Ti used in the construction of Vkj . ¤ Proof of Theorem 12.4.4. We are now ready to prove the following quantitative version of our theorem (which clearly implies it): Let r, m > 0 be integers, and let G be a graph of tree-width 2 at least r4m (r+2) . Then G contains either the r × r grid m or K as a minor. 2
c, k
Since K r contains the r × r grid as a subgraphm we may assume that 2 ≤ m ≤ r2 . Put c := r4(r+2) , and let k := c2( 2 ) . Then c > 216 and hence 2m + 3 ≤ cm , so G has tree-width at least 2
cm = cm k > (2m + 3)k > (m + 1)(2k − 1) + k − 1 , (A, B) T
enough for Lemma 12.4.5 to ensure that G contains a k-mesh (A, B) of order (m + 1)(2k − 1). Let T ⊆ A be a tree associated with the
premesh (A, B); then X := V (A ∩ B) ⊆ V (T ). By Lemma 12.4.6, T has |X|/(2k − 1) − 1 = m disjoint subtrees each containing at least k vertices of X; let A1 , . . . , Am be the vertex sets of these trees. By definition of a k-mesh, B contains for all 1 ≤ i < j ≤ m a set Pij of k disjoint Ai –Aj paths that have no inner vertices in A. These sets Pij will shrink a little and be otherwise modified later in the proof, but they will always consist of ‘many’ disjoint Ai –Aj paths. One option in our proof will be to find single paths Pij ∈ Pij that are disjoint for different pairs ij and thus link up the sets Ai to form a K m minor of G. If this fails, we shall instead exhibit two specific sets Pij and Ppq such that many paths of Pij meet many paths of Ppq , forming an r × r grid between them by Lemma 12.4.9. Let us impose a linear ordering on the index pairs ij¡ by ¢ fixing an arbitrary bijection σ : { ij | 1 ≤ i < j ≤ m } → { 0, 1, . . . , m 2 − 1 }. For ` = 0, 1, . . . in turn, we shall consider the pair pq with σ(pq) = ` and choose an Ap –Aq path Ppq that is disjoint from all previously selected such paths, i.e. from the paths Pst with σ(st) < `. At the same time, we shall replace all the ‘later’ sets Pij —or what has become of them—by smaller sets containing only paths that are disjoint from Ppq . Thus for 0 1 each pair ij, we shall define a sequence Pij = Pij , Pij , . . . of smaller and ` smaller sets of paths, which eventually collapses to Pij = { Pij } when ` has risen to ` = σ(ij). ¡ ¢ More formally, let `∗ ≤ m 2 be the greatest integer such that, for ` all 0 ≤ ` < `∗ and all 1 6 i < j 6 m, there exist sets Pij satisfying the following five conditions: ` (i) Pij is a non-empty set of disjoint Ai –Aj paths in B that meet A only in their endpoints. S ` ` ` Whenever a set Pij is defined, we shall write Hij := Pij for the union of its paths. ` has exactly one element Pij , and Pij does (ii) If σ(ij) < ` then Pij ` not meet any path belonging to a set Pst with ij 6= st. ` | = k/c2` . (iii) If σ(ij) = `, then |Pij ` | = k/c2`+1 . (iv) If σ(ij) > `, then |Pij ` ` ) \ E(Hpq ) there are (v) If ` = σ(pq) < σ(ij), then for every e ∈ E(Hij ` ` no k/c2`+1 disjoint Ai –Aj paths in the graph (Hpq ∪ Hij ) − e. ` Note that, by (iv), the paths considered in (v) do exist in Hij . The ` purpose of (v) is to force those paths to reuse edges from Hpq when` ever possible, using¡ new ¢ edges e ∈/ Hpq only if necessary. Note further m that since σ(ij) < 2 by definition of σ, conditions (iii) and (iv) give ` |Pij | ≥ c2 whenever¡σ(ij) ¢ ≥ `. m Clearly if `∗ = m 2 then by (i) and (ii) we have a (subdivided) ¡K ¢ m ∗ minor with branch sets A1 , . . . , Am in G. Suppose then that ` < 2 .
X A1 , . . . , Am Pij
`∗
` Hij
` pq
P ij
0 Let us show that `∗ > 0. Let pq := S σ −1 (0) and put Ppq := Ppq . To 0 0 ) define Pij for σ(ij) > 0 put Hij := Pij , let F ⊆ E(Hij ) \ E(Hpq 0 be maximal such that (Hpq ∪ Hij ) − F still contains k/c disjoint Ai –Aj 0 paths, and let Pij be such a set of paths. Since the vertices from Ap ∪ Aq 0 have degree 1 in Hpq ∪ Hij unless they also lie in Ai ∪ Aj , these paths 0 therefore satisfy (i)–(v) have no inner vertices in A. Our choices of Pij for ` = 0. Having shown that `∗ > 0, let us now consider ` := `∗ − 1. Thus, conditions (i)–(v) are satisfied for ` but cannot be satisfied for ` + 1. ` contains a path P that avoids a set Qij of Let pq := σ −1 (`). If Ppq ` ` some |Pij |/c of the paths in Pij for all ij with σ(ij) > `, then we can `+1 define Pij for all ij as before (with a contradiction). Indeed, letSst := `+1 := Qst . For σ(ij) > ` + 1 write Hij := Qij , σ −1 (` + 1) and put Pst `+1 `+1 ) be maximal such that (Hst ∪ Hij ) − F still let F ⊆ E(Hij ) \ E(Hst `+1 ` 2 be such a set contains at least |Pij |/c disjoint Ai –Aj paths, and let Pij `+1 `+1 ` := { P } and Pij := Pij = { Pij` } for σ(ij) < ` of paths. Setting Ppq `+1 that contradicts the maximality of `∗ . then gives us a family of sets Pij ` Thus for every path P ∈ Ppq there exists a pair ij with σ(ij) > ` ` ` such that ¡m¢P avoids fewer than |Pij |/c of the paths in Pij . For some ` d|Ppq |/ 2 e of these P that pair ij will be the same; let P denote the ¡ ¢set ` of those¡ P¢, and keep ij fixed from now on. Note that |P| ≥ |Ppq |/ m 2 = ` by (iii) and (iv). c |Pij |/ m 2 ` ` Let us use Lemma 12.4.7 to find sets V ⊆ P ⊆ Ppq and H ⊆ Pij such that ³ ´ c ` ≥ |Pij | |V| > 12 |P| 2 m |H| = r2
and every path in V meets every path in H. We have to check that the ` in which P ∈ P is adjacent bipartite graph with vertex sets P and Pij ` ∈ to Q Pij whenever P ∩ Q = ∅ does not have too many edges. Since ` |/c neighbours (by definition of P), this every P ∈ P has fewer than |Pij graph indeed has at most ` ` |/c 6 |P||Pij |/6r2 |P||Pij
± ` 6 b|P|/2c |Pij | 2r2 ¡ ` ¢ 6 b|P|/2c |Pij |/r2 − 1 ¢± ¡ ¢¡ ` | − r2 r2 = |P| − d|P|/2e |Pij
edges, as required. Hence, V and H exist as claimed. Although all the (‘vertical’) paths in V meet all the (‘horizontal’) paths in H, these paths do not necessarily intersect in such an orderly way as required for Lemma 12.4.9. In order to divide the paths from H into segments, and to select paths from V meeting them only in the
appropriate segments, we shall first pick a path Q ∈ H to serve as a yardstick: we shall divide Q into segments each meeting lots of paths from V, select a ‘non-crossing’ subset V1 , . . . , Vd of these vertical paths, one from each segment (which is the most delicate task; we shall need ` here), and finally divide condition (v) from the definition of the sets Pij the other horizontal paths into the ‘induced’ segments, accommodating one Vn each. So let us pick a path Q ∈ H, and put
√ d := b c/mc = br2r+4/mc ≥ r2r+2 .
` ` Note that |V| > (c/m2 )|Pij | > d2 |Pij |. For n = 1, 2, . . . , d − 1 let en be the first edge of Q (on its way from Ai to Aj ) such that the initial component Qn of Q − en meets at least ` ` nd |Pij | different paths from V, and such that en is not an edge of Hpq . As any two vertices of Q that lie on different paths from V are separated ` ` , each of these Qn meets exactly nd |Pij | in Q by an edge not in Hpq 2 ` paths from V. Put Q0 := ∅ and Qd := Q. Since |V| ≥ d |Pij |, we have thus divided Q into d consecutive disjoint segments Q0n := Qn − Qn−1 ` (n = 1, . . . , d) each meeting at least d |Pij | paths from V. For each n = 1, . . . , d − 1, Menger’s theorem (3.3.1) and conditions ` ` ` ∪ Hij has a set Sn of |Pij | − 1 vertices such (iv) and (v) imply that Hpq ` ` that (Hpq ∪ Hij ) − en − Sn contains no path from Ai to Aj . Let S denote ` the union of all these sets Sn . Then |S| < d |Pij |, so each Q0n meets at ∈ least one path Vn V that avoids S (Fig. 12.4.5).
Q ...
en−1 Q0n en
Q01 , . . . , Q0d Sn S Vn
e d −1 Q0d
en Qn
z{
| Sn−1 Ai
r2 − 1
Sn Vn
Fig. 12.4.5. Vn meets every horizontal path but avoids S
Clearly, each Sn consists of a choice of exactly one vertex x from ` \ { Q }. Denote the initial component of P − x by Pn , every path P ∈ Pij put P0 := ∅ and Pd := P , and let Pn0 := Pn − Pn−1 for n = 1, . . . , d. The separation properties of the sets Sn now imply that Vn ∩ P ⊆ Pn0 for
P10 , . . . , Pd0
n = 1, . . . , d (and hence in particular that Pn0 6= ∅, ie. that Pn−1 ⊂ Pn ). Indeed Vn cannot meet Pn−1 , because Pn−1 ∪ Vn ∪ (Q − Qn−1 ) would ` ` ∪ Hij ) − en−1 − Sn−1 , and likewise then contain an Ai –Aj path in (Hpq (consider Sn ) Vn cannot meet P − Pn . Thus for all n = 1, . . . , d, the path Vn meets every path P ∈ H \ { Q } precisely in its nth segment Pn0 . Applying Lemma 12.4.9 to the path systems H \ { Q } and { V1 , . . . , Vd } now yields the desired grid minor. ¤
12.5 The graph minor theorem Hereditary graph properties, those that are closed under taking minors, occur frequently in graph theory. Among the most natural examples are the properties of being embeddable in some fixed surface, such as planarity. By Kuratowski’s theorem, planarity can be expressed by forbidding the minors K 5 and K3,3 . This is a good characterization of planarity in the following sense. Suppose we wish to persuade someone that a certain graph is planar: this is easy (at least intuitively) if we can produce a drawing of the graph. But how do we persuade someone that a graph is non-planar? By Kuratowski’s theorem, there is also an easy way to do that: we just have to exhibit an M K 5 or M K3,3 in our graph, as an easily checked ‘certificate’ for non-planarity. Our simple Proposition 12.4.2 is another example of a good characterization: if a graph has tree width < 3, we can prove this by exhibiting a suitable tree-decomposition; if not, we can produce an M K 4 as evidence. Theorems that characterize a hereditary property P by a set H of forbidden minors are doubtless among the most attractive results in graph theory. As we saw in the proof of Proposition 12.4.1, there is always some such characterization: that where H is the complement P of P. However, one naturally seeks to make H as small as possible. And as it turns out, there is indeed a unique smallest such set H: the set HP := { H | H is 4-minimal in P } satisfies P = Forb4 (H) and is contained in every other such set H. Proposition 12.5.1. P = Forb4 (HP ), and HP ⊆ H for every set H ¤ with P = Forb4 (H). Clearly, the elements of HP are incomparable under the minor relation 4. Now the graph minor theorem of Robertson & Seymour says that any set of 4-incomparable graphs must be finite:
12.5 The graph minor theorem
Theorem 12.5.2. (Graph Minor Theorem; Robertson & Seymour) The finite graphs are well-quasi-ordered by the minor relation 4. So every HP is finite, i.e. every hereditary graph property can be represented by finitely many forbidden minors: Corollary 12.5.3. Every graph property that is closed under taking ¤ minors can be expressed as Forb4 (H) with finite H. As a special case of Corollary 12.5.3 we have, at least in principle, a Kuratowski-type theorem for every surface: Corollary 12.5.4. For every surface S there exists a finite set of graphs H1 , . . . , Hn such that Forb4 (H1 , . . . , Hn ) contains precisely the graphs not embeddable in S. The minimal set of forbidden minors has been determined explicitly for only one surface other than the sphere: for the projective plane it is known to consist of 35 forbidden minors. It is not difficult to show that the number of forbidden minors grows rapidly with the genus of the surface (Exercise 34). The complete proof of the graph minor theorem would fill a book or two. For all its complexity in detail, however, its basic idea is easy to grasp. We have to show that every infinite sequence G0 , G1 , G2 , . . . of finite graphs contains a good pair: two graphs Gi 4 Gj with i < j. We may assume that G0 64 Gi for all i > 1, since G0 forms a good pair with any graph Gi of which it is a minor. Thus all the graphs G1 , G2 , . . . lie in Forb4 (G0 ), and we may use the structure common to these graphs in our search for a good pair. We have already seen how this works when G0 is planar: then the graphs in Forb4 (G0 ) have bounded tree-width (Theorem 12.4.3) and are therefore well-quasi-ordered by Theorem 12.3.7. In general, we need only consider the cases of G0 = K n : since G0 4 K n for n := |G0 |, we may assume that K n 64 Gi for all i > 1. The proof now follows the same lines as above: again the graphs in Forb4 (K n ) can be characterized by their tree-decompositions, and again their tree structure helps, as in Kruskal’s theorem, with the proof that they are well-quasi-ordered. The parts in these tree-decompositions are no longer restricted in terms of order now, but they are constrained in more subtle structural terms. Roughly speaking, for every n there exists a finite set S of closed surfaces such that every graph without a K n minor has a simplicial tree-decomposition into parts each ‘nearly’ embedding in
one of the surfaces S ∈ S. (The ‘nearly’ hides a measure of disorderliness that depends on n but not on the graph to be embedded.) By a generalization of Theorem 12.3.7—and hence of Kruskal’s theorem—it now suffices, essentially, to prove that the set of all the parts in these treedecompositions is well-quasi-ordered: then the graphs decomposing into these parts are well-quasi-ordered, too. Since S is finite, every infinite sequence of such parts has an infinite subsequence whose members are all (nearly) embeddable in the same surface S ∈ S. Thus all we have to show is that, given any closed surface S, all the graphs embeddable in S are well-quasi-ordered by the minor relation. This is shown by induction on the genus of S (more precisely, on 2 − χ(S), where χ(S) denotes the Euler characteristic of S) using the same approach as before: if H0 , H1 , H2 , . . . is an infinite sequence of graphs embeddable in S, we may assume that none of the graphs H1 , H2 , . . . contains H0 as a minor. If S = S 2 we are back in the case that H0 is planar, so the induction starts. For the induction step we now assume that S 6= S 2 . Again, the exclusion of H0 as a minor constrains the structure of the graphs H1 , H2 , . . ., this time topologically: each Hi with i > 1 has an embedding in S which meets some noncontractible closed curve Ci ⊆ S in no more than a bounded number of vertices (and no edges), say in Xi ⊆ V (Hi ). (The bound on |Xi | depends on H0 , but not on Hi .) Cutting along Ci , and sewing a disc on to each of the one or two closed boundary curves arising from the cut, we obtain one or two new closed surfaces of larger Euler characteristic. If the cut produces only one new surface Si , then our embedding of Hi − Xi still counts as a near-embedding of Hi in Si (since Xi is small). If this happens for infinitely many i, then infinitely many of the surfaces Si are also the same, and the induction hypothesis gives us a good pair among the corresponding graphs Hi . On the other hand, if we get two surfaces Si0 and Si00 for infinitely many i (without loss of generality the same two surfaces), then Hi decomposes accordingly into subgraphs Hi0 and Hi00 embedded in these surfaces, with V (Hi0 ∩ Hi00 ) = Xi . The set of all these subgraphs taken together is again well-quasi-ordered by the induction hypothesis, and hence so are the pairs (Hi0 , Hi00 ) by Lemma 12.1.3. Using a sharpening of the lemma that takes into account not only the graphs Hi0 and Hi00 themselves but also how Xi lies inside them, we finally obtain indices i, j not only with Hi0 4 Hj0 and Hi00 4 Hj00 , but also such that these minor embeddings extend to the desired minor embedding of Hi in Hj —completing the proof of the minor theorem. In addition to its impact on ‘pure’ graph theory, the graph minor theorem has had far-reaching algorithmic consequences. Using their tree structure theorem for the graphs in Forb4 (K n ), Robertson & Seymour have shown that testing for any fixed minor is ‘fast’: for every graph H
there is a polynomial-time algorithm7 that decides whether or not the input graph contains H as a minor. By the minor theorem, then, every hereditary graph property P can be decided in polynomial (even cubic) time: if H1 , . . . , Hk are the corresponding minimal forbidden minors, then testing a graph G for membership in P reduces to testing the k assertions Hi 4 G! The following example gives an indication of how deeply this algorithmic corollary affects the complexity theory of graph algorithms. Let us call a graph knotless if it can be embedded in R3 so that none of its cycles forms a non-trivial knot. Before the graph minor theorem, it was an open problem whether knotlessness is decidable, that is, whether any algorithm exists (no matter how slow) that decides for any given graph whether or not that graph is knotless. To this day, no such algorithm is known. The property of knotlessness, however, is easily ‘seen’ to be hereditary: contracting an edge of a graph embedded in 3-space will not create a knot where none had been before. Hence, by the minor theorem, there exists an algorithm that decides knotlessness—even in polynomial (cubic) time! However spectacular such unexpected solutions to long-standing problems may be, viewing the graph minor theorem merely in terms of its corollaries will not do it justice. At least as important are the techniques developed for its proof, the various ways in which minors are handled or constructed. Most of these have not even been touched upon here, yet they seem set to influence the development of graph theory for many years to come.
Exercises 1.− Let 6 be a quasi-ordering on a set X. Call two elements x, y ∈ X equivalent if both x 6 y and y 6 x. Show that this is indeed an equivalence relation on X, and that 6 induces a partial ordering on the set of equivalence classes. 2.
Let (A, 6) be a quasi-ordering. For subsets X ⊆ A write Forb6 (X) := { a
A | a 6> x for all x
X }.
Show that 6 is a well-quasi-ordering on A if and only if every subset B ⊆ A that is closed under > (i.e. such that x 6 y ∈ B ⇒ x ∈ B) can be written as B = Forb6 (X) with finite X. 3.
on H
Prove Proposition 12.1.1 and Corollary 12.1.2 directly, without using Ramsey’s theorem. indeed a cubic one—although with a typically enormous constant depending
278 4.
Given a quasi-ordering (X, 6) and subsets A, B ⊆ X, write A 60 B if there exists an order preserving injection f : A → B with a 6 f (a) for all a ∈ A. Does Lemma 12.1.3 still hold if the quasi-ordering considered for [X]
5.− Show that the relation 6 between rooted trees defined in the text is indeed a quasi-ordering. 6.
Show that the finite trees are not well-quasi-ordered by the subgraph relation.
The last step of the proof of Kruskal’s theorem considers a ‘topological’ embedding of Tm in Tn that maps the root of Tm to the root of Tn . Suppose we assume inductively that the trees of Am are embedded in the trees of An in the same way, with roots mapped to roots. We thus seem to obtain a proof that the finite rooted trees are well-quasi-ordered by the subgraph relation, even with roots mapped to roots. Where is the error?
8.+ Show that the finite graphs are not well-quasi-ordered by the topological minor relation. 9.+ Given k ∈ N, is the class { G | G 6⊇ P k } well-quasi-ordered by the subgraph relation? 10.
Show that a graph has tree-width at most 1 if and only if it is a forest.
Let G be a graph, T a set, and (Vt )t ∈ T a family of subsets of V (G) satisfying (T1) and (T2) from the definition of a tree-decomposition. Show that there exists a tree on T that makes (T3) true if and only if there exists an enumeration t1 , . . . , tn S of T such that for every k = 2, . . . , n there is a j < k satisfying Vtk ∩ i
Prove the following converse of Lemma 12.3.1: if (T, V) satisfies condition (T1) and the statement of the lemma, then (T, V) is a treedecomposition of G.
Can the tree-width of a subdivision of a graph G be smaller than tw(G)? Can it be larger?
Let (T, (Vt )t ∈ T ) be a tree-decomposition of a graph G. For each vertex v ∈ G, set Tv := { t ∈ T | v ∈ Vt }. Show that Tv is always connected in T . More generally, for which subsets U ⊆ V (G) is the set { t ∈ T | Vt ∩ U 6= ∅ } always connected in T (i.e. for all tree-decompositions)?
15.− Show that the tree-width of a graph is one less than its bramble number. 16.
Apply Theorem 12.3.9 to show that the k × k grid has tree-width at least k, and find a tree-decomposition of width exactly k.
Let B be a maximum-order bramble in a graph G. Show that every minimum-width tree-decomposition of G has a unique part covering B.
18.+ In the second half of the proof of Theorem 12.3.9, let H 0 be the union of H and the paths P1 , . . . , P` , let H 00 be the graph obtained from H 0 by contracting each Pi , and let (T, (Wt00 )t ∈ T ) be the tree-decomposition induced on H 00 (as in Lemma 12.3.3) by the decomposition that (T, (Vt )t ∈ T ) induces on H 0 . Is this, after the obvious identification of H 00 with H, the same decomposition as the one used in the proof, i.e. is Wt00 = Wt for all t ∈ T ? 19.
Show that any graph with a simplicial tree-decomposition into kcolourable parts is itself k-colourable.
Let H be a set of graphs, and let G be constructed recursively from elements of H by pasting along complete subgraphs. Show that G has a simplicial tree-decomposition into elements of H.
Given a tree-decomposition (T, (Vt )t ∈ T ) of G and t ∈ T , let Ht denote the graph obtained from G [ Vt ] by adding all the edges xy such that x, y ∈ Vt ∩ Vt0 for some neighbour t0 of t in T ; the graphs Ht are called the torsos of this tree-decomposition. Show that G has no K 5 minor if and only if G has a tree-decomposition in which every torso is either planar or a copy of the Wagner graph W (Fig. 8.3.1).
22.+ Call a graph irreducible if it is not separated by any complete subgraph. Every (finite) graph G can be decomposed into irreducible induced subgraphs, as follows. If G has a separating complete subgraph S, then decompose G into proper induced subgraphs G0 and G00 with G = G0 ∪ G00 and G0 ∩ G00 = S. Then decompose G0 and G00 in the same way, and so on, until all the graphs obtained are irreducible. By Exercise 20, G has a simplicial tree-decomposition into these irreducible subgraphs. Show that they are uniquely determined if the complete separators were all chosen minimal. 23.+ If F is a family of sets, then the graph G on F with XY ∈ E(G) ⇔ X ∩ Y 6= ∅ is called the intersection graph of F. Show that a graph is chordal if and only if it is isomorphic to the intersection graph of a family of (vertex sets of) subtrees of a tree. 24.
A tree-decomposition of a graph is called a path-decomposition if its decomposition tree is a path. Show that a graph has a path-decomposition into complete graphs if and only if it is isomorphic to an interval graph. (Interval graphs are defined in Ex. 37, Ch. 5.)
(continued) The path-width pw(G) of a graph G is the least width of a path-decomposition of G. Prove the following analogue of Corollary 12.3.12 for path-width: every graph G satisfies pw(G) = min ω(H) − 1, where the minimum is taken over all interval graphs H containing G.
26.+ Do trees have unbounded path-width?
Let P be a hereditary graph property. Show that strengthening the notion of a minor (for example, to that of topological minor) increases the set of forbidden minors required to characterize P.
Deduce from the minor theorem that every hereditary property can be expressed by forbidding finitely many topological minors. Is the same true for every property that is closed under taking topological minors?
Show that every horizontal path in the k × k grid is externally kconnected in that grid.
30.+ Show that the tree-width of a graph is large if and only if it contains a large externally k-connected set of vertices, with k large. For example, show that graphs of tree-width < k contain no externally (k + 1)connected set of 3k vertices, and that graphs containing no externally (k + 1)-connected set of 3k vertices have tree-width < 4k. 31.+ (continued) Find an N → N2 function k 7→ (h, `) such that every graph with an externally `-connected set of h vertices contains a bramble of order at least k. Deduce the weakening of Theorem 12.3.9 that, given k, every graph of large enough tree-width contains a bramble of order at least k. 32.
Without using the minor theorem, show that the chromatic number of the graphs in any 4-antichain is bounded.
Seymour’s self-minor conjecture asserts that ‘every countably infinite graph is a proper minor of itself’. Make this assertion precise, and deduce the minor theorem from it.
Given an orientable surface S of genus g, find a lower bound in terms of g for the number of forbidden minors needed to characterize embeddability in S. (Hint. The smallest genus of an orientable surface in which a given graph can be embedded is called the (orientable) genus of that graph. Use the theorem that the genus of a graph is equal to the sum of the genera of its blocks.)
Notes Kruskal’s theorem on the well-quasi-ordering of finite trees was first published in J.A. Kruskal, Well-quasi ordering, the tree theorem, and V´ aszonyi’s conjecture, Trans. Amer. Math. Soc. 95 (1960), 210–225. Our proof is due to NashWilliams, who introduced the versatile proof technique of choosing a ‘minimal bad sequence’. This technique was also used in our proof of Higman’s Lemma 12.1.3. Nash-Williams generalized Kruskal’s theorem to infinite graphs. This extension is much more difficult than the finite case; it is one of the deepest theorems in infinite graph theory. The general graph minor theorem becomes false for arbitrary infinite graphs, as shown by R. Thomas, A counterexample to ‘Wagner’s conjecture’ for infinite graphs, Math. Proc. Camb. Phil. Soc. 103
(1988), 55–57. Whether or not the minor theorem extends to countable graphs remains an open problem. The notions of tree-decomposition and tree-width were first introduced (under different names) by R. Halin, S-functions for graphs, J. Geometry 8 (1976), 171–186. Among other things, Halin showed that grids can have arbitrarily large tree-width. Robertson & Seymour reintroduced the two concepts, apparently unaware of Halin’s paper, with direct reference to K. Wagner, ¨ Uber eine Eigenschaft der ebenen Komplexe, Math. Ann. 114 (1937), 570– 590. (This is the classic paper that introduced simplicial tree-decompositions to prove Theorem 8.3.4; cf. Exercise 21.) Simplicial tree-decompositions are treated in depth in R. Diestel, Graph Decompositions, Oxford University Press 1990. Robertson & Seymour themselves usually refer to the graph minor theorem as Wagner’s conjecture. It seems that Wagner did indeed discuss this problem in the 1960s with his then students Halin and Mader. However, Wagner apparently never conjectured a positive solution; he certainly rejected any credit for the ‘conjecture’ when it had been proved. Robertson & Seymour’s proof of the graph minor theorem is given in the numbers IV–VII, IX–XII and XIV–XX of their series of over 20 papers under the common title of Graph Minors, which has been appearing in the Journal of Combinatorial Theory, Series B, since 1983. Of their theorems cited in this chapter, Theorem 12.3.7 is from Graph Minors IV, while Theorems 12.4.3 and 12.4.4 are from Graph Minors V. Our short proof of these latter theorems is from R. Diestel, K.Yu. Gorbunov, T.R. Jensen & C. Thomassen, Highly connected sets and the excluded grid theorem, J. Combin. Theory B 75 (1999), 61–73. Theorem 12.3.9 is due to P.D. Seymour & R. Thomas, Graph searching and a min-max theorem for tree-width, J. Combin. Theory B 58 (1993), 22–33. Our proof is a simplification of the original proof. B.A. Reed gives an instructive introductory survey on tree-width and graph minors, including some algorithmic aspects, in (R.A. Bailey, ed) Surveys in Combinatorics 1997 , Cambridge University Press 1997, 87–162. Reed also introduced the term ‘bramble’; in Seymour & Thomas’s paper, brambles are called ‘screens’. The obstructions to small tree-width actually used in the proof of the graph minor theorem are not brambles but so-called tangles. Tangles are more powerful than brambles and well worth studying. See Graph Minors X or Reed’s survey for an introduction to tangles and their relation to brambles and tree-decompositions. Theorem 12.3.10 is due to R. Thomas, A Menger-like property of treewidth; the finite case, J. Combin. Theory B 48 (1990), 67–76. As a forerunner to Theorem 12.4.3, Robertson & Seymour proved its following analogue for path-width (Graph Minors I): excluding a graph H as a minor bounds the path-width of a graph if and only if H is a forest. A short proof of this result, with optimal bounds, can be found in the first edition of this book, or in R. Diestel, Graph Minors I: a short proof of the path width theorem, Combinatorics, Probability and Computing 4 (1995), 27–30. The 35 minimal forbidden minors for graphs to be embedded in the projective plane were determined by D. Archdeacon, A Kuratowski theorem for the projective plane, J. Graph Theory 5 (1981), 243–246. An upper bound for
the number of forbidden minors needed for an arbitrary closed surface is given in P.D. Seymour, A bound on the excluded minors for a surface, J. Combin. Theory B (to appear). B. Mohar, Embedding graphs in an arbitrary surface in linear time, Proc. 28th Ann. ACM STOC (Philadelphia 1996), 392–397, has developed a set of algorithms, one for each surface, that decide embeddability in that surface in linear time. As a corollary, Mohar obtains an independent and constructive proof of the ‘generalized Kuratowski theorem’, Corollary 12.5.4. Another independent and short proof of this corollary, which builds on Theorem 12.4.3 and Graph Minors IV but on no other papers of the Graph Minors series, was found by C. Thomassen, A simpler proof of the excluded minor theorem for higher surfaces, J. Combin. Theory B 70 (1997), 306–311. A survey of the classical forbidden minor theorems is given in Chapter 6.1 of R. Diestel, Graph Decompositions, Oxford University Press 1990. More recent developments are surveyed in R. Thomas, Recent excluded minor theorems, in (J.D. Lamb & D.A. Preece, eds) Surveys in Combinatorics 1999 , Cambridge University Press 1999, 201–222. For every graph X, Graph Minors XIII gives an explicit algorithm that decides in cubic time for every input graph G whether X 4 G. The constants in the cubic polynomials bounding the running time of these algorithms depend on X but are constructively bounded from above. For an overview of the algorithmic implications of the Graph Minors series, see Johnson’s NPcompleteness column in J. Algorithms 8 (1987), 285–303. The concept of a ‘good characterization’ of a graph property was first suggested by J. Edmonds, Minimum partition of a matroid into independent subsets, J. Research of the National Bureau of Standards (B) 69 (1965) 67–72. In the language of complexity theory, a characterization is good if it specifies two assertions about a graph such that, given any graph G, the first assertion holds for G if and only if the second fails, and such that each assertion, if true for G, provides a certificate for its truth. Thus every good characterization has the corollary that the decision problem corresponding to the property it characterizes lies in NP ∩ co-NP.
Hints for all the Exercises
Caveat. These hints are intended to set on the right track anyone who has already spent some time over an exercise but somehow failed to make much progress. They are not designed to be particularly intelligible without such an initial attempt, and they will rarely spoil the fun by giving away the key idea. They may, however, narrow ones mind by focusing on what is just one of several possible ways to think about a problem. . .
Hints for Chapter 1 1.− How many edges are there at each vertex? 2.
Average degree and edges: consider the vertex degrees. Diameter: how do you determine the distance between two vertices from the corresponding 0–1 sequences? Girth: does the graph have a cycle of length 3? Circumference: partition the d-dimensional cube into cubes of lower dimension and use induction.
Consider how the path intersects C. Where can you see cycles, and can they all be short?
4.− Can you find graphs for which Proposition 1.3.2 holds with equality? 5. +
Estimate the distances within G as seen from a central vertex. Consider the cases d = 2 and d > 2 separately. For d > 2, give a sharper bound on |Di | for i > 0 than the one used in the proof of Proposition 1.3.3.
7.− Assume the contrary, and derive a contradiction. 8.− Find two vertices that are linked by two independent paths.
(i) Straightforward from the definitions. (ii) Prove κ > n by induction on n: partition the n-dimensional cube into cubes of lower dimension, and show inductively that the deletion of < n vertices leaves a connected subgraph.
For the first inequality, consider the endvertices of a set of λ(G) edges whose deletion disconnects G. Use the definition of λ(G) to show the second inequality.
11.− Try to find counterexamples for k = 1. 12.
Rephrase (i) and (ii) as statements about the existence of two N → N functions. To show the equivalence, express each of these functions in terms of the other. Show that (iii) may hold even if (i) and (ii) do not, and strengthen (iii) to remedy this.
13.+ Try to imitate the proof assuming ε(G) > 2k instead of condition (ii). Why does this fail, and why does condition (ii) remedy the problem? 14.
Show (i) ⇒ (ii) ⇒ (iii) ⇒ (iv) ⇒ (i) from the definitions of the relevant concepts.
Consider paths emanating from a vertex of maximum degree.
Theorem 1.5.1.
Induction.
The easiest solution is to apply induction on |T |. What kind of vertex of T will be best to delete in the induction step?
Induction on |T | is a possibility, but not the only one.
Count the edges.
Show that if a graph contains any odd cycle at all it also contains an induced one.
Apply Proposition 1.2.2. Split the subgraph thus found into two sides so that every vertex has many neighbours on the opposite side.
Try to carry the proof for finite graphs over to the infinite case. Where does it fail?
24.− Use Proposition 1.9.2. 25.
Why do all the cuts E(v) generate the cut space? Will they still do so if we omit one of them? Or even two?
Start with the case that the graph considered is a cycle.
Induction on |F r E(T )| for given F
Induction on |D ∩ E(T )| for a given cut D.
Apply Theorem 1.9.6.
C(G).
Hints for Chapter 2
Hints for Chapter 2 1.
Compare the given matching with a matching of maximum cardinality.
Augmenting paths.
If you have S $ S 0 ⊆ A with |S| = |N (S)| in the finite case, the marriage condition ensures that N (S) $ N (S 0 ): increasing S makes more neighbours available. Use the fact that this fails when S is infinite.
Apply the marriage theorem.
Construct a bipartite graph in which A is one side, and the other side consists of a suitable number of copies of the sets Ai . Define the edge set of the graph so that the desired result can be derived from the marriage theorem.
6.+ Construct chains in the power set lattice of X as follows. For each k < n/2, use the marriage theorem to find a 1–1 map ϕ from the set A of k-subsets to the set B of (k + 1)-subsets of X such that Y ⊆ ϕ(Y ) for all Y ∈ A. 7.
Decide where the leaves should go: in factor-critical components or in S?
Distinguish between the cases of |S| ≤ 1 and |S| ≥ 2.
The case S = ∅ is easy. In the other case, look for a vertex that meets every maximum-cardinality matching. What are the consequences of this for the other vertices?
For the ‘if’ direction consider the graph suggested in the hint: does it have a 1-factor? If not, then consider the set of vertices supplied by Tutte’s 1-factor theorem. For an alternative solution, apply the remarks on maximum-cardinality matchings which follow Theorem 2.2.3.
11.− Corollary 2.2.2. 12.
Let G be a bipartite graph that satisfies the marriage condition, with bipartition (A, B) say. Reduce the problem to the case of |A| = |B|. To verify the premise of Tutte’s theorem for a given set S ⊆ V (G), bound |S| from below in terms of the number of components of G − S that contain more vertices from A than from B and vice versa.
13.− Consider any smallest path cover. 14. 15.
Direct all the edges from A to B. Dilworth.
Start with the set of minimal elements in P .
Think of the elements of A as being smaller than their neighbours in B.
Let (x, y) 6 (x0 , y 0 ) if and only if x 6 x0 and y 6 y 0 .
Hints for Chapter 3 1.− Recall the definitions of ‘separate’ and ‘component’. 2. Describe in words what the picture suggests. 3. Use Exercise 1 to answer the first question. The second requires an elementary calculation, which the figure may already suggest. 4. Only the first part needs arguing; the second then follows by symmetry. So suppose a component of G − X is not met by X 0 , and refer to Exercise 1. Where does X 0 lie? Are all our assumptions about X 0 consistent? 5.− How can a block fail to be a maximal 2-connected subgraph? And what else follows then? 6. Deduce the connectedness of the block graph from that of the graph itself, and its acyclicity from the maximality of each block. 7. Prove the statement inductively using Proposition 3.1.2. Alternatively, choose a cycle through one of the two vertices and with minimum distance from the other vertex. Show that this distance cannot be positive. 8. Belonging to the same block is an equivalence relation on the edge set; see Exercise 5. 9. Induction along Proposition 3.1.2. 10. Assuming that G/xy is not 3-connected, distinguish the cases when vxy lies inside or outside a separating set of at most 2 vertices. 11. (i) Consider the edges incident with a smaller separator. (ii) Induction shows that all the graphs obtained by the construction are cubic and 3-connected. For the converse, consider a maximal subgraph T H ⊆ G such that H is constructible as stated; then show that H = G. 12.− Can any choice of X and P as suggested by Menger’s theorem fail? 13. Choose the disjoint A–B paths in L(G) minimal. 14. Consider a longest cycle C. How are the other vertices joined to C? 15. Consider a cycle through as many of the k given vertices as possible. If one them is missed, can you re-route the cycle through it? 16. Consider the graph of the hint. Show that any subset of its vertices that meets all H-paths (but not H) corresponds to a similar subset of E(G) r E(H). What does a pair of independent H-paths in the auxiliary graph correspond to in G? 17.− How many paths can a single K 2m+1 accomodate? 18. Choose suitable degrees for the vertices in B. 19.+ Let H be the (edgeless) graph on the new vertices. Consider the sets X and F that Mader’s theorem provides if G0 does not contain |G|/2 independent H-paths. If G has no 1-factor, use these to find a suitable set that can play the role of S in Tutte’s theorem. 20. Think small. 21.− If two vertices s, t are separated by fewer than 2k − 1 vertices, extend { s } and { t } to k-sets S and T showing that G is not k-linked.
Embed the vertices inductively. Where should you not put the new vertex?
2.− Figure 1.6.2. 3.− Make the given graph connected. 4.
This is a generalization of Corollary 4.2.8.
Imitate the proof of Corollary 4.2.8.
Proposition 4.2.10.
8.− Express the difference between the two drawings as a formal statement about vertices, faces, and the incidences between them. 9.
Combinatorially: use the definition. Topologically: express the relative position of the short (respectively, the long) branches of G0 formally as a property of G0 which any topological ismorphism would preserve but G lacks.
10.− Reflexivity, symmetry, transitivity. 11.
Look for a graph whose drawings all look the same, but which admits an automorphism that does not extend to a homeomorphism of the plane. Interpret this automorphism as σ2 ◦ σ1−1 .
12.+ Star-shape: every inner face contains a point that sees the entire face boundary. 13.
Work with plane rather than planar graphs.
(i) The set X may be infinite. (ii) If Y is a T X, then every T Y is also a T X.
15.− By the next exercise, any counterexample can be disconnected by at most two vertices. 16.
Incorporate the extra condition into the induction hypothesis of the proof. It may help to disallow polygons with 180 degree angles.
Number of edges.
Use that maximal planar graphs are 3-connected, and that the neighbours of each vertex induce a cycle.
If G = G1 ∪ G2 with G1 ∩ G2 = K 2 , we have a problem. This will go away if we embed a little more than necessary.
Use a suitable modification of the given graph G to simulate outerplanarity.
Use the fact that C(G) is the direct sum of C(G1 ) and C(G2 ).
Euler.
The face boundaries generate C(G).
Which are the faces that e∗ (viewed as a polygonal arc) can meet? How many vertices does it have?
26.− Join two given vertices of the dual by a straight line, and use this to find a path between them in the dual graph.
27.+ To show existence, define the required bijections F → V ∗ , E → E ∗ , V → F ∗ successively in this order, while at the same time constructing G∗ . Show that connectedness is necessary to ensure that these three functions can all be made bijective. 28.
Solve the previous exercise first.
Use the bijections that come with the two duals to define the desired isomorphism and to prove that it is combinatorial.
Apply Menger’s theorem and Proposition 4.6.1. For (iii), consider a 4-connected graph with six vertices.
Apply induction on n, starting with part (i) of the previous exercise.
For the forward implication, consider G0 := G∗ . For the converse, apply a suitable planarity criterion.
Hints for Chapter 5 1.− Duality. 2.− Whenever more than three countries have some point in common, apply a small local change to the map where this happens. 3.
Where does the five colour proof use the fact that v has no more neighbours than there are colours?
How can the colourings of different blocks interfere with each other?
Use a colouring of G to derive a suitable ordering.
Consider how the removal of certain edges may lead the greedy algorithm to use more colours.
Describe more precisely how to implement this alternative algorithm. Then, where is the difference to the traditional greedy algorithm?
Compare the number of edges in a subgraph H as in 5.2.2 with the number m of edges in G.
To find f , consider a given graph of small colouring number and partition it inductively into a small number of forest. For g, use Proposition 5.2.2 and the easy direction of Theorem 3.5.4.
10.− Remove vertices successively until the graph becomes critically kchromatic. What can you say about the degree of any vertex that remains? 11. 12.
Proposition 1.6.1. +
Modify colourings of the two sides of a hypothetical cut of fewer than k − 1 edges so that they combine to a (k − 1)-colouring of the entire graph (with a contradiction). Proposition 1.3.1.
14.− For which graphs with large maximum degree does Proposition 5.2.2 give a particularly small upper bound?
15.+ (i) How will v1 and v2 be coloured, and how vn ? (ii) Consider the subgraph induced by the neighbours of vn . 16.
For the induction start, explicitly calculate PG (k) for |G| = n and kGk = 0.
17.+ Derive from the polynomial the number of edges and the number of components of G; see the previous exercise. 18. −
Imitate the proof of Theorem 5.2.5.
Kn,n .
How are edge colourings related to matchings?
Construct a bipartite ∆(G)-regular graph that contains G as subgraph. It may be necessary to add some vertices.
22.+ Induction on k. In the induction step k → k + 1, consider using several copies of the graph you found for k. 23.− Vertex degrees. 24.
Kn,n . To choose n so that Kn,n is not even k-choosable, consider lists of k-subsets of a k2 -set.
25.− Vizing’s theorem. 26.
All you need are the definitions, Proposition 5.2.2, and a standard argument from Chapter 1.2.
27.+ Try induction on r. In the induction step, you would like to to delete one pair of vertices and only one colour from the other vertices’ lists. What can you say about the lists if this is impossible? This information alone will enable you to find a colouring directly, without even looking at the graph again. 28.
Show that χ00 (G) 6 ch0 (G) + 2, and use this to deduce χ00 (G) 6 ∆(G) + 3 from the list colouring conjecture.
29.− Do bipartite graphs have a kernel? 30.+ Call a set S of vertices in a directed graph D a core if D contains a directed v–S path for every vertex v ∈ D − S. If, in addition, D contains no directed path between any two vertices of S, call S a strong core. Show first that every core contains a strong core. Next, define inductively a partition of V (D) into ‘levels’ L0 , . . . , Ln such that, for even i, Li is a suitable strong core in Di := D − (L0 ∪ . . . ∪ Li−1 ), while for odd i, Li consists of the vertices of Di that send an edge to Li−1 . Show that, if D has no directed odd cycle, the even levels together form a kernel of D. 31.
Construct the orientation needed for Lemma 5.4.3 in steps: if, in the current orientation, there are still vertices v with d+ (v) > 3, reverse the directions of an edge at v and take care of the knock-on effect of this change. If you need to bound the average degree of a bipartite planar graph, remember Euler’s formula.
32.− Start with a non-perfect graph. 33.− Do odd cycles or their complements satisfy (∗)? 34.
Exercise 12, Chapter 3.
Look at the complement.
Define the colour classes of a given induced subgraph H ⊆ G inductively, starting with the class of all minimal elements.
(i) Can the vertices on an induced cycle contain each other as intervals? (ii) Use the natural ordering of the reals.
Compare ω(H) with ∆(G) (where H = L(G)).
39.+ Which graphs are such that their line graphs contain no induced cycles of odd length > 5? To prove that the edges of such a graph G can be coloured with ω(L(G)) colours, imitate the proof of Vizing’s theorem. 40. +
Use A as a colour class. (i) Induction. (ii) Assume that G contains no induced P 3 . Suppose some H has a maximal complete subgraph K and a maximal set A of independent vertices disjoint from K. For each vertex v ∈ K, consider the set of neighbours of v in A. How do these sets intersect? Is there a smallest one?
42.+ Start with a candidate for the set O, i.e. a set of maximal complete subgraphs covering the vertex set of G. If all the elements of O happen to have order ω(G), how does the existence of A follow from the perfection of G? If not, can you expand G (maintaining perfection) so that they do and adapt the A for the expanded graph to G? 43.+ Reduce the general case to the case when all but one of the Gx are trivial; then imitate the proof of Lemma 5.5.4. 44.
Apply the property of H1 to the graphs in H2 , and vice versa.
Hints for Chapter 6 1.− Move the vertices, one by one, from S to S. How does the value of f (S, S) change each time? 2.
(i) Trick the algorithm into repeatedly using the middle edge in alternating directions. (ii) At any given time during the algorithm, consider for each vertex v the shortest s–v walk that qualifies as an initial segment of an augmenting path. Show for each v that the length of this s–v walk never decreases during the algorithm. Now consider an edge which is used twice for an augmenting path, in the same direction. Show that the second of these paths must have been longer than the first. Now derive the desired bound.
3.+ For the edge version, define the capacity function so that a flow of maximum value gives rise to sufficiently many edge-disjoint paths. For the vertex version, split every vertex x into two adjacent vertices x− , x+ . Define the edges of the new graph and their capacities in such a way that positive flow through an edge x− x+ corresponds to the use of x by a path in G.
4.− H-flows are nowhere zero, by definition. 5.− Use the definition and Proposition 6.1.1. 6.− Do subgraphs also count as minors? 7.− Try k = 2, 3, . . . in turn. In searching for a k-flow, tentatively fix the flow value through an edge and investigate which consequences this has for the adjacent edges. 8. 9. 10.
To establish uniqueness, consider cuts of a special type. Express G as the union of cycles. Combine Z2 -flows on suitable subgraphs to a flow on G.
11.+ Begin by sending a small amount of flow through every edge outside T . 12.
View G as the union of suitably chosen cycles.
Corollary 6.3.2 and Proposition 6.4.1.
14.− Duality. 15.
Take as H your favourite graph of large flow number. Can you decrease its flow number by adding edges?
17.+ Theorem 6.5.3. 18.− Search among small cubic graphs. 19. 20.
Theorem 6.5.3. (i) Theorem 6.5.3. (ii) Yes it can. Show, by considering a smallest counterexample, that if every 3-connected cubic planar multigraph is 3-edge-colourable (and hence has a 4-flow), then so is every bridgeless cubic planar multigraph.
21.+ For the ‘only if’ implication apply Proposition 6.1.1. Conversely, consider a circulation f on G, with values in { 0, ±1, . . . , ±(k − 1) }, that respects the given orientation (i.e. is positive or zero on the edge directions assigned by D) and is zero on as few edges as possible. Then show that f is nowhere zero, as follows. If f is zero on e = st ∈ E and D directs e from t to s, define a network N = (G, s, t, c) such that any flow in N of positive total value contradicts the choice of f , but any cut in N of zero capacity contradicts the property assumed for D. 22.− Convert the given multigraph into a graph with the same flow properties.
Hints for Chapter 7 1.− Straightforward from the definition. 2.− When constructing the graphs, start by fixing the colour classes. 3.
It is not difficult to determine an upper bound for ex(n, K1,r ). What remains to be proved is that this bound can be achieved for all r and n.
Proposition 1.7.2 (ii).
Proposition 1.2.2 and Corollary 1.5.4.
6.+ What is the maximum number of edges in a graph of the structure given by Theorem 2.2.3 if it has no matching of size k? What is the optimal distribution of vertices between S and the components of G − S? Is there always a graph whose number of edges attains the corresponding upper bound? 7.
Consider a vertex x in G − x.
Choose k and i so that n = (r − 1)k + i with 0 6 i < r − 1. Treat the case of i = 0 first, ¡ i ¢and then show for the general case that tr−1 (n) = 2 2 1 r−2 (n − i ) + . 2 r−1 2
The bounds given in the hint are the sizes of two particularly simple Tur´ an graphs—which ones?
G of maximum degree, and count the edges
10.+ How can you choose v so that the number of edges does not decrease? Where in the graph can the operation be repeated, and what does the situation look like when nothing new happens? 11.
Choose among the m vertices a set of s vertices that are still incident with as many edges as possible.
For the first inequality, double the vertex set of an extremal graph for Ks,t to obtain a bipartite graph with twice as many edges but still not containing a Ks,t .
13.+ For the displayed inequality, count the pairs (x, Y ) such that x ∈ A and Y ⊆ B, with |Y | = r and x adjacent ¡to¢all of Y . For the bound on ex(n, Kr,r ), use the estimate (s/t)t ≤ st ≤ st and the fact that the function z 7→ z r is convex. 14.
1 Assume that the upper density is larger than 1 − r−1 . What does this mean precisely, and what does the Erd˝ os-Stone theorem then imply?
Complete graphs.
Average degree.
Consider a longest path P in G. Where do its endvertices have their neighbours? Can G [ P ] contain a cycle on V (P )?
1 (k 2
− 1)n edges force a subgraph of suitable minimum degree?
20.− Why would it be impractical to include, say, 1-element sets X, Y in the comparison? 21.− Apply the definition of an ²-regular pair. 22.
Sparse graphs have few edges. How does that affect the average degree condition in the definition of ²-regularity?
For the induction step, partition the vertex set of the given graph G into two sets V1 and V2 so that colourings of G [ V1 ] and G [ V2 ] can be combined to a colouring of G.
2. −
Imitate the start of the proof of Lemma 8.1.3. Does a large chromatic number force up the average degree? If in doubt, consult Chapter 5.
4.+ Try parallel paths in the grid as branch sets. 5.+ How can we best make a T K 2r fit into a Ks,s when we want to keep s small? 6.
Split the argument into the cases of k = 0 and k > 1.
How are the two lemmas used in the proof of the theorem?
Study the motivational chat preceding the definition of f in the proof.
9.+ Consider your favourite graphs with high average degree and low chromatic number. Which trees do they contain induced? Is there some reason to expect that exactly these trees may always be found induced in graphs of large average degree and small chromatic number? 10.− What does planarity have to do with minors? 11.− Consider a suitable supergraph. 12.− Average degree. 13.+ Show by induction on |G| that any 3-colouring of an induced cycle in G 6< K 4 extends to all of G. 14.+ Reduce the statement to critical k-chromatic graphs and apply Vizing’s theorem. 15.
(i) is easy. In the first part of (ii), distinguish between the cases that the graph is or is not separated by a K χ(G)−1 . Show the second part by induction on the chromatic number. In the induction step split the vertex set of the graph into two subsets.
Induction on the number of construction steps.
Induction on |G|.
Note the previous exercise.
Which of the graphs constructed as in Theorem 8.3.4 have the largest average degree?
Which of the graphs constructed as in the hint have the largest average degree?
Consider the subgraph of G induced by the neighbours of x.
Hints for Chapter 9 1.− Can you colour the edges of K 5 red and green without creating a red or a green triangle? Can you do the same for a K 6 ? 2. +
Induction on c. In the induction step, unite two of the colour classes. Choose a well-ordering of R, and compare it with the natural ordering. Use the fact that countable unions of countable sets are countable.
4.+ The first and second question are easy. To prove the theorem of Erd˝ os and Szekeres, use induction on k for fixed `, and consider in the induction step the last elements of increasing subsequences of length k. Alternatively, apply Dilworth’s Theorem. 5.
Use the fact that n > 4 points span a convex polygon if and only if every four of them do.
Translate the given k-partition of { 1, 2, . . . , n } into a k-colouring of the edges of K n .
(i) is easy. For (ii) use the existence of R(2, k, 3).
Begin by finding infinitely many sets whose pairwise intersections all have the same size.
The exercise offers more information than you need. Consult Chapter 8.1 to see what is relevant.
Consider an auxiliary graph whose vertices are coloured finite subgraphs of the given graph.
Imitate the proof of Proposition 9.2.1.
The lower bound is easy. Given a colouring for the upper bound, consider a vertex and the neighbours joined to it by suitably coloured edges.
13.− Given H1 and H2 , construct a graph H for which the G of Theorem 9.3.1 satisfies (∗). 14.
Show inductively for k = 0, . . . , m that ω(Gk ) = ω(H).
For the induction step, construct G(H1 , H2 ) from the disjoint union of G(H1 , H20 ) and G(H10 , H2 ) by joining some new vertices in a suitable way.
Infinity lemma.
17.− How exactly does Proposition 9.4.1 fail if we delete K r from the statement?
Hints for Chapter 10 1.
Consider the union of two colour classes.
Will the proof of Proposition 10.1.2 go through if we assume χ(G) > |G|/k instead of α(G) 6 k? What do k-connected graphs look like that satisfy the first condition but not the second?
Examine an edge that gets added in one sequence but not in another.
Hints for Chapter 10
Figure 10.1.1.
Induction on k with n fixed; for the induction step consider G.
6.− Recall the definition of a hamiltonian sequence. 7.− On which kind of vertices does the Chv´ atal condition come to bear? To check the validity of the condition for G, first find such a vertex. 8.
How does an arbitrary connected graph differ from the kind of graph whose square contains a Hamilton cycle by Fleischner’s theorem? How could this difference obstruct the existence of a Hamilton cycle?
9.+ In the induction step consider a minimal cut. 10.
Condition (∗) in the proof of Fleischner’s theorem.
How can a Hamilton path P ∈ H be modified into another? In how many ways? What has this got to do with the degree in G of the last vertex of P ?
Hints for Chapter 11 1.− Consider a fixed choice of m edges on { 0, 1, . . . , n }. What is the probability that G ∈ G(n, p) has precisely this edge set? 2.
Consider the appropriate indicator random variables, as in the proof of Lemma 11.1.5.
Consider the appropriate indicator random variables.
Erd˝ os.
What would be the measure of the set { G } for a fixed G?
Consider the complementary properties.
P2,1 .
Apply Lemma 11.3.2.
Induction on |H| with the aid of Exercise 6.
10.+ (i) Given a pair U, U 0 , calculate the probability that every other vertex is joined incorrectly to U ∪ U 0 . What, then, is the probability that this happens for some pair U, U 0 ? (ii) Enumerate the vertices of G and G0 jointly, and construct an isomorphism G → G0 inductively. 11.
Imitate the proof of Lemma 11.2.1.
Imitate the proof of Proposition 11.3.1. To bound the probabilities involved, use the inequality 1 − x 6 e−x as in the proof of Lemma 11.2.1.
13.+ (i) Calculate the expected number of isolated vertices, and apply Lemma 11.4.2 as in the proof of Theorem 11.4.3. (ii) Linearity. 14.+ Chapter 8.2, the proof of Erd˝ os’s theorem, and a bit of Chebyshev.
For the first problem modify an increasing property slightly, so that it ceases to be increasing but keeps its threshold function. For the second, look for an increasing property whose probability does not really depend on p.
16.− Permutations of V (H). 17.− This is a result from the text in disguise. 18.− Balance. 19.
For p/t → 0 apply Lemmas 11.1.4 and 11.1.5. For p/t → ∞ apply Corollary 11.4.4.
There are only finitely many trees of order k.
21.+ Show first that no such threshold function t = t(n) can tend to zero as n → ∞. Then use Exercise 12. 22.+ Examine the various steps in the proof of Theorem 11.4.3, and note which changes will be needed. In the final steps of the proof, how are the sums AF defined, and why is the sum of all the AF with ||F || = ∅ equal to A0 ? For ||F || 6= ∅, calculate a bound on AF , and show that each AF /µ2 tends to zero as n → ∞, as before.
Hints for Chapter 12 1.− Antisymmetry. 2.
Proposition 12.1.1.
To prove Proposition 12.1.1, consider an infinite sequence in which every strictly decreasing subsequence is finite. How does the last element of a maximal decreasing subsequence compare with the elements that come after it? For Corollary 12.1.2, start by proving that at least one element forms a good pair with infinitely many later elements.
An obvious approach is to try to imitate the proof of Lemma 12.1.3 for 60 ; if it fails, what is the reason? Alternatively, you might try to modify the injective map produced by Lemma 12.1.3 into an orderpreserving one, without losing the property of a 6 f (a) for all a.
5.− This is an exercise in precision: ‘easy to see’ is not a proof. . . 6.
Start by finding two trees T, T 0 with |T | < |T 0 | but T 66 T 0 ; then iterate.
Does the original proof ever map the root of a tree to an ordinary vertex of another tree?
8.+ When we try to embed a graph T G in another graph H, the branch vertices of the T G can be mapped only to certain vertices of H. Enlarge G to a similar graph H that does not contain G as a topological minor because these vertices of H are inconveniently positioned in H. Then iterate this example to obtain an infinite antichain. 9.+ It is. One possible proof uses normal spanning trees with labels, and imitates the proof of Kruskal’s theorem. 10.
Why are there no cycles of tree-width 1?
For the forward implication, apply Corollary 1.5.2. For the converse, use induction on k.
To prove (T2), consider the edge e of Figure 12.3.1. Checking (T3) is easy.
For the first question, recall Proposition 12.3.6. For the second, try to modify a tree-decomposition of G into one of the T G without increasing its width.
Lemma 12.3.1 relates the separation properties of a graph G to those of its decomposition tree T . This exercise illuminates this relationship from the dual viewpoint of connectedness: how are the connected subgraphs of G related to those of T ?
15.− This is just a reformulation of Theorem 12.3.9. 16.
Modify the proof given in the text that the k × k grid has tree-width at least k − 1.
Existence was shown in Theorem 12.3.9; the task is to show uniqueness.
18.+ Work out an explicit description of the sets Wt0 similar to the definition of the Wt , and compare the two. 19.
Use the previous exercise and a result from Chapter 8.3. And don’t despair at a subgraph of W !
22.+ Show that the parts are precisely the maximal irreducible induced subgraphs of G. 23.+ Exercise 14. 24.
For the forward implication, interpret the subpaths of the decomposition path as intervals. Which subpath corresponds naturally to a given vertex of G?
Follow the proof of Corollary 12.3.12.
26.+ They do. To prove it, show first that every connected graph G contains a path whose deletion decreases the path-width of G. Then apply induction on a suitable set of trees, deleting a suitable path in the induction step. 27.
Consider minimal sets such as XP in Proposition 12.5.1.
To answer the first part, construct for each forbidden minor X a finite set of graphs whose exclusion as topological minors is equivalent to forbidding X as a minor. For the second part recall Exercise 8.
Find the required paths one by one.
30.+ One direction is just a weakening of Lemma 12.4.5. For the other, imitate the proof of Lemma 12.3.4. 31.+ Let X be an externally `-connected set of h vertices in a graph G, where h and ` are large. Consider a small separator S in G: clearly, most of X will lie in the same component of G − S. Try to make these ‘large’ components, perhaps together with their separators S, into the desired connected vertex sets.
Consult Chapter 8.2 for substructures to be found in graphs of large chromatic number.
Derive the minor theorem first for connected graphs.
Page numbers in italics refer to definitions; in the case of author names, they refer to theorems due to that author. The alphabetical order ignores letters that stand as variables; for example, ‘k-colouring’ is listed under the letter c. abstract dual, 88 –89 graph, 3, 67, 76, 238 acyclic, 12, 60 adjacency matrix, 24 adjacent, 3 Ahuja, R.K., 145 algebraic colouring theory, 121 flow theory, 128–143 graph theory, ix, 20–25, 28 planarity criteria, 85–86 algorithmic graph theory, 145, 276–277, 281–282 almost, 238, 247–248 Alon, N., 106, 121–122, 249 alternating path, 29 walk, 52 antichain, 40, 41, 42, 252 Appel, K., 121 arboricity, 61, 99, 118 arc, 68 Archdeacon, D., 281 articulation point, see cutvertex at, 2 augmenting path for matching, 29, 40, 285 for network flow, 127, 144 automorphism, 3
average degree, 5 of bipartite planar graph, 289 bounded, 210 and chromatic number, 101, 106, 178, 185 and connectivity, 11 forcing minors, 169, 179, 184 forcing topological minors, 61, 170– 178 and girth, 237 and list colouring, 106 and minimum degree, 5–6 and number of edges, 5 and Ramsey numbers, 210 and regularity lemma, 154, 166 bad sequence, 252, 280 balanced, 243 Behzad, M., 122 Berge, C., 117 Berge graph, 117 between, 6, 68 Biggs, N.L., 28 bipartite graphs, 14 –15, 27, 91, 95 edge colouring of, 103, 119 flow number of cubic, 133–134 forced as subgraph, 152, 160 list-chromatic index of, 109–110, 122 matching in, 29–34 in Ramsey theory, 202–203
300 Birkhoff, G.D., 121 block, 43 graph, 44, 64 B¨ ohme, T., 66 Bollob´ as, B., 28, 65, 66, 166, 170, 210, 227, 228, 240, 241, 249, 250 bond, see (minimal) cut space, see cut space Bondy, J.A., 228 boundary of a face, 72 –73 bounded subset of R2 , 70 bramble, 258 –260, 281 number, 260, 278 order of, 258 branch set, 16 vertex, 18 bridge, 10, 36, 125, 135, 215 to bridge, 218 Brooks, R.L., 99, 118 theorem, 99 list colouring version, 121 Burr, S.A., 210 capacity, 126 function, 125 Catlin, P.A., 187 Cayley, A., 121, 248 central vertex, 9, 283 certificate, 111, 274, 282 chain, 13, 40, 41 Chebyshev inequality, 243, 295 Chen, G., 210 choice number, 105 and average degree, 106 of bipartite planar graphs, 119 of planar graphs, 106 k-choosable, 105 chord, 7 chordal, 111 –112, 120, 262, 279 k-chromatic, 95 chromatic index, 96, 103 of bipartite graphs, 103 vs. list-chromatic index, 105, 108 and maximum degree, 103–105 chromatic number, 95, 139 and K r -subgraphs, 100–101, 110–111 of almost all graphs, 240 and average degree, 101, 106, 178, 185 vs. choice number, 105–106 and connectivity, 100 and extremal graphs, 151
and flow number, 139 forcing minors, 181–185 forcing short cycles, 101, 237 forcing subgraphs, 100–101, 178, 209 forcing a triangle, 119, 209 and girth, 101, 237 as a global phenomenon, 101, 110 and maximum degree, 99 and minimum degree, 99, 100 and number of edges, 98 chromatic polynomial, 118, 146 Chv´ atal, V., 194, 215, 216, 228 circle on S 2 , 70 circuit, see cycle circulation, 124, 137, 146 circumference, 7 and connectivity, 64, 214 and minimum degree, 8 class 1 vs. class 2, 105 clique number, 110 –117, 202, 262 of random graph, 232 threshold function, 247 closed under addition, 128 under isomorphism, 238, 263 wrt. minors, 119, 144, 263 wrt. subgraphs, 119 wrt. supergraphs, 241 walk, 9, 19 cocycle space, see cut space k-colourable, 95 colour class, 95 colour-critical, see critically k-chromatic colouring, 95 –122 algorithms, 98, 117 and flows, 136–139 number, 99, 118, 119 plane graphs, 96–97, 136–139 in Ramsey theory, 191 total, 119 3-colour theorem, see three colour thm. 4-colour theorem, see four colour thm. 5-colour theorem, see five colour thm. combinatorial isomorphism, 77, 78 set theory, 210 compactness argument, 191, 210 comparability graph, 111, 119 complement of a bipartite graph, 111, 119 of a graph, 4 and perfection, 112, 290 of a property, 263 complete, 3
bipartite, 14 matching, see 1-factor minor, 179–184, 275 multipartite, 14, 151 part of path-decomposition, 279 part of tree-decomposition, 262 r-partite, 14 separator, 261, 279 subgraph, 101, 110–111, 147–151, 232, 247, 257 topological minor, 61–62, 170–178, 184, 186 complexity theory, 111, 274, 282 component, 10 connected, 9 2-connected graphs, 43–45 3-connected graphs, 45–49, 79–80 k-connected, 10, 64 externally, 264, 280 minimally connected, 12 minimally k-connected, 65 and vertex enumeration, 9, 13 connectedness, 9, 12, 297 connectivity, 10 –11, 43–66 and average degree, 11 and circumference, 64 and edge-connectivity, 11 external, 264, 280 and girth, 237 and Hamilton cycles, 215 and linkability, 62, 65 and minimum degree, 11 and plane duality, 91 and plane representation, 79–80 Ramsey properties, 207–208 of a random graph, 239 k-constructible, 101 –102, 118 contains, 3 contraction, 16 –18 and 3-connectedness, 45–46 and minors, 16–18 in multigraphs, 25–26 and tree-width, 256 convex drawing, 82, 90, 92 polygon, 209 core, 289 cover by antichains, 41 of a bramble, 258 by chains, 40, 42 by edges, 119 by paths, 39–40 by trees, 60–61, 89
by vertices, 30, 258 critical, 118 critically k-chromatic, 118, 293 cross-edges, 21, 58 crosses in grid, 258 crown, 208 cube d-dimensional, 26, 248 of a graph, G3 , 227 cubic graph, 5 connectivity of, 64 1-factor in, 36, 41 flow number of, 133–134, 135 cut, 21 capacity of, 126 -cycle duality, 136–138 -edge, see bridge flow across, 125 minimal, 22, 88 in network, 126 space, 22 –24, 28, 85, 89 cutvertex, 10, 43–44 cycle, 7 –9 -cut duality, 136–138 directed, 119 double cover conjecture, 141, 144 expected number, 234 Hamilton, 144, 213 –228 induced, 7–8, 21, 47, 86, 111, 117, 290 length, 7 long, 8, 26, 64, 118 in multigraphs, 25 non-separating, 47, 86 odd, 15, 99, 117, 290 with orientation, 136 –138 short, 101, 179–180, 235, 237 space, 21, 23–24, 27–28, 47–49, 85– 86, 89, 92–93 threshold function, 247 cyclomatic number, 21 degeneracy, see colouring number degree, 5 sequence, 216 deletion, 4 ∆-system, 209 dense graphs, 148, 150 density edge density, 148 of pair of vertex sets, 153 upper density, 166 depth-first search tree, 13, 27 Deuber, W., 197
302 diameter, 8 –9, 248 and girth, 8 and radius, 9 Diestel, R., 186, 281 difference of graphs, 4 digon, see double edge digraph, see directed graph Dilworth, R.P., 40, 285, 294 Dirac, G.A., 111, 186, 187, 214, 226 directed cycle, 119 edge, 25 graph, 25, 108, 119 path, 39 direction, 124 disjoint graphs, 3 distance, 8 double counting, 75, 92, 114–115, 234, 244 edge, 25 wheel, 208 drawing, 67, 76 –80 convex, 92 straight-line, 90 dual abstract, 88 –89, 91 and connectivity, 91 plane, 87, 91 duality cycles and cuts, 23–24, 88–89, 136 flows and colourings, 136–139, 291 of plane multigraphs, 87–89 edge, 2 crossing a partition, 21 directed, 25 double, 25 of a multigraph, 25 plane, 70 X–Y edge, 2 edge-chromatic number, see chromatic index edge colouring, 96, 103–105, 191 and flow number, 135 and matchings, 119 `-edge-connected, 10 edge-connectivity, 11, 55, 58 edge contraction, 16 and 3-connectedness, 45 vs. minors, 17 in multigraph, 25 edge cover, 119 edge density, 5, 148 and average degree, 5
forcing subgraphs, 147–167 forcing minors/topological minors, 169–180 and regularity lemma, 154, 166 edge-disjoint spanning trees, 58–61 edge-maximal, 4 vs. extremal, 149, 182 without M K 5 , 183 without T K 4 , 182 without T K 5 , T K3,3 , 84 without T K3,3 , 185 edge space, 20, 85 Edmonds, J., 42, 282 embedding of bipartite graphs, 202 –204 in the plane, 76, 80–93 in S 2 , 69–70, 77 in surface, 74, 92, 274–276, 280, 281– 282 empty graph, 2 end of edge, 2, 25 of path, 6 endpoints of arc, 68 endvertex, 2, 25 terminal vertex, 25 equivalence of planar embeddings, 76–80, 79, 90 of points in R2 , 68 in quasi-order, 277 Erd˝ os, P., 101, 121, 151, 152, 163, 166, 167, 187, 197, 208, 209, 210, 215, 228, 232, 235–237, 243, 249, 295 Erd˝ os-S´ os conjecture, 152, 166, 167 Euler, L., 18–19, 74 Euler characteristic, 276 formula, 74 –75, 89, 90, 289 tour, 19 –20, 291 Eulerian graph, 19 even degree, 19, 33 graph, 133, 135, 145 event, 231 evolution of random graphs, 241, 249 exceptional set, 153 excluded minors, see forbidden minors existence proof, probabilistic, 121, 229, 233, 235–237 expanding a vertex, 113 expectation, 233 –234, 242 exterior face, see outer face externally k-connected, 264, 280 extremal
bipartite graph, 165 vs. edge-maximal, 149, 182 graph theory, 147, 151, 160, 166 graph, 149 –150 without M K 5 , 183 without T K 4 , 182 without T K 5 , 184 without T K3,3 , 185 face, 70 factor, 29 1-factor, 29–38 1-factor theorem, 35, 42, 66 2-factor, 33 k-factor, 29 factor-critical, 36, 285 Fajtlowicz, S., 187 fan, 55 -version of Menger’s theorem, 55 finite graph, 2 first order sentence, 239 first point on frontier, 68 five colour theorem, 96, 121, 141 list version, 106, 121 five-flow conjecture, 140, 141 Fleischner, H., 218, 295 flow, 123–146, 125 –126 H-flow, 128 –133 k-flow, 131 –134, 140–143, 145 2-flow, 133 3-flow, 133–134, 141 4-flow, 134–135, 140–141 6-flow theorem, 141 –143 -colouring duality, 136–139, 291 conjectures, 140–141 group-valued, 128–133, 144 integral, 126, 128 network flow, 125 –128, 291 number, 131 –134, 140, 144 in plane graphs, 136–139 polynomial, 130, 146 total value of, 126 forbidden minors and chromatic number, 181–185 expressed by, 263, 274–277 minimal set of, 274, 280, 281 planar, 264 and tree-width, 263–274 forcibly hamiltonian, see hamiltonian sequence forcing M K r , 179–184, 186 T K 5 , 184, 187 T K r , 61, 170–178, 186
303 high connectivity, 11 induced trees, 178 large chromatic number, 101–103 linkability, 62–63, 66, 171–174 long cycles, 8, 26, 118, 213–228 long paths, 8, 166 minor with large minimum degree, 174, 179 short cycles, 179–180, 237 subgraph, 13, 147–167 tree, 13, 178 triangle, 119, 209 Ford, L.R. Jr., 127, 145 forest, 12 partitions, 60–61 minor, 281 four colour problem, 120, 186 four colour theorem, 96, 141, 145, 181, 183, 185, 215, 227 history, 120–121 four-flow conjecture, 140 –141 Frank, A., 65, 145 Frobenius, F.G, 42 from . . . to, 6 frontier, 68 Fulkerson, D.R., 122, 127, 145 Gallai, T., 39, 42, 66, 167 Gallai-Edmonds matching theorem, 36– 38, 42 Galvin, F., 109 Gasparian, G.S., 122 genus and colouring, 121 of a surface, 276 of a graph, 90, 280 geometric dual, see plane dual Gibbons, A., 145 Gilmore, P.C., 120 girth, 7 and average degree, 237 and chromatic number, 101, 121, 235–237 and connectivity, 237 and diameter, 8 and minimum degree, 8, 179–180, 237 and minors, 179–180 and planarity, 89 and topological minors, 178 Godsil, C., 28 Golumbic, M.C., 122 good characterization, 274, 282 pair, 252
304 sequence, 252 Gorbunov, K.Yu., 281 G¨ oring, F., 66 Graham, R.L., 210 graph, 2 –4, 25, 26 invariant, 3 minor theorem, 251, 274–277, 275 partition, 60 plane, 70 –76, 87–89, 96–97, 106–108, 136–139 process, 250 property, 238 simple, 26 graphic sequence, see degree sequence graph-theoretical isomorphism, 77 –78 greedy algorithm, 98, 108, 117 grid, 90, 184, 258 minor, 260, 264–274 theorem, 264 tree-width of, 260, 278, 281 Gr¨ otzsch, H., 97, 141, 145 group-valued flow, 128–133 Gr¨ unwald, T., 66 Guthrie, F., 120 Gy´ arf´ as, A., 178, 185 Hadwiger, H., 181, 186, 187 conjecture, 169–170, 181 –183, 185, 186–187 Hajnal, A., 197, 210 Haj´ os, G., 102, 187 construction, 101–102 Haken, W., 121 Halin, R., 65–66, 227, 280–281 Hall, P., 31, 42 Hamilton, W.R., 227 Hamilton closure, 226 Hamilton cycle, 213 –228 in almost all graphs, 241 and degree sequence, 216–218, 226 in G2 , 218–226 in G3 , 227 and the four colour theorem, 215 and 4-flows, 144, 215 and minimum degree, 214 in planar graphs, 215 power of, 226 sufficient conditions, 213–218 Hamilton path, 213, 218 hamiltonian graph, 213 sequence, 216 Harant, J., 66 head, see terminal vertex
Heawood, P.J., 121, 145 Heesch, H., 121 hereditary graph property, 263, 274–277 algorithmic decidability, 276–277 Higman, D.G., 252, 280 Hoffman, A.J., 120 hypergraph, 25 in (a graph), 7 incidence, 2 encoding of planar embedding, see combinatorial isomorphism map, 25–26 matrix, 24 incident, 2, 72 increasing property, 241, 248 independence number, 110 –117 and connectivity, 214–215 and Hamilton cycles, 215 and long cycles, 118 and path cover, 39 of random graph, 232, 248 independent edges, 3, 29–38 events, 231 paths, 7, 55, 56–57, 283 vertices, 3, 39, 110, 232 indicator random variable, 234, 295 induced subgraph, 3, 111, 116–117, 290 of almost all graphs, 238, 248 cycle, 7–8, 21, 47, 75, 86, 111, 117, 290 of all imperfect graphs, 116–117, 120 of all large connected graphs, 207 in Ramsey theory, 196–206 in random graph, 232, 249 tree, 178 infinite graphs, ix, 2, 28, 41, 166, 209, 248, 280 infinity lemma, 192, 210, 294 initial vertex, 25 inner face, 70 inner vertex, 6 integral flow, 126, 128 function, 126 random variable, 242 interior of an arc, 68 ˚, 6–7 of a path, P internally disjoint, see independent intersection, 3 graph, 279 interval graph, 120, 279
into, 255 intuition, 70, 231 invariant, 3 irreducible graph, 279 isolated vertex, 5, 248 isomorphic, 3 isomorphism, 3 of plane graphs, 76–80 isthmus, see bridge Jaeger, F., 146 Janson, S., 249 Jensen, T.R., 120, 146, 281 Johnson, D., 282 join, 2 Jordan, C., 68, 70 Jung, H.A., 62, 186 Kahn, J., 122 Karo´ nski, M., 249 Kempe, A.B., 121, 227 kernel of incidence matrix, 24 of directed graph, 108 –109,119 Kirchhoff’s law, 123, 124 Klein four-group, 135 Kleitman, D.J., 121 knotless graph, 277 knot theory, 146 Kohayakawa, Y., 167 Koll´ ar, J., 167 Koml´ os, J., 167, 170, 186, 210, 226 K¨ onig, D., 30, 42, 52, 103, 119, 192, 210 duality theorem, 30, 39, 111 infinity lemma, 192, 210, 294 K¨ onigsberg bridges, 19 Kostochka, A.V., 179 Kruskal, J.A., 253, 280, 296 Kuratowski, C., 80 –84, 274 Kuratowski-type characterization, 90, 274–275, 281–282 Larman, D.G., 62 Latin square, 119 leaf, 12, 27 lean tree-decomposition, 261 length of a cycle, 7 of a path, 6, 8 of a walk, 9 line (edge), 2 graph, 4, 96, 185
305 linear algebra, 20–25, 47–49, 85–86, 116 linear programming, 145 linked by an arc, 68 by a path, 6 k-linked, 61 –63, 66 vs. k-connected, 62, 65 (k, `)-linked, 170 set, 170 tree-decomposition, 261 vertices, 6, 68 list -chromatic index, 105, 108–110, 121– 122 -chromatic number, see choice number colouring, 105 –110, 121–122 bipartite graphs, 108–110, 119 Brooks’s theorem, 121 conjecture, 108, 119, 122 k-list-colourable, see k-choosable logarithms, 1 loop, 25 Lov´ asz, L., 42, 112, 115, 121, 122, 167 L Ã uczak, T., 249, 250 MacLane, S., 85, 92 Mader, W., 11, 56 –57, 61, 65, 66, 178, 184, 186, 187 Magnanti, T.L., 145 Mani, P., 62 map colouring, 95–97, 117, 120, 136 Markov chain, 250 Markov’s inequality, 233, 237, 242, 244 marriage theorem, 31, 33, 42, 285 matchable, 36 matching, 29 –42 in bipartite graphs, 29–34, 111 and edge colouring, 119 in general graphs, 34–38 of vertex set, 29 M´ at´ e, A., 210 matroid theory, 66, 93 max-flow min-cut theorem, 125, 127, 144, 145 maximal, 4 acyclic graph, 12 planar graph, 80, 84, 90, 92, 183, 185 plane graph, 73, 80 maximum degree, 5 bounded, 161, 194 and chromatic number, 99 and chromatic index, 103–105 and list-chromatic index, 110, 122
306 and radius, 9, 26 and Ramsey numbers, 194–196 Menger, K., 42, 50 –55, 64, 144, 288 k-mesh, 265 Milgram, A.N., 39 minimal, 4 connected graph, 12 k-connected graph, 65 cut, 22, 88, 136 set of forbidden minors, 274, 280, 281–282 non-planar graph, 90 separating set, 63 minimum degree, 5 and average degree, 5 and choice number, 106 and chromatic number, 99, 100 and circumference, 8 and connectivity, 11, 65–66 forcing Hamilton cycle, 214, 226 forcing long cycles, 8 forcing long paths, 8, 166 forcing short cycles, 179–180, 237 forcing trees, 13 and girth, 178, 179–180, 237 and linkability, 171 minor, 16–19, 17 K3,3 , 92, 185 K 4 , 182, 263 K 5 , 183, 186 K 5 and K3,3 , 80–84 K 6 , 183 K r , 180, 181 of all large 3- or 4-connected graphs, 208 forbidden, 181–185, 263 –277, 279, 280, 281–282 forced, 174, 179–186 infinite, 280 of multigraph, 26 Petersen graph, 140 and planarity, 80–84, 90 relation, 18, 274 theorem, 251, 274–277, 275 for trees, 253–254 proof, 275–276 vs. topological minor, 18–19, 80 and WQO, 251–277 (see also topological minor) M¨ obius crown, 208 ladder, 183 Mohar, B., 92, 121, 281–282 moment
first, see Markov’s inequality second, 242–247 monochromatic (in Ramsey theory) induced subgraph, 196–206 (vertex) set, 191 –193 subgraph, 191, 193–196 multigraph, 25 –26 list chromatic index of, 122 plane, 87 multiple edge, 25 Murty, U.S.R., 228 Nash-Williams, C.St.J.A., 58, 60, 66, 280 neighbour, 3, 4 Neˇsetˇril, J., 210, 211 network, 125 –128 theory, 145 node (vertex), 2 normal tree, 13 –14, 27, 139, 144, 296 nowhere dense, 61 zero, 128, 146 null, see empty obstruction to small tree-width, 258–260, 264– 265, 280, 281 octahedron, 11, 15 odd component, 34 cycle, 15, 99, 117, 290 degree, 5 on, 2 one-factor theorem, 35, 66 Oporowski, B., 208 order of deletion/contraction, 17 of a bramble, 258 of a graph, 2 of a mesh or premesh, 265 partial, 13, 18, 27, 40, 41, 120, 277 quasi-, 251 –252, 277–278 tree-, 13, 27 well-quasi-, 251 –253, 275, 277, 278, 280 orientable surface, 280 plane as, 137 orientation, 25, 108, 145, 289 cycle with, 136 –137 oriented graph, 25 Orlin, J.B., 145 outer face, 70, 76–77
outerplanar, 91 Oxley, J.G., 93, 208 Palmer, E.M., 249 parallel edges, 25 paths, 293 parity, 5, 34, 37, 227 part of tree-decomposition, 255 partially ordered set, 40, 41, 42 r-partite, 14 partition, 1, 60, 191 pasting, 111, 182, 183, 185, 261 path, 6 –9 a–b-path, 7, 55 A–B-path, 7, 50–55 H-path, 7, 44–45, 56–57, 64, 65, 66 alternating, 29, 32 between given pairs of vertices, 61– 63, 66, 170 cover, 39 –40, 285 -decomposition, 279 directed, 39 disjoint paths, 39, 50–55 edge-disjoint, 55, 57, 58 -hamiltonian sequence, 218 independent paths, 7, 55, 56–57, 283 induced, 207 length, 6 linkage, 61–63, 66, 170, 172 long, 8 -width, 279, 281 Pelik´ an, J., 185 perfect, 111 –117, 119–120, 122 graph conjecture, 117 graph theorem, 112, 115, 117, 122 matching, see 1-factor Petersen, J., 33, 36 Petersen graph, 140 –141 physics, 146 piecewise linear, 67 planar, 80 –89, 274 embedding, 76, 80–93 planarity criteria Kuratowski, 84 MacLane, 85 Tutte, 86 Whitney, 89 plane dual, 87 duality, 87–89, 91, 136–139, 288 graph, 70 –76, multigraph, 87 –89, 136–139 triangulation, 73, 75, 261
Plummer, M.D., 42 point (vertex), 2 pointwise greater, 216 polygon, 68 polygonal arc, 68, 69 P´ osa, L., 197, 226 power of a graph, 218 precision, 296 premesh, 265 probabilistic method, 229, 235–238, 249 projective plane, 275, 281 Pr¨ omel, H.J., 117, 122 property, 238 of almost all graphs, 238–241, 247– 248 hereditary, 263 increasing, 241 pseudo-random graph, 210 Pym, J.S., 66 quasi-ordering, 251 –252, 277–278 radius, 9 and diameter, 9, 26 and maximum degree, 9, 26 Rado, R., 210 Rado’s selection lemma, 210 Ramsey, F.P., 190 –193 Ramsey graph, 197 -minimal, 196 numbers, 191, 193 –194, 209, 210, 232 Ramsey theory, 189–208 and connectivity, 207–208 induced, 196–206 infinite, 192, 208, 210 random graph, 179, 194, 229–250, 231 evolution, 241 infinite, 248 process, 250 uniform model, 250 random variable, 233 indicator r.v., 234, 295 reducible configuration, 121 Reed, B.A., 281 refining a partition, 1, 155–159 region, 68 –70 on S 2 , 70 regular, 5, 33, 226 ²-regular pair, 153, 166 partition, 153 regularity
308 graph, 161 inflated, Rs , 194 lemma, 148, 153–164, 154, 167, 210 R´ enyi, A., 243, 249 Richardson, M., 119 rigid-circuit, see chordal ˇ ıha, S., 228 R´ Robertson, N., 66, 121, 183, 186, 257, 264, 275, 281 R¨ odl, V., 167, 194, 197, 211 R´ onyai, L., 167 root, 13 rooted tree, 13, 253, 278 Rothschild, B.L., 210 Royle, G.F., 28 Ruci´ nski, A., 249 Sanders, D.P., 121 S´ ark¨ ozy, G.N., 226 saturated, see edge-maximal Schelp, R.H., 210 Schoenflies, A.M., 70 Schrijver, A., 145 Schur, I, 209 Scott, A.D., 167, 178, 209 second moment, 242 –247 self-minor conjecture, 280 separate a graph, 10, 50, 55, 56 the plane, 68 separating set, 10 sequential colouring, see greedy algorithm series-parallel, 185 k-set, 1 set system, see hypergraph Seymour, P.D., 66, 92, 121, 141, 183, 186, 187, 226, 257, 258, 264, 275, 280, 281 shift-graph, 209 Simonovits, M., 166, 167, 210 simple basis, 85, 92–93 graph, 26 simplicial tree-decomposition, 261, 275, 279, 281 sink, 125 six-flow theorem, 141 snark, 141 planar, 141, 145, 215 S´ os, V., 152, 166, 167 source, 125 spanned subgraph, 3 spanning
subgraph, 3 trees, 13, 14 edge disjoint, 58–60 number of, 248 sparse graphs, 147, 169–185, 194 Spencer, J.H., 210, 249 Sperner’s lemma, 41 square of graph, 218 Latin, 119 stability number, see independence number stable set, 3 standard basis, 20 star, 15, 166, 196 induced, 207 star-shape, 287 Steger, A., 117, 122 Steinitz, E., 92 stereographic projection, 69 Stone, A.H., 151, 160 straight line segment, 68 strong core, 289 subcontraction, see minor subdividing vertex, 18 subdivision, 18 subgraph, 3 of all large k-connected graphs, 207– 208 forced by edge density, 147–164 of high connectivity, 11 induced, 3 of large minimum degree, 5–6, 99, 118 sum of edge sets, 20 of flows, 133 supergraph, 3 symmetric difference, 20, 29–30, 40, 53 system of distinct representatives, 41 Szab´ o, T., 167 Szekeres, G., 208, 209 Szemer´edi, E., 154, 170, 186, 194, 226 see also regularity lemma tail, see initial vertex Tait, P.G., 121, 227–228 tangle, 281 Tarsi, M., 121 terminal vertex, 25 Thomas, R., 121, 183, 208, 210, 258, 280 Thomason, A.G., 66, 170, 179, 186, 241
Thomassen, C., 65, 92, 106, 121, 179, 185, 187, 228, 281, 282 three colour theorem, 97 three-flow conjecture, 141 threshold function, 241 –247, 250 Toft, B., 120, 146 topological isomorphism, 76, 78, 88 topological minor, 17 –18 K3,3 , 92, 185 K 4 , 182, 185, 263 K 5 , 92, 184 K 5 and K3,3 , 75, 80–84 5 , 185 K− K r , 61, 170–178 of all large 2-connected graphs, 207 forced by average degree, 61, 170–178 forced by chromatic number, 181 forced by girth, 178 induced, 178 as order relation, 18 vs. ordinary minor, 18–19, 80 and planarity, 75, 80–84, 90 tree (induced), 178 and WQO of general graphs, 278 and WQO of trees, 253 torso, 279 total chromatic number, 119 total colouring, 119 conjecture, 119, 122 total value of a flow, 126 touching sets, 258 tournament, 227 transitive graph, 41 travelling salesman problem, 227 tree, 12 –14 cover, 61 as forced substructure, 13, 178, 185 normal, 13 –14, 27, 139, 144, 296 -order, 13 threshold function for, 247 well-quasi-ordering of trees, 253–254 tree-decomposition, 186, 255 –262, 278, 280–281 induced on subgraphs, 256 induced on minors, 256 lean, 261 obstructions, 258–260, 264–265, 280, 281 part of, 255 simplicial, 261, 275, 279, 281 width of, 257 tree-width, 257 –274 and brambles, 258–260, 278, 281 duality theorem, 258 –260
309 and forbidden minors, 263–274 of grid, 260, 278, 281 of a minor, 257 of a subdivision, 278 obstructions to small, 258–260, 264– 265, 280, 281 triangle, 3 triangulated, see chordal triangulation, see plane triangulation trivial graph, 2 Trotter, W.T., 194 Tur´ an, P., 150 theorem, 150, 195 graph, 149 –152, 166, 292 Tutte, W.T., 35, 46, 47, 58, 65, 66, 86, 92, 128, 131, 139, 145, 146, 215, 228 flow conjectures, 140 –141 Tutte polynomial, 146 Tychonov, A.N., 210 unbalanced subgraph, 247, 249 uniformity lemma, see regularity lemma union, 3 unmatched, 29 upper density, 166 Urquhart, A., 121 valency (degree), 5 value of a flow, 126 variance, 242 vertex, 2 -chromatic number, 95 colouring, 95, 98–103 -connectivity, 10 cover, 30 cut, see separating set of a plane graph, 70 space, 20 -transitive, 41 Vince, A., 249 Vizing, V.G., 103, 121, 122, 289, 290, 293 Voigt, M., 121 Wagner, K., 84, 93, 183, 184, 185, 186, 281 ‘Wagner’s Conjecture’, 281 Wagner graph, 183, 261–262, 279 walk, 9 alternating, 52 closed, 9 length, 9
310 well-ordering, 294 well-quasi-ordering, 251 –282 Welsh, D.J.A., 146 wheel, 46 theorem, 46, 65
Index Whitney, H., 66, 80, 89 width of tree-decomposition, 257 Winkler, P., 249 Zykov, A.A., 166
Symbol Index
The entries in this index are divided into two groups. Entries involving only mathematical symbols (i.e. no letters except variables) are listed on the first page, grouped loosely by logical function. The entry ‘[ ]’, for example, refers to the definition of induced subgraphs H [ U ] on page 4 as well as to the definition of face boundaries G [ f ] on page 72. Entries involving fixed letters as constituent parts are listed on the second page, in typographical groups ordered alphabetically by those letters. Letters standing as variables are ignored in the ordering. ∅ = ' ⊆ 6 4
2 3 3 3 251 16
4, 19, 128 4, 70, 128 2 70 3 3 4
r ∪ ∩ ∗ bc de | | k k [ ] [ ]k , [ ]
1 1 2, 126 2, 153 4, 72 1, 250
h , i 19 / 15, 16, 24 C⊥, F ⊥, . . . 19 0, 1, 2, . . . 1 (n)k , . . . 232 2 E(v), E 0 (w), . . . 2 E(X, Y ), E 0 (U, W ), . . . (e, x, y), . . . 124 →
E, F , C , . . . ←
e, E , F , . . . 124 f (X, Y ), g(U, W ), . . . 124 G∗ , F ∗ , → e ∗ , . . . 88, 136, 140 2 3 G , H , ... 216 G, X, G, . . . 4, 124, 258 126 (S, S), . . . 2, 7 xy, x1 . . . xk , . . . xP, P x, xP y, xP yQz, . . . 7 ˚, ˚ P xQ, . . . 7, 68 xT y, . . . 13
312 F2 N Zn
CG C(G) C ∗ (G) E(G) G(n, p) PH Pi,j V(G)
34 20 21 19 228 241 236 19
Ck E(G) E(X) F (G) Forb4 (X ) G(H1 , H2 ) Kn Kn1 ,...,nr Ksr L(G) MX N (v), N (U ) N + (v) P Pk PG R(H) R(H1 , H2 ) R(k, c, r) R(r) Rs Sn TX T r−1 (n) V (G)
7 2 231 70 257 196 3 14 14 4 15 4 108 229 6 118 191 191 191 189 161 69 16 149 2
ch(G) ch0 (G)
col(G) d(G) d(v) d+ (v) d(x, y) d(X, Y ) diam(G) ex(n, H) f ∗ (v) g(G) i init(e) log, ln pw(G) q(G) rad(G) tr−1 (n) ter(e) tw(G) ve , vxy , vU v ∗ (f )
99 5 5 108 8 153 8 149 88 7 1 23 1 259 34 9 149 23 255 15, 16 88
∆(G) α(G) δ(G) ε(G) κ(G) κG (H) λ(G) λG (H) µ π : S 2 r { (0, 0, 1) } → R2 σk : Z → Zk σ2 ϕ(G) χ(G) χ0 (G) χ00 (G) ω(G)
5 110 5 5 10 56 11 56 240 69 131 240 131 95 96 119 110
Reinhard Diestel received a PhD from the University of Cambridge, following research 1983–86 as a scholar of Trinity College under B´ela Bollob´ as. He was a Fellow of St. John’s College, Cambridge, from 1986 to 1990. Research appointments and scholarships have taken him to Bielefeld (Germany), Oxford and the US. He became a professor in Chemnitz in 1994 and has held a chair at Hamburg since 1999. Reinhard Diestel’s main area of research is graph theory, including infinite graph theory. He has published numerous papers and a research monograph, Graph Decompositions (Oxford 1990).
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Eur. Phys. J. C (1998) 1: 21-30
Multi-photon final states in e+e− collisions at ∝s =130-172 GeV
The OPAL Collaboration
K. Ackerstaff1, G. Alexander2, J. Allison3, N. Altekamp4, K. J. Anderson5, S. Anderson6, S. Arcelli7, S. Asai8, D. Axen, G. Azuelos9,10, A. H. Ball11, E. Barberio1, R. J. Barlow3, R. Bartoldus12, J. R. Batley4, S. Baumann12, J. Bechtluft13, C. Beeston3, T. Behnke1, A. N. Bell14, K. W. Bella15, G. Bella2, S. Bentvelsen1, S. Bethke13, O. Biebel13, A. Biguzzi4, S. D. Bird3, V. Blobel16, I. J. Bloodworth14, J. E. Bloomer14, M. Bobinskilo17, P. Bock18, D. Bonacorsi7, M. Boutemeur19, B. T. Bouwens6, S. Braibant6, L. Brigliadori7, R. M. Brown15, H. J. Burckhart1, C. Burgard1, R. Biirgin17, P. Capiluppi7, R. K. Carnegie20, A. A. Carter21, J. R. Carter4, C. Y. Chang11, D. G. Charlton14,22, D. Chrisman23, P. E. L. Clarke24, I. Cohen2, J. E. Conboy24, O. C. Cooke1, M. Cuffiani7, S. Dado25, C. Dallapiccola11, G. M. Dallavalle7, R. Davis26, S. De Jong6, L. A. del Pozo23, K. Desch12, B. Dienes27,28, M. S. Dixit29, E. do Couto e Silva6, M. Doucet9, E. Duchovni30, G. Duckeck19, I. P. Duerdoth3, D. Eatough3, J. E. G. Edwards3, P. G. Estabrooks20, H. G. Evans5, M. Evans21, F. Fabbri7, M. Fanti7, A. A. Faust26, F. Fiedler16, M. Fierro7, H. M. Fischer12, I. Fleck1, R. Folman30, D. G. Fong11, M. Foucher11, A. Fürtjes1, D. I. Futyan3, P. Gagnon29, J. W. Gary23, J. Gascon9, S. M. Gascon-Shotkin11, N. I. Geddes15, C. Geich-Gimbel12, T. Geralis15, G. Giacomelli7, P. Giacomelli23, R. Giacomelli7, V. Gibson4, W. R. Gibson4, D. M. Gingrich26,10, D. Glenzinski5, J. Goldberg25, M. J. Goodrick4, W. Gorn23, C. Grandi7, E. Gross30, J. Grunhaus2, M. Gruwé1, C. Hajdu31, G. G. Hanson6, M. Hansroul1, M. Hapke21, C. K. Hargrove29, P. A. Hart5, C. Hartmann12, M. Hauschild1, C. M. Hawkes4, R. Hawkings16, R. J. Hemingway20, M. Herndon11, G. Herten17, R. D. Heuer1, M. D. Hildreth1, J. C. Hill4, S. J. Hillier14, P. R. Hobson32, R. J. Homer14, A. K. Honma33,10, D. Horvath31,34, K. R. Hossain26, R. Howard35, P. Hüntemeyer16, D. E. Hutchcroft4, P. Igo-Kemenes18, D. C. Imrie32, M. R. Ingram3, K. Ishii8, A. Jawahery11, P. W. Jeffreys15, H. Jeremie9, M. Jimack14, A. Joly9, C. R. Jones4, G. Jones3, M. Jones20, U. Jost18, P. Jovanovic14, T. R. Junk1, D. Karlen20, V. Kartvelishvili3, K. Kawagoe8, T. Kawamoto8, P. I. Kayal26, R. K. Keeler33, R. G. Kellogg11, B. W. Kennedy15, J. Kirk35, A. Klier30, S. Kluth1, T. Kobayashi8, M. Kobello17, D. S. Koetke20, T. P. Kokott12, M. Kolrep17, S. Komamiya8, T. Kress18, P. Krieger20, J. von Krogh18, P. Kyberd21, G. D. Lafferty3, R. Lahmann11, W. P. Lai36, D. Lanske13, J. Lauber24, S. R. Lautenschlager37, J. G. Layter23, D. Lazic25, A. M. Lee37, E. Lefebvre9, D. Lellouch30, J. Letts6, L. Levinson30, S. L. Lloyd21, F. K. Loebinger3, G. D. Long33, M. J. Losty29, J. Ludwig17, A. Macchiolo7, A. Macpherson26, M. Mannelli1, S. Marcellini7, C. Markus12, A. J. Martin21, J. P. Martin9, G. Martinez11, T. Mashimo8, P. Mättig12, W. J. McDonald26, J. McKenna35, E. A. Mckigney24, T. J. McMahon14, R. A. McPherson1, F. Meijers1, S. Menke12, F. S. Merritt5, H. Mes29, J. Meyer16, A. Michelini7, G. Mikenberg30, D. J. Miller24, A. Mincer25,38, R. Mir30, W. Mohr17, A. Montanari7, T. Mori8, M. Morii8, U. Müller12, S. Mihara8, K. Nagai30, I. Nakamura8, H. A. Neal1, B. Nellen12, R. Nisius1, S. W. O'Neale14, F. G. Oakham29, F. Odorici7, H. O. Ogren6, A. Oh16, N. J. Oldershaw3, M. J. Oreglia5, S. Orito8, J. Palinkas27,28, G. Pasztor31, J. R. Pater3, G. N. Patriek15, J. Patt17, M. J. Pearce14, R. Perez-Ochoa1, S. Petzold16, P. Pfeifenschneider13, J. E. Pilcher5, J. Pinfold26, D. E. Plane1, P. Poffenberger33, B. Poli7, A. Posthaus12, D. L. Rees14, D. Rigby14, S. Robertson33, S. A. Robins25, N. Rodning26, J. M. Roney33, A. Rooke24, E. Ros1, A. M. Rossi7, P. Routenburg26, Y. Rozen25, K. Runge17, O. Runolfsson1, U. Ruppel13, D. R. Rust6, R. Rylko32, K. Sachs17, T. Saeki8, E. K. G. Sarkisyan2, C. Sbarra35, A. D. Schaile19, O. Schaile19, F. Scharf12, P. Scharff-Hansen1, P. Schenk19, J. Schieck18, P. Schleper18, B. Schmitt1, S. Schmitt18, A. Schöning1, M. Schröder1, H. C. Schultz-Coulon17, M. Schumacher12, C. Schwick1, W. G. Scott15, T. G. Shears3, B. C. Shen23, C. H. Shepherd-Themistocleous1, P. Sherwood24, G. P. Siroli7, A. Sittler16, A. Skillman24, A. Skuja11, A. M. Smith1, G. A. Snow11, R. Sobie33, S. Söldner-Rembold17, R. W. Springer26, M. Sproston15, K. Stephens3, J. Steuerer16, B. Stockhausen12, K. Stoll17, D. Strom36, P. Szymanski15, R. Tafirout9, S. D. Talbot14, S. Tanaka8, P. Taras9, S. Tarem25, R. Teuscher1, M. Thiergen17, M. A. Thomson4, E. von Törne12, S. Towers20, I. Trigger9, Z. Trócsányi27, E. Tsur2, A. S. Turcot5, M. F. Turner-Watson1, P. Utzat18, R. Van Kooten6, M. Verzocchi17, P. Vikas9, E. H. Vokurka3, H. Voss12, F. Wackerle17, A. Wagner16, C. P. Wards4, D. R. Wards4, P. M. Watkins14, A. T. Watson14, N. K. Watson14, P. S. Wells1, N. Wermes12, J. S. White33, B. Wilkens17, G. W. Wilson16, J. A. Wilson14, G. Wolf30, T. R. Wyatt3, S. Yamashita8, G. Yekutieli30, V. Zacek9 and D. Zer-Zion1
14 School of Physics and Space Research, University of Birmingham, B15 2TT, Birmingham, UK
7 Dipartimento di Fisica dell' Università di Bologna and INFN, I-40126, Bologna, Italy
12 Physikalisches Institut, Universität Bonn, D-53115, Bonn, Germany
23 Department of Physics, University of California, 92521, Riverside, CA, USA
4 Cavendish Laboratory, CB3 0HE, Cambridge, UK
20 Ottawa-Carleton Institute for Physics, Department of Physics, Carleton University, K1S 5B6, Ottawa, Ontario, Canada
29 Centre for Research in Particle Physics, Carleton University, K1S 5B6, Ottawa, Ontario, Canada
1 CERN, European Organisation for Particle Physics, CH-1211, Geneva 23, Switzerland
5 Enrico Fermi Institute and Department of Physics, University of Chicago, 60637, Chicago, IL, USA
17 Fakultät für Physik, Albert Ludwigs Universität, D-79104, Freiburg, Germany
18 Physikalisches Institut, Universität Heidelberg, D-69120, Heidelberg, Germany
6 Department of Physics, Indiana University, Swain Hall West 117, 47405, Bloomington, IN, USA
21 Queen Mary and Westfield College, University of London, E1 4NS, London, UK
13 III Physikalisches Institut, Technische Hochschule Aachen, Sommerfeldstrasse 26-28, D-52056, Aachen, Germany
24 University College London, WC1E 6BT, London, UK
3 Department of Physics, Schuster Laboratory, The University, M13 9PL, Manchester, UK
11 Department of Physics, University of Maryland, 20742, College Park, MD, USA
9 Laboratoire de Physique Nucléaire, Université de Montréal, H3C 3J7, Montréal, Quebec, Canada
36 Department of Physics, University of Oregon, 97403, Eugene, OR, USA
15 Rutherford Appleton Laboratory, OX11 0QX, Chilton, Didcot, Oxfordshire, UK
25 Department of Physics, Technion-Israel Institute of Technology, 32000, Haifa, Israel
2 Department of Physics and Astronomy, Tel Aviv University, 69978, Tel Aviv, Israel
8 International Centre for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, 113, Japan
32 Brunel University, U138 3PH, Uxbridge, Middlesex, UK
30 Particle Physics Department, Weizmann Institute of Science, 76100, Rehovot, Israel
16 II Institut für Experimental Physik, Universität Hamburg/DESY, Notkestrasse 85, D-22607, Hamburg, Germany
33 Department of Physics, University of Victoria, P O Box 3055, V8W 3P6, Victoria, BC, Canada
35 Department of Physics, University of British Columbia, V6T 1Z1, Vancouver, BC, Canada
26 Department of Physics, University of Alberta, T6G 2J1, Edmonton, AB, Canada
37 Dept of Physics, Duke University, 27708-0305, Durham, NC, USA
31 Research Institute for Particle and Nuclear Physics, P O Box 49, H-1525, Budapest, Hungary
27 Institute of Nuclear Research, P O Box 51, H-4001, Debrecen, Hungary
19 Sektion Physik, Ludwigs-Maximilians-Universitat München, Am Coulombwall 1, D-85748, Garching, Germany
10 TRIUMF, V6T 2A3, Vancouver, Canada
22 Royal Society University Research Fellow, Canada
34 Institute of Nuclear Research, Debrecen, Hungary
28 Department of Experimental Physics, Lajos Kossuth University, Debrecen, Hungary
38 Department of Physics, New York University, 1003, NY, USA
The process e+e− →, γγ(γ) is studied using data recorded with the OPAL detector at LEP. The data sample corresponds to a total integrated luminosity of 25.38 pb−1 taken at centre-of-mass energies of 130–172 GeV. The measured cross-sections agree well with the expectation from QED. In a combined fit using data from all centre-of-mass energies, the angular distribution is used to obtain improved limits on the cut-off parameters: Λ+ > 195 GeV and Λ− > 210 GeV (95% CL). In addition, limits on nonstandard e+e−γ couplings and contact interactions, as well as a 95% CL mass limit for an excited electron,Me*= > 194 GeV for an e+e−γ coupling κ = 1, are determined.
Determination of the cross-section at LEP 2
Single- and multi-photon production in e$^{+}$e$^{-}$ collisions at $\sqrt{s}$ up to 209 GeV
Eur. Phys. J. C 28, 1-13 (2003)
Multi-photon production in e$^+$e$^-$ collisions at $\sqrt{s} = $181–209 GeV
Tests of the standard model and constraints on new physics from measurements of fermion-pair production at 130–172 GeV at LEP
Measurement of the cross-sec tion for the process $\gamma\gamma\to \mathrm{p\bar{p}}$ at $\sqrt{s_{\rm ee}} = 183-189\,$GeV at LEP
Eur. Phys. J. C 28, 45-54 (2003)
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Posted on Wed, Apr 25, 2018 Mon, Apr 23, 2018 by HolyLandJustice.org
Natalie Portman explains why she refused to accept the Genesis Prize
Natalie Portman speaking at the Environmental Media Association’s 27th Annual EMA Awards in Santa Monica, Sep 23, 2017. (photo: Jerod Harris / Getty Images)
It’s about Netanyahu.
By Staff | Jewish Telegraphic Agency | Apr 20, 2018
“Like many Israelis and Jews around the world, I can be critical of the leadership in Israel without wanting to boycott the entire nation. I treasure my Israeli friends and family, Israeli food, books, art, cinema, and dance. Israel was created exactly 70 years ago as a haven for refugees from the Holocaust. But the mistreatment of those suffering from today’s atrocities is simply not in line with my Jewish values. Because I care about Israel, I must stand up against violence, corruption, inequality, and abuse of power.”
— Natalie Portman
Natalie Portman said she wouldn’t attend a prize ceremony in Israel because of her feelings about its prime minister, Benjamin Netanyahu, and “atrocities” committed on his watch, but emphasized that she would not shun Israel itself.
The Jerusalem-born director and actor, posting Friday night on Instagram, explained her decision not to accept in person the $2 million Genesis Prize, which calls itself the “Jewish Nobel,” after a day of speculation in the media that she was turning down the prize because she was joining the movement to boycott, divest from and sanction Israel. The prize foundation had the day before announced Portman’s decision not to attend the ceremony.
“I chose not to attend because I did not want to appear as endorsing Benjamin Netanyahu, who was to be giving a speech at the ceremony,” said Portman, who in 2011 won a best actress Oscar.
“By the same token, I am not part of the BDS movement and do not endorse it,” Portman said.
She did not explain what she was referring to by “atrocities.” Israel has drawn sharp criticism in recent months for confrontations with Palestinian protesters on its Gaza border. Israeli troops have killed over 30 Palestinians and wounded hundreds. Israel says the protesters are not peaceful and have tossed rocks and explosive devices at troops.
Read the full article here →
CategoriesNews Tags#BDS, #boycott, Genesis Prize, Natalie Portman, Netanyahu
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Cycle A-Z
And why is it so difficult to get a diagnosis?
by Nicole Telfer, Science Content Producer; and Jen Bell, Writer — March 26, 2018
For many reasons, it is difficult to know how common endometriosis is, just as it is difficult for even a single person to get a diagnosis of endometriosis. On average, someone who presents with symptoms of endometriosis goes on average seven years (from three years to eleven years depending on the country) from the onset of symptoms until getting a diagnosis (1). In places where healthcare is government-funded, the wait for a diagnosis can take even longer, compared to healthcare that is self- or insurance-funded (1).
How prevalent is endometriosis?
Research has tried to determine how common endometriosis is. According to the American College of Obstetrician and Gynecologists, endometriosis may affect about 1 in 10 women of reproductive age (2). But studies that try to predict the prevalence of endometriosis have found a wide range, from less than 1 out of 100, up to 15 out of every 100 women of reproductive age (3-5).
In population studies, where data from a large group of people are used to determine how common a disease is within that population, endometriosis has been reported with less prevalence, at around 1-2% of all women (as shown in the UK and Italy) (3,4). The problem with these studies is that they don’t account for people with asymptomatic endometriosis, who wouldn’t know they have the disease.
In attempts to account for asymptomatic cases, other studies have focused on individuals undergoing pelvic surgery (for various reasons). They look at how often endometriosis is found/observed during surgery. In these studies, the prevalence of endometriosis is often found to be much higher than in large-scale population studies. For example, in one study of women in Michigan undergoing hysterectomies, 3 out of 20 were found to have endometriosis (5). Focusing more specifically on people who got a hysterectomy for the reason of chronic pelvic pain, 2 out of 5 were found to have endometriosis during their surgery (5). This shows a large proportion of people with chronic pelvic pain have endometriosis.
Of the people who got a hysterectomy for reasons other than endometriosis or chronic pelvic pain, 1 in 12 had evidence of endometriosis present (5). This is really important, as it demonstrates that not everyone with endometriosis has pelvic pain.
The bias with these studies lies within the populations they focus on. The people studied are usually women attending gynecological clinics or hospitals, which reflects a smaller, less-representative population sample of people who already have gynecological problems, for which they’re seeking care (3).
The struggle to get an endometriosis diagnosis
It’s difficult to know how common endometriosis is, because diagnosis is so complicated.
Symptoms differ greatly
Endometriosis symptoms can differ greatly from person to person. Most people with endometriosis present with pelvic pain and dysmenorrhea (painful menstruation). These symptoms can be can be mistaken for normal menstrual symptoms, especially if they are present from the first period (1,2,6). Transgender and non-binary people affected by endometriosis may find it harder to get a diagnosis and appropriate healthcare.
Other people with endometriosis may have bowel and/or urinary pain as their predominant symptoms. Others may have no physical symptoms at all — up to a quarter of people with endometriosis are asymptomatic (2,7). Women with endometriosis may also be twice as likely to struggle with infertility, a symptom that is noticed only when someone has difficulty becoming pregnant (8). Because of this wide variety of endometriosis presentations, it can take several visits and potentially years for a healthcare provider to refer a patient onwards to a gynecologist or secondary care specialist to receive a diagnosis (6).
Another reason for delayed diagnosis is likely due to hormonal symptom suppression. When the reproductive hormones stop cycling because of pregnancy, breastfeeding, or use of hormonal contraceptives, pain symptoms may temporarily stop, and a person with endometriosis may not seek medical help (6). Hormonal contraceptives are often prescribed to decrease and regulate menstrual pain and excessive menstrual bleeding, as well as a treatment for endometriosis symptoms. When cycling resumes, symptoms can reoccur.
Diagnosis requires surgery
Getting a diagnosis currently requires a surgical procedure, to confirm that endometriosis-like tissue is visible outside of the uterus. Diagnosis often also requires a biopsy (tissue sample) for confirmation (2). Undergoing surgery to achieve a diagnosis is not something that usually happens immediately, as this is expensive, time-consuming, and like every surgical procedure, carries risks. Researchers are trying to find other ways of diagnosing endometriosis without a surgical procedure. Some of these could include examining the cellular components of menstrual fluid, and differences in menstrual blood-derived stem cells (9,10). More research is needed here.
Even when a healthcare provider feels confident enough to refer a patient to get laparoscopic surgical investigation, the next problem is actually finding and locating the endometrial-like tissue. Endometrial-like tissue can present in many places within the pelvis, such as on the ovaries, behind the uterus, on the peritoneum (the membrane that lines the abdomen and pelvis), in the fallopian tubes, and along the bowels, amongst other places. It can be difficult to locate these endometrial-like lesions. There is also evidence to suggest that perhaps these lesions may change over time or may be difficult to relocate—in some reported cases, lesions found in one surgery could not be located in a later surgery (5).
All of these factors of access, differing symptoms, symptom suppression, and difficulty finding a conclusive diagnosis contribute to why it can be so difficult to accurately determine how many people actually have endometriosis.
Is endometriosis more common in certain populations?
Endometriosis is diagnosed at different rates around the world, which could reflect differing access to healthcare, as well as different rates of the disease across populations. Research suggests that white women are more likely to be diagnosed with the disease, while black and Latina/Hispanic women are least likely to be diagnosed. In the United States, data from a large population study published in 2004 found that women identified as African-American and Hispanic were diagnosed with endometriosis at a 40% lower rate than women identified as Caucasian (11). It’s unknown whether this reflects lower rates of the illness, or is related to the discrimination experienced by women of color in the U.S. healthcare system, from inadequate access to healthcare to racial bias in pain treatment (12-14).
There may be a genetic link to endometriosis. Studies show that identical twins (monozygotic twins) are more likely than non-identical twins (dizygotic twins) to have endometriosis (15,16). Other research has found a 5 to 10 times increase in risk of having endometriosis if a person’s first degree relative (like a mother or a sister) was also diagnosed with the disease (17-18).
Weight may have an influence on endometriosis, as people with high body mass indexes (BMIs) may be less likely to be diagnosed with endometriosis (3,11). Research also shows that people with lower BMI (lower weight) may be more likely to present with endometriosis symptoms (20).
More research, awareness, and access to diagnosis and treatment is needed world-wide to better determine the prevalence of endometriosis.
Think you might have endometriosis symptoms?
If you have painful periods and pelvic pain, see your healthcare provider and let them know if you think something is wrong. For more information, read in detail about endometriosis symptoms, diagnosis and treatment.
Whether you are trying to get a diagnosis or to access appropriate medical care, there are endometriosis support organizations around the world who are there to help. If you’re looking for a trans-friendly OB/GYN you can find some tips in this guide.
Download Clue to track pain, bleeding, and other symptoms. This information that may help with diagnosis and in forming a management plan.
Nnoaham KE, Hummelshoj L, Webster P, d'Hooghe T, de Cicco Nardone F, de Cicco Nardone C, Jenkinson C, Kennedy SH, Zondervan KT; World Endometriosis Research Foundation Global Study of Women's Health consortium. Impact of endometriosis on quality of life and work productivity: a multicenter study across ten countries. Fertil Steril. 2011 Aug;96(2):366-373.e8.
The American College of Obstetricians and Gynecologists. FAQ013: Endometriosis. October 2012.
Ballard KD, Seaman HE, de Vries CS, Wright JT. Can symptomatology help in the diagnosis of endometriosis? Findings from a national case-control study--Part 1. BJOG. 2008 Oct;115(11):1382-91.Hickey M, Ballard K, Farquhar C. Endometriosis. BMJ. 2014 Mar 19;348:g1752.
Incidence and Estimated Prevalence of Morassutto C, Monasta L, Ricci G, Barbone F, Ronfani L. Endometriosis and Adenomyosis in Northeast Italy: A Data Linkage Study. PLoS One. 2016 Apr 21;11(4):e0154227.
Mowers EL, Lim CS, Skinner B, Mahnert N, Kamdar N, Morgan DM, As-Sanie S. Prevalence of Endometriosis During Abdominal or Laparoscopic Hysterectomy for Chronic Pelvic Pain. Obstet Gynecol. 2016 Jun;127(6):1045-53.
Ballard K, Lowton K, Wright J. What's the delay? A qualitative study of women's experiences of reaching a diagnosis of endometriosis. Fertil Steril. 2006 Nov;86(5):1296-301.
Bulletti C, Coccia ME, Battistoni S, Borini A. Endometriosis and infertility. J Assist Reprod Genet. 2010 Aug;27(8):441-7.
Prescott J, Farland LV, Tobias DK, Gaskins AJ, Spiegelman D, Chavarro JE, Rich-Edwards JW, Barbieri RL, Missmer SA. A prospective cohort study of endometriosis and subsequent risk of infertility. Hum Reprod. 2016 Jul;31(7):1475-82.
Warren LA, Shih A, Renteira SM, Seckin T, Blau B, Simpfendorfer K, Lee A, Metz CN, Gregersen PK. Analysis of menstrual effluent: diagnostic potential for endometriosis. Molecular Medicine. 2018 Mar 19;24(1).
Feinstein Institute.Feinstein Institute discovery promises improved diagnosis and understanding of endometriosis. PR Newswire. 2018 Mar 18. Date cited Mar 26 2018. Available from: https://www.prnewswire.com/news-releases/feinstein-institute-discovery-promises-improved-diagnosis-and-understanding-of-endometriosis-300615467.html.
Missmer SA, Hankinson SE, Spiegelman D, Barbieri RL, Marshall LM, Hunter DJ. Incidence of laparoscopically confirmed endometriosis by demographic, anthropometric, and lifestyle factors. Am J Epidemiol. 2004 Oct 15;160(8):784-96.
Centers for Disease Control and Prevention. African American health: creating equal opportunities for health. 2017 Jul 3. Date cited: Mar 26 2018. Available from: https://www.cdc.gov/vitalsigns/aahealth/index.html
Hoffman KM, Trawalter S, Axt JR,Oliver MN. Racial bias in pain assessment and treatment recommendations, and false beliefs about biological differences between blacks and whites. Proc Natl Acad Sci USA. 2016 Apr19;113(16):4296–4301.
Mossey JM. Defining Racial and Ethnic Disparities in Pain Management. Clin Orthop Relat Res. 2011 Jul;469(7): 859–1870.
Treloar SA, O'Connor DT, O'Connor VM, Martin NG. Genetic influences on endometriosis in an Australian twin sample. Fertil Steril. 1999 Apr;71(4):701-10.
Saha R, Pettersson HJ, Svedberg P, Olovsson M, Bergqvist A, Marions L, Tornvall P, Kuja-Halkola R. Heritability of endometriosis. Fertil Steril. 2015 Oct;104(4):947-952.
Matalliotakis IM, Arici A, Cakmak H, Goumenou AG, Koumantakis G, Mahutte NG. Familial aggregation of endometriosis in the Yale Series. Arch Gynecol Obstet. 2008 Dec;278(6):507-11.
Moen MH, Magnus P. The familial risk of endometriosis. Acta Obstet Gynecol Scand. 1993 Oct;72(7):560-4.
Stefansson H, Geirsson RT, Steinthorsdottir V, Jonsson H, Manolescu A, Kong A, Ingadottir G, Gulcher J, Stefansson K. Genetic factors contribute to the risk of developing endometriosis. Hum Reprod. 2002 Mar;17(3):555-9.
Hediger ML, Hartnett HJ, Louis GM. Association of endometriosis with body size and figure. Fertil Steril. 2005 Nov;84(5):1366-74.
Perimenopause and libido: a personal story
I’d heard that experiences of menopause vary, but there’s one thing I wasn’t prepared for: my skyrocketing sex drive.
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Archives for posts with tag: Michelle Bauer
Apolitical Home Viewing: Richard Gabai Double Grabber
March 2, 2013 //
Bikini Drive-In (1995) ****1/2 One of the quintessential Fred Olen Ray classics, Bikini Drive-In features all of the traits his fans have come to expect over the years: campy acting from a mix of has-beens and shapely young performers, genuine American trash culture nostalgia, a man in a monster suit, broad humor, and heaping helpings of big, bare breasts! Or the world’s cheapest special effect, as Ray might put it. The plot, a variation on the old motley-crew-of-underdogs-bands-together-to-raise-money-to-save-the-[insert school, summer camp, or recreation venue] Roller Boogie or Screwball Hotel type, finds beach babe Ashlie Rhey inheriting a decrepit drive-in theater and having to fight to save it from real estate gangster David Friedman.
Thousands of dollars have to be raised in one weekend – what to do? Fortunately, the mogul’s son, the adorably dorky Richard Gabai, has the hots for Ashlie and comes to her rescue with the idea of turning the family-friendly but deadsville drive-in into a bacchanalian gonzo bikini-infested party headquarters and showing exploitation films like Ray’s own Hollywood Chainsaw Hookers. All of this, of course, is a fine excuse to show scantily clad floozies cleaning up the drive-in montage-style in preparation for the gala opening (and turning the hoses on each other, naturally). What then follows during the film’s final act is one of the greatest party/riot/saturnalia sequences in memory – maybe not quite as happening as Animal House or Bachelor Party, but pretty mightily crazy and loose.
The cast is a real bonanza for fans of the Wynorski-Ray-DeCoteau-Sloane heyday of low-budget L.A. cinema. Michelle Bauer appears to sizzling effect as a sultry scream queen duped into appearing at the gala re-opening; seedy Ross Hagen is one of Friedman’s henchmen; Tane McClure, renowned stripper Nikki Fritz, and porn actress Sarah Bellomo (aka Roxanne Blaze) are among the film’s many bimbos; and Becky LeBeau (so memorable as the nearsighted stripper in Not of This Earth), in addition to performing some of Bikini Drive-In‘s pleasantly cheesy soft rock songs, plays a stripper recruited to seduce cocky disc jockey Fred Olen Ray. Other cameos include Gordon Mitchell, Forrest Ackerman, Jim Wynorski, and (posthumously, via photograph) even John Carradine. Bikini Drive-In is essential viewing for any fan of Ray, Gabai, big breasts, or drive-in movies, and the interior sets are a treasure trove of posters for vintage exploitation films like Death Curse of Tartu, Sting of Death, Cannibal Girls, and Wild, Free, and Hungry. 4.5 of 5 possible stars. Recommended.
Assault of the Party Nerds II: The Heavy Petting Detective (1995) **** First of all, any nerd movie or cheap trash aficionado who is not yet an admirer of the redoubtable Richard Gabai and has not yet watched the incomparable Assault of the Party Nerds needs to do so immediately. Gabai, an actor who better than any other strikes a captivating balance between accessibly handsome and hopelessly if charmingly dweeby and made a semi-star of sorts of himself in that 1989 Revenge of the Nerds-inspired opus, returns as writer-director-star of its sequel, The Heavy Petting Detective, which, clearly designed with the intention of pleasing fans of the original, has also reunited several members of its cast, including Christopher Dempsey and Robert Dorfmann as secretly gay jocks Bud and Chip; scream queens Michelle Bauer and Linnea Quigley as airheads Muffin and Bambi; and even, in a cameo, hairy Richard Rifkin as the World’s Oldest Living Active. New and welcome additions to the Party Nerds coterie include Laugh-In‘s Arte Johnson; Batman‘s Burt Ward; USA Up All Night‘s Rhonda Shear (sporting some outrageous hair and kooky outfits that have to be seen); Tane McClure as Dempsey’s seductive secretary; and Tony Scaduto, Spridle Esponda, and Steve Rosenbaum as a trio of next-generation party nerds.
Long since having graduated, Gabai’s alter ego Ritchie Spencer is currently working as a private detective and finds himself mixed up in a wacky imbroglio involving his old greek life acquaintances and rivals when Burt Ward hires him to investigate his son-in-law, who just happens to be the narcissistic and villainous Bud, now married to Muffin and working as an executive at her father’s company. Bud, having discovered that Muffin has actually inherited the business, concocts a fiendish scheme to sow discord between his wife and her family and so get her to sign the company over to him. In the course of his investigation, which has to compete for Spencer’s time with a concurrent case involving an elusive potato chip truck driver, Spencer also catches up with Bambi, who, while still somewhat ditzy, has become a cynical, sexually jaded golddigger. Also complicating matters is the fact that the nerds’ fraternity has fallen on hard times and that the jocks, it turns out, own the deed on the property and are threatening to evict the brothers. Can the nerds save their frat house? Will Muffin ever win her husband’s affection again? Will Spencer ever grow up? Will the new generation of party nerds rise to the occasion like their forebears and manage to lose their virginity before they graduate? Naturally, and in the venerable Party Nerds tradition, everything comes to a head at a zany fraternity party.
Though not quite as classic as Assault of the Party Nerds, The Heavy Petting Detective is in some ways superior and offers a lot to recommend it. In addition to the over-the-top commitment of its entirely colorful cast, the film is fast-paced and never slows down long enough to be boring, even when the humor is occasionally (or usually) lame. Gabai’s pop ‘n’ roll band, the Checks, provides several upbeat songs (some also featured in Bikini Drive-In) that contribute to the movie’s tempo and harmless, friendly feeling for the viewer. A few gags are repeated from Assault of the Party Nerds, which, depending on individual taste and affection for the original, could be a plus or a minus. In the end, however, what probably matters most for partisans of independent VHS glory days, is that The Heavy Petting Detective brings Michelle Bauer, Richard Gabai, and Linnea Quigley together again to do their things, and what, in all honesty, could be better than that? 4 of 5 possible checks.
Tags Animal House, Arte Johnson, Ashlie Rhey, Assault of the Party Nerds, Bachelor Party, Batman, Bikini Drive-In, Burt Ward, Christopher Dempsey, David DeCoteau, David Friedman, Death Curse of Tartu, drive-in, drive-in movies, Forrest Ackerman, fraternity, Fred Olen Ray, Gordon Mitchell, Hollywood Chainsaw Hookers, Jim Wynorski, John Carradine, Kelly Bundy Era, Linnea Quigley, Michelle Bauer, nerd, Nikki Fritz, Not of This Earth, Rhonda Shear, Richard Gabai, Richard Rifkin, Rick Sloane, Robert Dorfmann, Roller Boogie, Ross Hagen, Roxanne Blaze, Sarah Bellomo, Screwball Hotel, Spridle Esponda, Steve Rosenbaum, Sting of Death, Tane McClure, The Checks, The Heavy Petting Detective, Tony Scaduto, USA Up All Night
1313: Cougar Cult ***
David DeCoteau, along with Fred Olen Ray and Jim Wynorski, was one of the more heroic and endearing directors to emerge in the era of VHS. He is especially noteworthy to horror fans of a nostalgic bent for having made two low-budget wonders, Sorority Babes in the Slimeball Bowl-O-Rama and Nightmare Sisters, which brought together Michelle Bauer, Linnea Quigley, and Brinke Stevens, the three premier scream queens of the period. Now, in 1313: Cougar Cult, the four great screen queens – Bauer, Quigley, Stevens, and DeCoteau – are reunited for one more roll in the trash, this one about a trio of supernatural pagan sisters who turn into cougars – literally! – and devour the young men they succeed in luring into their tackily decorated Malibu mansion.
Photogenic Ryan Curry, Bryce Durfee, and Jack Kubacki star as college students who show up (and end up showing a lot) to take jobs as the cougars’ houseboys. There is something resembling a plot in 1313: Cougar Cult – something about ritual sacrifices to please an ancient Amazonian deity – but the film is really just an exercise in bisexually friendly cheesecake, with Bauer, Quigley, and Stevens slinking around and acting horny, and lots of long, lingering shots of young actors washing their sculpted torsos or sensually writhing in sleep. Harboring no illusions about what it is, the film is at times playfully self-deprecating – and even annoyingly so when the sisters’ transformation into their carnivore forms is depicted by the cartoonish superimposition of cougar heads over the actresses’ faces.
1313: Cougar Cult will appeal primarily to two mostly separate groups: those who enjoy ogling half-naked young men and those who fondly remember the scream queens’ work in the low-budget video gems of the 80s and early 90s. It will, unfortunately, frustrate many in this latter group because 1313: Cougar Cult is ultimately little more than a gigantic tease. For having a premise built on three evil middle-aged women’s insatiable lust, the film is remarkably tame and devoid of explicit heterosexual action. Bauer, Quigley, and Stevens are very sexy women, their vintage notwithstanding; and while, having reached a certain stage in their careers, they may be understandably reluctant to undress or engage in simulated sex onscreen (note: do yourselves a favor and see Assault of the Party Nerds), the fact that nothing of the sort appears in 1313: Cougar Cult is still a pretty grievous disappointment. What but sadism, for instance, could motivate a film in which Brinke Stevens informs a young stud he will have the pleasure of oiling and massaging her – and the viewer never even gets to see it?
Most puzzling of all, perhaps, is that whole decades had to pass before the three venerable cuties could be brought back together. That occasion, sadly, contents itself with being coquettish and uber-campy rather than satisfyingly sleazy or even vaguely horrific; but no Amazonian deity dictates that the actresses’ collaborations have to stop with this one. They will, if the gods of video nerd garbage are benevolent, be making more films as a trio in the not-too-distant future. Meanwhile, fans must content themselves with the picturesquely animal lust on Stevens and Bauer’s faces in this film as they softly paw Bryce Durfee’s body – that and the gratifying moment when Quigley, speaking in a ludicrously demonic voice, commands the audience, “Come to Mama.”
3 of 5 possible stars – one apiece for each of these enticingly mature scream queens.
Ideological Content Analysis indicates that 1313: Cougar Cult is:
5. Anti-state. The cougars pay their manservants cash, seeing no reason to involve the government in their private transactions.
4. Drug-ambivalent. Smoking – smoking cigarettes, that is – is bad for your health.
3. Innocently class-conscious. The decadent rich prey upon the weak, sexually and as cannibals.
2. Feminist. Women give the orders.
1. Hedonistic. The human body is beautiful and a source of fun. The fun, furthermore, should be prolonged for as long as humanly or cougarly possible.
Tags 1313: Cougar Cult, anti-state, Assault of the Party Nerds, Brinke Stevens, Bryce Durfee, cannibalism, class warfare, cougar, David DeCoteau, drug-ambivalent, feminist, Fred Olen Ray, gay interest, hedonism, Jack Kubacki, Jim Wynorski, Linnea Quigley, Michelle Bauer, Nightmare Sisters, pro-slut, Rapid Heart Pictures, Ryan Curry, scream queens, shower scene, Sorority Babes, VHS
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The Congress
You are here: Home / 2014 Films / The Congress
Nov. 4. Part of our 4th annual evening of Films By & About Women. Hosted by Hadassah, ORT, Na‘Amat, SHALVA and the Women’s Division of Israel Bonds.
123 minutes. 2013. Director: Ari Folman (Waltz with Bashir). With Robin Wright (House of Cards), Harvey Keitel (The Piano), Jon Hamm (Mad Men) and Paul Giamatti (Sideways). In English.
Genres: Dystopian Sci-Fi, Live Action/Animation
Official Selection, Cannes Film Festival
An aging actress (Robin Wright, playing a version of herself) decides to take her final job: preserving her digital likeness for a future Hollywood. Through a deal brokered by her longtime agent, her alias will be controlled by Miramount Studios, and will star in any film they want with no restrictions. In return, she receives healthy compensation and her digitized character will stay forever young. Will she ultimately go back to living in the world of truth, or surrender?
The Dove Flyer Shadow in Baghdad
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The Game of Nations, Congo-Style
Here's a podcast interview at Electric Politics with Larry Devlin about his new memoir Chief of Station, Congo about his years as the CIA's man in the Congo, in which he says he wasn't responsible for the murder of the decolonized state's first President, Patrice Lumumba.
Strange as it seems now, in 1960, everybody -- the UN, Washington, Moscow -- kind of imagined the future of the world was being determined on the banks of the Congo. Now, we just try not to think about the place. The CIA's man Mobutu was a prime stinker, but the place sure hasn't improved in the decade since he's been gone. Apres Mobutu, le Deluge, for which Mobutu and America bear much responsibility, but then maybe 35 years apres le Deluge is not so bad in tropical Africa. Anyway, it makes me tired to think about it.
Eisenhower liked to use the CIA as a cheap alternative to fighting the Cold War using the Army. (Similarly, he pushed ahead into the nuclear ICBM deterrent as an alternative to matching the Red Army tank for tank and man for man.) Not only did it save money and American lives, but it slowed the rise of the "military-industrial complex" that Eisenhower detested, and sidestepped the kind of war fever among the public that had made McCarthyism so popular during Truman's Korean War. Playing Machiavellian games among the Congo's elite was a lot better than sending American troops to the heart of darkness.
Eisenhower's VP, Richard Nixon, called Ike, who pretended to be a kindly old duffer in public, the most devious man he had known.
By Steve Sailer on 5/05/2007 Labels: Congo, Eisenhower, game of nations, heart of darkness
Steve, if you can't be bothered, why should we?
No Steve, it was more Ghana, one of the first nations to gain it's independence and with a fairly good infrastructure and trained bureaucracy from the Brits.
While Ghana is not the pits of say, Cote D'Ivore or Liberia or the Congo, it's a typical African kleptocracy without any minimal attention paid to economic development.
While both say Congo and Malaysia started off with the same per-capita-income and GDP, at least in Malaysia (and other Asian countries) the kleptocrats understood they could steal more money and get richer if the people themselves were richer (and this also had the happy coincidence of making them less prone to coups).
Partly IMHO this is due to less tribalism, i.e. Malays knew who they were, as did Indonesians, Thais, etc. They had historical nations with national identities that predated colonialism and survived after it. Africa was then and now a collection of squabbling tribes with no idea of nationhood.
And yes Ike was a masterful leader. Neither caving to the Soviets who WERE aggressive nor seeking un-needed confrontations like JFK.
Stuff in the Congo may have been pointless in and of itself but it served to deter Soviet Adventurism like putting missiles in Cuba or the Berlin Blockade or other stupid stunts.
No one in the Politburo could argue that Ike wasn't a serious guy and could be pushed around with aggressive behavior with impunity.
So maybe Ike wasn't a great intellectual but learned a thing or two corralling Patton and Monty and Bradley, FDR, Truman, Churchill, Stalin, and of course Marshall.
Plus Ike could tell MacArthur to go away and shut up. And make it stick.
As a side note I knew people who had worked under Kwame Nkrumah's goverment. They were extremely disappointed in the failure of his government and those after to offer anything on the order of Lee Kwan Yew whom they found a very wise leader.
These were well educated men who were not stupid or uninformed. Many were quite brilliant in law, history, etc. as my Undergrad Professors. To a man they were quite open about how unhappy they were about Africa's total inability to govern themselves in contrast to the high hopes everyone had for Nkrumah.
Don't forget that DeGaulle in his War Memoirs seriously considered an Algerian Strategy with manpower gathered as far South as Brazzaville, factories and everything. At least the man wanted to keep fighting. Africa was not always considered to be the inevitable sinkhole it is today.
The USA´s and USSR´s twin efforts to bring down European colonies is one of mankind´s darkest chapter.
African wouildn´t be the sinkhole it is today if colonial rule had been allowed to remain in place for another 50 or 100 years.
Ike and the CIA have a lot to answer for.
The Belgians left the Congo with something like 300 miles of paved roads and six native born university graduates at independence. If ever there was a colony set up for failure from the get-go, it was the Congo. It was almost as bad as when they switched allegiance from the Tutsi to the Hutu in Rwanda (because the better educated Tutsi were the main agitators for independence) just before they bugged out. At least the British left India with a working bureaucracy, railroad, and phone system.
At this point, the world might be better off sawing off the northern and eastern parts of the Congo and giving them to Uganda and Rwanda, which are much better run states and more or less rule the regions by proxy as it is.
michael farris said...
I think it's pretty much beyond debate that the Belgians were the worst colonial power in Africa, hands down, no contest, they left royal rat fucks that no other european country could compete with.
I think it's pretty much beyond debate that the Belgians were the worst colonial power in Africa
It would be interesting to read an honest comparison of former colonies* contrasting their degree of success since independence with the level of investment and general decency of their former overlords. No publishable book will discuss failings of the native inhabitants, but a clever author could put much between the lines. Has such a study every been published?
*By "former colonies," I mean 19th/early 20th c. colonies, not the earlier efforts in the Americas and ANZ where the colonists decimated or drove off the aboriginals and took the place over lock, stock and barrel.
After fits and starts, Africa has started to develop homegrown Lee Kwan Yews (often explictly modeled on the original), notably Yoweri Museveni in Uganda, Paul Kagame in Rwanda, and Isaias Afewerki in Eritrea with their emphasis on social cohesion and economic growth.
Wow, this is the first iSteve.com comment thread in a long time which is on-topic. Excellent!
Don't forget that DeGaulle in his War Memoirs seriously considered an Algerian Strategy with manpower gathered as far South as Brazzaville, factories and everything.
Charles DeG.'s hopes and dreams were not necessarily realistic.
... It is my understanding that the majority of "Free French" enlisted men in Europe were Algerian and other African Muslims. This does tend to put France's current problems with Muslims in a somewhat different light ... not that Free French forces ever did much real fighting in 1944 and '45 ... maybe some skirmishing with anti-Gaullist French factions.
P.S. Perusing photos of French soldiers in 1914-18, one can see African and Viet Namese-looking faces.
There's a movie about those Free French Algerians that served in the second World War coming out called Days of Glory.
Now, we just try not to think about the place.
I think over 4 million Congolese have died in the recent wars there. Largely to supply diamonds to the (orthodox Jewish) diamond merchants of Amsterdam, via Rwanda. Compare 4 million Congolese dying in the last 10 years to, say, 6 million Jews dying 50 years ago. Which gets more press?
It would be interesting to read an honest comparison of former colonies* contrasting their degree of success since independence with the level of investment and general decency of their former overlords.
If you look at economic maps of post-indepedence Africa, it's the Francophone countries that are the poorest.
I'd be equally interesting to see post-colonial outcomes in Africa correlated with what stage of state formation the societies were in when they were colonized. Did basically tribal societies (many of them yoked together in state borders drawn thousands of miles away) have the same outcomes as countries that were on well on their way to becoming nation-states or empires when they were colonized?
"Compare 4 million Congolese dying in the last 10 years to, say, 6 million Jews dying 50 years ago. Which gets more press?"
The Jews were killed deliberately. The Congolese were killed randomly by sheer accident.
(must...keep...straight...face)
Plus, the goyim aren't important anyway. But every hair on a Jewish head is sacred.
"interesting to see post-colonial outcomes in Africa correlated with what stage of state formation the societies were in when they were colonized"
Look at Detroit after the Whites left. Or, for a dose of reality, look up "Africa Addio" on youtube (or elsewhere). Er, there's your African civilization. It ain't wood carvings in Pier One.
I do understand that the Honorable Middle Kingdom of Mooganshi'Daq'uan was on the verge of achieving space flight...before de white debbils clapped its scientists in chains. Oh the horror.
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Claressa Shields makes history with consecutive world title wins
2012 Olympic gold medalist Claressa Shields (Flint, Mich.) continued her incredible reign on Friday with a championship bout victory at the 2016 Women’s World Championships in Astana, Kazakhstan. Shields is the first American female boxer ever to win two elite world titles and the first U.S. boxer to claim consecutive
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Oscar® winner Jeremy Irons returns in season three of The Borgias in his Golden Globe® nominated role as Pope Alexander. After surviving a near fatal assassination attempt, he responds with an iron will by ruthlessly purging the Vatican of anyone who might be disloyal to him. Alexander’s true master plan is to establish the Papacy as a hereditary monarchy across the heart of Italy – for father and son to rule the world. But he must come to accept that his children are independently ready to wield their own power. Cesare (Francois Arnaud), now the military prince and daring guerrilla fighter, is so eager for action that he comes perilously close to war with his own father’s army. His sister Lucrezia (Holliday Grainger) is equally frustrated when her husband, the Neapolitan prince Alfonso, proves to be a disappointment. Feeling desperate to secure a future for herself and her child, she enters the dangerous fray of Neapolitan politics and learns the art of poisoning. As their passions grow, and as mistrust of all others becomes more ingrained, the siblings finally give in to their desires and embark on a passionate incestuous relationship. With both that scandalous secret and the unspoken agonies of Juan’s death lingering between them, the family is riven by paranoia and suspicion. THE BORGIAS is a Canadian-Irish-Hungarian Treaty co-production. Academy Award®-winning director and Emmy nominee Neil Jordan serves as creator, executive producer, writer and director of select episodes. Jack Rapke, Darryl Frank, John Weber, Sheila Hockin and James Flynn also serve as executive producers.
The Borgias, Season 3
© The Borgias (c) 2013 Borg Films kft / LB Television Productions Limited/Borgias III Productions Inc. A Hungary – Ireland- Canada Co-Production. All Rights Reserved.
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The exodus of 300,000 people in photos" />
Gender and sex
Karabakh stories
Letters from prison
From far and near
Unheard Voices
Photo archive: Georgian families leaving Abkhazia during the 1992-1993 Georgian-Abkhaz war
The exodus of 300,000 people in photos
These images were captured between 1992 and 1993 during the Georgian-Abkhaz war. They are currently kept in the archives of the Georgian National Library. They depict Georgian families leaving their homes in Abkhazia.
We dedicated this photostory to the 26th anniversary of the end of the armed conflict, a date that is commemorated by both sides from polar-opposite perspectives.
A solution to the conflict has not been reached to this day. It is far from settled as the sides’ positions remain the same: Georgia insists on its territorial integrity, while Abkhazia insists on it independence.
So far, Abkhazia’s status as an independent state has been recognised by Russia and five other nations. All western countries and the rest of the international community support Georgia’s territorial integrity.
The armed conflict began on 14 August 1992 and ended on 27 September 1993 with the defeat of the Georgian military forces.
According to incomplete data, more than 13,000 people lost their lives. More than 1,000 people are missing. Their families still have no knowledge of where many of them are buried.
As many as 300,000 people were displaced from Abkhazia as a result of the war, a majority of whom were ethnic Georgians. This photo essay is about them.
Abkhazia, 1993.
Ochamchire railway station in Abkhazia, 1993. Photo: Shah Aivazov.
Georgian displaced persons, 1993. Georgian National Library Archive. Photo: Shah Aivazov.
Abkhazia, 1993. Georgian National Library Archive.
Displaced persons in Sukhumi airport, 1993.
Displaced persons leaving Abkhazia. Bridge across the Inguri river, 1993.
Toponyms and terminology used in the article, and views, opinions and strategies expressed in it do not necessarily reflect the views and opinions of JAMnews or any employees thereof. JAMnews reserves the right to delete comments it considers to be offensive, inflammatory, threatening, or otherwise unacceptable
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The Fantasy Book on The Return of Kurt Angle (American Alpha, Brock Lesnar, Bray Wyatt)
Michael McMonigle | May 12, 2017 | Columns, Top Story | No Comments
There are times in life when you have an idea in place. You have a plan all worked out. You know what you are going to say and what you are going to do. It’s there, in front of you, waiting for you to put it in motion. And then life happens. You can’t always do whatever you want to do. Sometimes you just have to go in the direction life takes you. Working with the flow often gets you farther than working against it. However, sometimes you wind up in the wrong location and have to recalibrate.
With that being said, it’s time to Fantasy Book some wrestling. Kurt Angle has made it known many times that he wishes to wrestle again. Whether his body can stand up to the physical pounding is another story. But it has been in a news quite a bit lately (mostly due to Kurt himself talking about it), so I thought I would fantasy book a possible return for our hero.
The way I see it, there are a couple very obvious paths on which Angle can return. He could be fired as GM and go to SmackDown Live! where he would unite with American Alpha to form a “Goofy Americans” unit. He could play cheerleader to the team, he could play mentor to the guys, he could even play the “player-coach” angle where he has them watch what he does in the ring.
One thing that I think could work, and play to everyone’s strengths, is Angle going over to SD and begin hanging out with Jordan and Gable. Gable could proudly talk about his “Ready, Willing, and Gable” catchphrase which Angle would dismiss. He would basically insult Gable and Jordan a lot while telling them that he loves their work and wants to help them. This would confuse Jordan and Gable for weeks, until Angle tells them to just watch what he does. Then Angle would return to the ring against Jinder Mahal or someone. This would turn into a “Coach” Angle preaching to American Alpha to “Do what he does, not what he says.” The comedy out of the communication confusion between the three in contrast to the impressive ring work would be excellent.
The second obvious path, and the one that would be a slightly tougher sell, is that Angle remains Raw’s GM for quite a while. Eventually Brock Lesnar and Paul Heyman return and run down the Raw roster. Lesnar actually wrestles a couple times on Raw, just annihilating his opponents. Lesnar could also destroy his planned SummerSlam opponent (whoever that may be) and putting him on the shelf. Angle, now having to deal with a depleted roster due to Lesnar’s rampaging, confronts Lesnar and Heyman and threatens them. Lesnar does not take kindly to this and Ubers Angle to Suplex City.
After a week of selling an injury, Angle can make his return and declare that he is finished with his GM role. He can be upset that Stephanie McMahon didn’t suspend Lesnar or something if that is necessary to get the storyline line approved. Then he can say that before he resigns, he has one more thing he has to do as GM. He still needs to complete the SummerSlam card, and Lesnar’s actions have put the Universal title in question at that event. So, his last act as GM is to name Lesnar’s opponent for SummerSlam. Of course he announces himself as that opponent, drops the mic, and heads to the PPV.
Why would this be a tougher sell? A couple of reasons actually. First, it involves awarding an Universal title match to someone who hasn’t wrestled in the company for years. However, given the recent Goldberg precedent, The Rock’s return a couple years ago, or even John Cena returning to steal the World Title from AJ Styles, I think we can let that slide a bit. Second, it doesn’t help any of the current wrestlers on the roster. True, but I still think that match has enough cache to be interesting to fans. Third, the main event of arguably the second biggest PPV of the year will be headlined by a part-timer and someone coming out of semi-retirement. Again, recent WWE precedent makes this issue fairly moot. Finally, and perhaps most importantly, I am not sure how well Angle’s neck can hold out in a match against Lesnar. I know these guys have wrestled before, in a pretty good match, mind you, and they are both excellent amateur wrestlers, so I think they would have a good match. But Lesnar’s thing now is how many German suplexes he can throw on an opponent. Having Kurt take a dozen or so bumps on his neck can not be a good thing. This match is not worth having Angle not being able to walk in a year or two.
To be honest, I like both of those angles detailed above. Obvious or not, they sort of work for me. But there is one more story that I think can be told. Angle is at a point in his career where working with younger wrestlers is beneficial to those wrestlers’ development. It is also beneficial to how those newer guys are seen by the audience. If you have The Rock come in and destroy someone new, that person is sort of buried right away. But if you have someone relatively new get a signature victory over someone like Triple H, it could jumpstart a stuttering face turn (see Seth Rollins).
So what if Angle embraced working with some of the younger superstars. Just working with Angle would teach these guys a lot, but if they could come out on top in a feud with Angle, all the better.
To fantasy book this, I would have Angle resign as Raw General Manager. He would say his heart is not in management, it is in wrestling. And if he wants to do it, and he still can do it, then why not? He announces that he has booked a physical and if he passes, the next time the Raw crowd sees him, it will be inside of the ring.
Angle’s first few matches back would be glorified squashes. Then he would take on Bo Dallas. Angle would win fairly easily in their first match. The next week, Dallas would call out Angle saying that he wasn’t ready last week and that Angle’s victory was soft. He can even steal the Big Cass catchphrase, but make sure to spell it properly and insult Big Cass at the same time. Angle would come out and defeat him again.
The next week, Angle would come out and say that Dallas has been calling and calling and texting and emailing and calling trying to get one more shot at Angle. Angle says that if Bo wants one more match against him, that’s fine, but that’s it. The match will be more competitive this time, with the announcers playing up how Dallas has learned from his previously encounters with Angle. In the end, Dallas will win with a surprise small package. Angle will be shocked, but make a congratulatory statement later.
The next week Angle would call out Dallas and say that he was impressed last week… but maybe he was taking him lightly. He is an Olympic gold medalist after all, and Bo Dallas is just Bo Dallas. Incensed, Dallas will grab the microphone and shove Angle down. Dallas will lay into Angle verbally saying that the “great” Kurt Angle is no more. Dallas will begin third-person speak here, marking a minor change in his character. He says that Bo Dallas took that away from him. In turn, that makes Bo Dallas great. And Bo Dallas is not a gold medalist, but he is more than “just Bo Dallas.” Bo Dallas is greatness and nastiness. He says that Bo Dallas is the brother of the devil and that Angle better Bo-lieve.
This will set up a match on a PPV between Dallas and Angle. The match will be a very good match thanks to Angle, but Dallas will be made to look really good. Angle will get the win with an Angle Slam and the ankle lock after a hard fought contest. Post-match, Angle will look to extend a hand to Dallas in a show of respect. This brief series of matches could turn Dallas into a legitimate challenge for other wrestlers and not just comedy fodder.
But wait, there’s more. After Angle extends his hand to Dallas, Dallas hesitates. Finally, he begins to stretch out his hand but the lights go out. When they come back on, Dallas is no where to be found and Bray Wyatt is in the ring behind Angle. Wyatt jumps Angle from behind, beats him down, and hits him with Sister Abigail. This will be the angle that helps rebuild Bray Wyatt. Angle should be able to get some good-to-great matches out of Wyatt. Wyatt should be able to scare Angle without resorting to silly supernatural gimmicks. In fact, Wyatt could mention Angle’s past demons and how they have been coaching him. Things like that.
For this to work, Wyatt needs to come out on top here. Angle can get a win or two, and even chase Wyatt off once or twice, but at the end of the day, this storyline needs to be viewed as Wyatt pretty much owning Angle. Wyatt needs the rebuild a lot more than Angle does. Kurt, even if he is pretty much decimated in this feud, can always go back to his gold medal winning as a point to re-establish himself. But if Wyatt can take down, if not out, a Hall of Famer like Kurt Angle, maybe it is time to take him seriously again.
During this whole battle with Angle, Bo Dallas would be away and off TV. After Wyatt beats Angle for good at the end of the feud, you have several options. Dallas could join his brother in the Wyatt Family. Dallas could acknowledge his brother as his brother but become very annoyed that Wyatt felt he had to step into his battle against Angle. Dallas could return and not say anything about Bray Wyatt, allowing the possibility of that reveal to come at a later time. And Angle could go on to fight The Miz or Cesaro or another new guy after successfully helping Bo Dallas and Bray Wyatt get over.
So, what do you think? Do you like any of these options better than the others? Which way should Angle go? Sound off in the comments below.
Tags: American Alpha, Big Cass, Bo Dallas, Bray Wyatt, Brock Lesnar, Cesaro, Kurt Angle, paul heyman, SummerSlam, The Miz
mmcmonigle
Human. I think.
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Effective as of December 15, 2009.
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Bio essence
Bio-Water Sunscreen Spf 50+ Pa++ (Hydrating)
Bio Water Cooling Sunscreen is a water-based formula which provide long hours of full face and body sun protection, yet feel so light on skin. Specially formulated with Bio-Essence Miracle [more] [more] Bio Water which is low in mineral contents and rich in trace minerals, this sunscreen instantly provides 2X cooling and moisturizing effect on the Skin. [less]
Uploaded by: sandloover on 09/30/2018
Water, Cyclopentasiloxane, Alcohol Denat, Titanium Dioxide, Ethylhexyl Methoxycinnamate, Butyl Methoxydibenzoylmethane, Benzophenone-3, Butylene Glycol, Phospholipids, [more]C12-15 Alkyl Benzoate, Stearic Acid, Aluminum Hydroxide, Polyhydroxystearic Acid, Aluminum Stearate, Propanediol, Sodium Acrylate/Sodium Acryloyldimethyl Taurate Copolymer, Isohexadecane, Polysorbate 80, Sodium Hyaluronate, Citrus Grandis (Grapefruit) Fruit Extract, Ethylhexylglycerin, Ppg-26-Buteth-26, Peg-40 Hydrogenated Castor Oil, Carbomer, Tranexamic Acid, Niacinamide, Euglena Gracilis Extract, Glycerin, Tocopherol, Triethanolamine, Fragrance, Allantoin, Disodium Edta
Anti-acne: Niacinamide
Antioxidant: Tocopherol
Cell-communicating ingredient: Niacinamide
Skin brightening: Niacinamide
Skin-identical ingredient: Phospholipids, Sodium Hyaluronate, Glycerin
Soothing: Allantoin
Sunscreen: Titanium Dioxide, Ethylhexyl Methoxycinnamate, Butyl Methoxydibenzoylmethane, Benzophenone-3
Antimicrobial/antibacterial: Alcohol Denat
Buffering: Triethanolamine
Chelating: Disodium Edta
Colorant: Aluminum Stearate
Emollient: Cyclopentasiloxane, Phospholipids, C12-15 Alkyl Benzoate, Stearic Acid, Aluminum Hydroxide, Isohexadecane
Emulsifying: Polyhydroxystearic Acid, Polysorbate 80, Peg-40 Hydrogenated Castor Oil
Moisturizer/humectant: Butylene Glycol, Aluminum Hydroxide, Propanediol, Sodium Hyaluronate, Niacinamide, Glycerin
Perfuming: Citrus Grandis (Grapefruit) Fruit Extract, Fragrance
Preservative: Ethylhexylglycerin
Solvent: Water, Cyclopentasiloxane, Alcohol Denat, Butylene Glycol, Propanediol, Isohexadecane
Surfactant/cleansing: Peg-40 Hydrogenated Castor Oil
Viscosity controlling: Alcohol Denat, Stearic Acid, Aluminum Hydroxide, Aluminum Stearate, Sodium Acrylate/Sodium Acryloyldimethyl Taurate Copolymer, Carbomer
Water solvent
Cyclopentasiloxane emollient, solvent
Alcohol Denat antimicrobial/antibacterial, solvent, viscosity controlling icky
Titanium Dioxide sunscreen goodie
Ethylhexyl Methoxycinnamate sunscreen 0, 0
Butyl Methoxydibenzoylmethane sunscreen goodie
Benzophenone-3 sunscreen 0, 0 icky
Phospholipids skin-identical ingredient, emollient goodie
C12-15 Alkyl Benzoate emollient
Stearic Acid emollient, viscosity controlling 0, 2-3
Aluminum Hydroxide emollient, moisturizer/humectant, viscosity controlling
Polyhydroxystearic Acid emulsifying
Aluminum Stearate colorant, viscosity controlling
Propanediol solvent, moisturizer/humectant
Sodium Acrylate/Sodium Acryloyldimethyl Taurate Copolymer viscosity controlling
Isohexadecane emollient, solvent
Sodium Hyaluronate skin-identical ingredient, moisturizer/humectant 0, 0 goodie
Citrus Grandis (Grapefruit) Fruit Extract perfuming
Ppg-26-Buteth-26
Peg-40 Hydrogenated Castor Oil emulsifying, surfactant/cleansing
Niacinamide cell-communicating ingredient, skin brightening, anti-acne, moisturizer/humectant superstar
Euglena Gracilis Extract
Triethanolamine buffering 0, 2
Fragrance perfuming icky
Allantoin soothing 0, 0 goodie
Disodium Edta chelating
Bio essence Bio-Water Sunscreen Spf 50+ Pa++ (Hydrating)
Also-called: Aqua | What-it-does: solvent
What-it-does: emollient, solvent
A super commonly used 5 unit long, cyclic structured silicone that is water-thin and does not stay on the skin but evaporates from it (called volatile silicone). Similar to other silicones, it gives skin and hair a silky, smooth feel.
It's often combined with the non-volatile (i.e. stays on the skin) dimethicone as the two together form a water-resistant, breathable protective barrier on the skin without a negative tacky feel.
Alcohol Denat - icky
What-it-does: antimicrobial/antibacterial, solvent, viscosity controlling, astringent
It's a super common and super debated skincare ingredient
It has several benefits: great solvent, penetration enhancer, creates cosmetically elegant, light formulas, great astringent and antimicrobial
It can be very drying if it's in the first few ingredients on an ingredient list
Some experts even think that regular exposure to alcohol damages skin barrier and causes inflammation though it's a debated opinion (read more in geeky details tab)
Read all the geeky details about Alcohol Denat. here >>
Titanium Dioxide - goodie
Also-called: Octinoxate, Octyl Methoxycinnamate | What-it-does: sunscreen | Irritancy: 0 | Comedogenicity: 0
A clear, oil-soluble, "cosmetically-elegant" liquid that is the most commonly used chemical sunscreen. It absorbs UVB radiation (at wavelengths: 280-320 nm) with a peak protection at 310nm.
It only protects against UVB and not UVA rays (the 320-400 nm range) – so always choose products that contain other sunscreens too. It is not very stable either, when exposed to sunlight, it kind of breaks down and loses its effectiveness (not instantly, but over time - it loses 10% of its SPF protection ability within 35 mins). To make it more stable it can be - and should be - combined with other sunscreen agents to give stable and broad-spectrum protection (the new generation sunscreen agent, Tinosorb S is a particularly good one for that).
Regarding safety, there are also some concerns around Octinoxate. In vitro (made in the lab not on real people) and animal studies have shown that it may produce hormonal (estrogen-like) effects. Do not panic, the studies were not conducted under real life conditions on real human people, so it is probably over-cautious to avoid Octinoxate altogether. However, if you are pregnant or a small child (under 2 yrs. old), choose a physical (zinc oxide/titanium dioxide) or new-generation Tinosorb based sunscreen, just to be on the super-safe side. :)
Overall, Ethylhexyl Methoxycinnamate is an old-school chemical sunscreen agent. There are plenty of better options for sun protection today, but it is considered "safe as used" (and sunscreens are pretty well regulated) and it is available worldwide (can be used up to 10% in the EU and up to 7.5% in the US).
Butyl Methoxydibenzoylmethane - goodie
Also-called: Avobenzone | What-it-does: sunscreen
The famous Avobenzone. It is a special snowflake as it is the only globally available chemical sunscreen agent that provides proper UVA protection (in the US, new generation sunscreen agents are not approved because of impossible FDA regulations). It is the global gold standard of UVA protection and is the most used UVA sunscreen in the world.
It gives very good protection across the whole UVA range (310-400 nm that is both UVA1 and UVA2) with a peak protection at 360 nm. The problem with it, though, is that it is not photostable and degrades in the sunlight. Wikipedia says that avobenzone loses 36% of its UV-absorption capacity after just one hour of sunlight (yep, this is one of the reasons why sunscreens have to be reapplied after a few hours).
The cosmetic's industry is trying to solve the problem by combining avobenzone with other UV filters that enhance its stability (like octocrylene, Tinosorb S or Ensulizole) or by encapsulating it and while both solutions help, neither is perfect. Interestingly, the combination of avobenzone with mineral sunscreens (that is titanium dioxide and zinc oxide) is not a good idea. In the US, it is flat out prohibited as avobenzone becomes unstable when combined with mineral sunscreens.
As for safety, avobenzone has a pretty good safety profile. It counts as non-irritating, and unlike some other chemical sunscreens, it shows no estrogenic effect. The maximum concentration of avobenzone permitted is 5% in the EU and 3% in the US.
Benzophenone-3 - icky
Also-called: Oxybenzone | What-it-does: sunscreen | Irritancy: 0 | Comedogenicity: 0
A chemical sunscreen agent that absorbs UVB and short UVA rays (280-350nm) with its peak protection at 288 nm. Unlike many other chemical sunscreens, it is highly stable but its UV absorbing abilities are weak so it always has to be combined with other sunscreen agents for proper protection. More often than not, it's used as a photostabilizer rather than a proper sunscreen agent as it can protect formulas nicely from UV damage.
Regarding safety, BP-3 is somewhat controversial. First, its molecules are small (228 Da) and very lipophilic (oil loving) and these properties result in very good absorption. The problem is that you want sunscreens on the top of your skin and not in your bloodstream, so for BP-3 this is a problem. In fact, it absorbs so well that 4 hours after application of a sunscreen product with BP-3, it can be detected in urine.
Another concern of BP-3 is that it shows some estrogenic activity, though it's probably not relevant when applied topically to the skin. Estrogenic activity was confirmed only in-vitro (in test tubes) and when taken orally by lab animals, and not when used topically as you would normally. In fact, a 2004 follow-up study to examine the estrogenic effect of sunscreens when used topically on the whole body found that "the endogenous levels of reproductive hormones were unaffected" (even though BP-3 could be detected both in plasma and urine, so its absorption is no doubt too good).
If that was not enough, Wikipedia claims that BP-3 is nowadays the most common allergen found in sunscreens, and the always-trustworthy smartskincare writes that "[benzophenones] have been shown in some studies to promote the generation of potentially harmful free radicals".
On the up side, sunscreens are pretty well regulated in several parts of the world, and BP-3 is considered "safe as used" and is an allowed sunscreen agent everywhere. It can be used in concentrations of up to 10% in the EU and up to 6% in the US.
Overall, BP-3 is probably our least favorite sunscreen agent and we prefer sunscreens without it. However, if you find a formula that you love and contains BP-3, we do not think that you should throw it away. A sunscreen with BP-3 is definitely better than no sunscreen.
Phospholipids - goodie
What-it-does: skin-identical ingredient, emollient
A type of lipid that's the major (about 75%) component of all cell membranes. As for skincare, it works as an emollient and skin-identical ingredient.
It has a water-loving head with two water-hating tails and this structure gives the molecule emulsifying properties. It is also often used to create liposomes, small spheres surrounded by phospholipid bi-layer designed to carry some active ingredient and help its absorption.
An often used emollient with a light and silky feel. It's very mild to both skin and eyes and spreads nicely and easily. It's often used in sunscreens as it's also an excellent solvent for sunscreen agents.
What-it-does: emollient, viscosity controlling | Irritancy: 0 | Comedogenicity: 2-3
A common multi-tasker fatty acid. It makes your skin feel nice and smooth (emollient), gives body to cream type products and helps to stabilize water and oil mixes (aka emulsions).
Aluminum Hydroxide
What-it-does: emollient, moisturizer/humectant, viscosity controlling
Officially, CosIng (the official EU ingredient database) lists Aluminum Hydroxide 's functions as opacifying (making the product white and non-transparent), as well as emollient and skin protectant.
However, with a little bit of digging, it turns out Aluminum Hyroxide often moonlights as a protective coating for UV filter superstar Titanium Dioxide. Specifically, it protects our skin from the harmful effects of nasty Reactive Oxygen Species (free radicals derived from oxygen such as Superoxide and Hydrogen Peroxide) generated when Titanium Dioxide is exposed to UV light. Btw, chlorine in swimming pool water depletes this protective coating, so one more reason to reapply your sunscreen after a dip in the pool on holiday.
Other than that, Aluminum Hydroxide also often shows up in composite pigment technologies where it is used the other way around (as the base material and not as the coating material) and helps to achieve higher color coverage with less pigment.
Polyhydroxystearic Acid
A so-called dispersant or dispersing agent that's used in inorganic (titanium dioxide/zinc oxide based) sunscreens or in make-up products to help to distribute the pigments nicely and evenly on the skin. It's also claimed to increase the UV absorption of the sunscreen formula as well as to reduce the annoying white cast left behind by inorganic sunscreens.
Aluminum Stearate
What-it-does: colorant, emulsion stabilising, viscosity controlling
Also-called: Zemea | What-it-does: solvent, moisturizer/humectant
Propanediol is a natural alternative for the often used and often bad-mouthed propylene glycol. It's produced sustainably from corn sugar and it's Ecocert approved.
It's quite a multi-tasker: can be used to improve skin moisturization, as a solvent, to boost preservative efficacy or to influence the sensory properties of the end formula.
Sodium Acrylate/Sodium Acryloyldimethyl Taurate Copolymer
Also-called: Part of Creagel EZ | What-it-does: viscosity controlling, emulsion stabilising
A copolymer is a big molecule that consists not of one but of two repeating subunits. This particular copolymer is a handy helper ingredient to form nice gel textures.
It usually comes to the formula combined with emollients (such as C13-14 Isoparaffin, Isohexadecane, Isononyl Isononanoate or Squalane) and can be used as an emulsifier and/or thickener to produce milky gel emulsions with a soft and non-tacky skin feel.
A light, velvety, unique skin feel liquid that is a good solvent and also makes the skin feel nice and smooth (aka emollient). It's often used in makeup products mixed with silicones to give shine and slip to the product. It's also great for cleansing dirt and oil from the skin as well as for taking off make-up.
A common little helper ingredient that helps water and oil to mix together, aka emulsifier.
The number at the end refers to the oil-loving part and the bigger the number the more emulsifying power it has. 20 is a weak emulsifier, rather called solubilizer used commonly in toners while 60 and 80 are more common in serums and creams.
Sodium Hyaluronate - goodie
What-it-does: skin-identical ingredient, moisturizer/humectant | Irritancy: 0 | Comedogenicity: 0
It’s the - sodium form - cousin of the famous NMF, hyaluronic acid (HA). If HA does not tell you anything we have a super detailed, geeky explanation about it here. The TL; DR version of HA is that it's a huge polymer (big molecule from repeated subunits) found in the skin that acts as a sponge helping the skin to hold onto water, being plump and elastic. HA is famous for its crazy water holding capacity as it can bind up to 1000 times its own weight in water.
As far as skincare goes, sodium hyaluronate and hyaluronic acid are pretty much the same and the two names are used interchangeably. As cosmetic chemist kindofstephen writes on reddit "sodium hyaluronate disassociates into hyaluronic acid molecule and a sodium atom in solution".
In spite of this, if you search for "hyaluronic acid vs sodium hyaluronate" you will find on multiple places that sodium hyaluronate is smaller and can penetrate the skin better. Chemically, this is definitely not true, as the two forms are almost the same, both are polymers and the subunits can be repeated in both forms as much as you like. (We also checked Prospector for sodium hyaluronate versions actually used in cosmetic products and found that the most common molecular weight was 1.5-1.8 million Da that absolutely counts as high molecular weight).
What seems to be a true difference, though, is that the salt form is more stable, easier to formulate and cheaper so it pops up more often on the ingredient lists.
If you wanna become a real HA-and-the-skin expert you can read way more about the topic at hyaluronic acid (including penetration-questions, differences between high and low molecular weight versions and a bunch of references to scientific literature).
Citrus Grandis (Grapefruit) Fruit Extract
What-it-does: astringent, perfuming
A helper ingredient that usually comes to the formula coupled with PEG-40 Hydrogenated Castor Oil. The two together work as surfactants and oil solubilizers. It's a non-sticky duo that works at low concentration and is often used to solubilize fragrance components into water-based formulas.
What-it-does: emulsifying, surfactant/cleansing
A mildly viscous, amber-colored liquid with fatty odor, made from Castor Oil and polyethylene glycol (PEG).
If it were a person, we’d say, it’s agile, diligent & multifunctional. It’s mostly used as an emulsifier and surfactant but most often it is used to solubilize fragrances into water-based formulas.
What-it-does: astringent
Niacinamide - superstar
Also-called: vitamin B3, nicotinamide | What-it-does: cell-communicating ingredient, skin brightening, anti-acne, moisturizer/humectant
A multi-functional skincare superstar with several proven benefits for the skin
Great anti-aging, wrinkle smoothing ingredient used at 4-5% concentration
Fades brown spots alone or in combination with amino sugar, acetyl glucosamine
Increases ceramide synthesis that results in a stronger, healthier skin barrier and better skin hydration
Can help to improve several skin conditions including acne, rosacea, and atopic dermatitis
Read all the geeky details about Niacinamide here >>
What-it-does: buffering | Irritancy: 0 | Comedogenicity: 2
It’s a little helper ingredient that helps to set the pH of a cosmetic formulation to be just right. It’s very alkaline (you know the opposite of being very acidic): a 1% solution has a pH of around 10.
It does not have the very best safety reputation but in general, you do not have to worry about it.
What is true is that if a product contains so-called N-nitrogenating agents (e.g.: preservatives like 2-Bromo-2-Nitropropane-1,3-Diol, 5-Bromo-5-Nitro- 1,3-Dioxane or sodium nitrate - so look out for things with nitro, nitra in the name) that together with TEA can form some not nice carcinogenic stuff (that is called nitrosamines). But with proper formulation that does not happen, TEA in itself is not a bad guy.
But let’s assume a bad combination of ingredients were used and the nitrosamines formed. :( Even in that case you are probably fine because as far as we know it cannot penetrate the skin.
But to be on the safe side, if you see Triethanolamine in an INCI and also something with nitra, nitro in the name of it just skip the product, that cannot hurt.
Fragrance - icky
Also-called: Fragrance, Parfum;Parfum/Fragrance | What-it-does: perfuming
Exactly what it sounds: nice smelling stuff put into cosmetic products so that the end product also smells nice. Fragrance in the US and parfum in the EU is a generic term on the ingredient list that is made up of 30 to 50 chemicals on average (but it can have as much as 200 components!).
If you are someone who likes to know what you put on your face than fragrance is not your best friend - no way to know what’s really in it.
Also, if your skin is sensitive, fragrance is again not your best friend. It’s the number one cause of contact allergy to cosmetics. It’s definitely a smart thing to avoid with sensitive skin (and fragrance of any type - natural is just as allergic as synthetic, if not worse!).
Allantoin - goodie
What-it-does: soothing | Irritancy: 0 | Comedogenicity: 0
Super common soothing ingredient. It can be found naturally in the roots & leaves of the comfrey plant, but more often than not what's in the cosmetic products is produced synthetically.
It's not only soothing but it' also skin-softening and protecting and can promote wound healing.
What-it-does: chelating
Super common little helper ingredient that helps products to remain nice and stable for a longer time. It does so by neutralizing the metal ions in the formula (that usually get into there from water) that would otherwise cause some not so nice changes.
Product: Bio essence Bio-Water Sunscreen Spf 50+ Pa++ (Hydrating)
what‑it‑does emollient | solvent
It's a super commonly used water-thin volatile silicone that gives skin and hair a silky, smooth feel. [more]
Alcohol with some additives to make it unconsumable. It is great solvent, penetration enhancer, creates cosmetically elegant, light formulas, great astringent, and antimicrobial. In large amounts, it can be very drying to the skin. [more]
Octinoxate - an old-school chemical sunscreen that absorbs UVB radiation (wavelengths: 280-320 nm). Not photostable and does not protect against UVA. [more]
Avobenzone - the only globally available chemical sunscreen that gives proper UVA protection. It is not photostable so has to be combined with ingredients that help to stabilize it. [more]
A chemical sunscreen agent that absorbs UVB and short UVA rays (280-350nm). It's a highly stable but weak UVB absorber, that's often used as a photostabilizer in non-sunscreen proudcts. [more]
A type of lipid that's the major component of all cell membranes. As for skincare, it works as an emollient and skin-identical ingredient. It's also often used to create liposomes. [more]
what‑it‑does emollient | viscosity controlling
irritancy, com. 0, 2-3
A common multi-tasker fatty acid that works as an emollient, thickener and emulsion stabilizer. [more]
what‑it‑does emollient | moisturizer/humectant | viscosity controlling
Officially, CosIng (the official EU ingredient database) lists Aluminum Hydroxide 's functions as opacifying (making the product white and non-transparent), as well as emollient and skin protectant.However, with a little bit of digging, it turns out Aluminum Hyroxide often moonlights as a protective coating for UV filter superstar Titanium Dioxide. [more]
A dispersing agent that's used in inorganic (titanium dioxide/zinc oxide based) sunscreens or in make-up products to help to distribute the pigments nicely and evenly on the skin. [more]
what‑it‑does colorant | viscosity controlling
A natural corn sugar derived glycol. It can be used to improve skin moisturization, as a solvent, to boost preservative efficacy or to influence the sensory properties of the end formula. [more]
A big molecule used as a helper ingredient to form nice gel textures. [more]
A light, velvety, unique skin feel liquid that is a good solvent and also makes the skin feel nice and smooth. [more]
A common little helper ingredient that helps water and oil to mix together, aka emulsifier. [more]
It's the salt form of famous humectant and natural moisturizing factor, hyaluronic acid. It can bind huge amounts of water and it's pretty much the current IT-moisturizer. [more]
A helper ingredient that usually comes to the formula coupled with PEG-40 Hydrogenated Castor Oil. The two together work as surfactants and oil solubilizers. [more]
what‑it‑does emulsifying | surfactant/cleansing
A mildly viscous, amber-colored liquid that works as an emulsifier and surfactant. [more]
what‑it‑does cell-communicating ingredient | skin brightening | anti-acne | moisturizer/humectant
A multi-functional skincare superstar that has clinically proven anti-aging, skin lightening, anti-inflammatory and barrier repair properties. [more]
Helps to set the pH of a cosmetic formulation to be right. It’s very alkaline. [more]
The generic term for nice smelling stuff put into cosmetic products so that the end product also smells nice. It is made up of 30 to 50 chemicals on average. [more]
Super common soothing ingredient. It can be found naturally in the roots & leaves of the comfrey plant, but more often than not what's in the cosmetic products is produced synthetically. It's not only soothing but it' [more]
what‑it‑does chelating
Super common little helper ingredient that helps products to remain nice and stable for a longer time. It does so by neutralizing the metal ions in the formula (that usually get into there from water) that would otherwise cause some not so nice changes. [more]
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