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<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Ramsey Graph Visualizer</title>
<script src="https://cdnjs.cloudflare.com/ajax/libs/d3/7.8.5/d3.min.js"></script>
<link rel="preconnect" href="https://fonts.googleapis.com">
<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
<link href="https://fonts.googleapis.com/css2?family=JetBrains+Mono:wght@400;700&family=Fraunces:opsz,wght@9..144,300;9..144,600&display=swap" rel="stylesheet">
<style>
:root {
--bg-primary: #0a0a0a;
--bg-secondary: #1a1a1a;
--border-color: #2a2a2a;
--text-primary: #e8e8e8;
--text-secondary: #888888;
--accent-red: #ff3366;
--accent-blue: #00d4ff;
--accent-green: #00ff88;
--mono: 'JetBrains Mono', monospace;
--serif: 'Fraunces', serif;
}
* { margin: 0; padding: 0; box-sizing: border-box; }
html, body {
height: 100%;
overflow: hidden;
}
body {
background: var(--bg-primary);
color: var(--text-primary);
font-family: var(--mono);
font-size: 13px;
display: flex;
flex-direction: column;
}
body::before {
content: '';
position: fixed;
top: 0; left: 0;
width: 100%; height: 100%;
background-image:
linear-gradient(rgba(255, 51, 102, 0.03) 1px, transparent 1px),
linear-gradient(90deg, rgba(255, 51, 102, 0.03) 1px, transparent 1px);
background-size: 40px 40px;
pointer-events: none;
z-index: 0;
animation: gridPulse 8s ease-in-out infinite;
}
@keyframes gridPulse {
0%, 100% { opacity: 0.3; }
50% { opacity: 0.6; }
}
.app {
position: relative;
z-index: 1;
display: flex;
flex-direction: column;
height: 100vh;
padding: 16px 24px;
gap: 12px;
}
header {
display: flex;
justify-content: space-between;
align-items: center;
padding-bottom: 12px;
border-bottom: 1px solid var(--border-color);
flex-shrink: 0;
}
.title-area {
display: flex;
align-items: baseline;
gap: 16px;
}
h1 {
font-family: var(--serif);
font-size: 28px;
font-weight: 600;
background: linear-gradient(135deg, var(--text-primary), var(--accent-red));
-webkit-background-clip: text;
-webkit-text-fill-color: transparent;
background-clip: text;
}
.subtitle {
font-size: 11px;
color: var(--text-secondary);
text-transform: uppercase;
letter-spacing: 0.1em;
}
.header-actions {
display: flex;
align-items: center;
gap: 12px;
}
.action-btn {
display: flex;
align-items: center;
gap: 6px;
padding: 8px 14px;
font-size: 12px;
border: 1px solid var(--border-color);
background: transparent;
color: var(--text-secondary);
cursor: pointer;
font-family: var(--mono);
transition: all 0.2s ease;
}
.action-btn:hover {
border-color: var(--accent-green);
color: var(--accent-green);
}
.btn-icon {
width: 16px;
height: 16px;
flex-shrink: 0;
}
.lang-toggle {
display: flex;
gap: 4px;
}
.lang-btn {
display: flex;
align-items: center;
gap: 6px;
padding: 6px 12px;
font-size: 12px;
border: 1px solid var(--border-color);
background: transparent;
color: var(--text-secondary);
cursor: pointer;
font-family: var(--mono);
transition: all 0.2s ease;
}
.lang-icon {
width: 14px;
height: 14px;
flex-shrink: 0;
}
.lang-btn.active {
border-color: var(--accent-blue);
background: var(--accent-blue);
color: var(--bg-primary);
}
.lang-btn:hover:not(.active) {
border-color: var(--accent-blue);
color: var(--accent-blue);
}
.main-content {
display: flex;
gap: 16px;
flex: 1;
min-height: 0;
}
.sidebar {
width: 280px;
flex-shrink: 0;
display: flex;
flex-direction: column;
gap: 12px;
}
.panel {
background: var(--bg-secondary);
border: 1px solid var(--border-color);
padding: 16px;
}
.panel-title {
font-size: 10px;
text-transform: uppercase;
letter-spacing: 0.15em;
color: var(--text-secondary);
margin-bottom: 12px;
display: flex;
align-items: center;
gap: 8px;
}
.panel-title::before {
content: '';
width: 8px;
height: 8px;
background: var(--accent-red);
}
.selector-grid {
display: grid;
grid-template-columns: 1fr 1fr 1fr;
gap: 8px;
margin-bottom: 12px;
}
.selector-item label {
display: block;
font-size: 10px;
color: var(--text-secondary);
margin-bottom: 4px;
text-transform: uppercase;
letter-spacing: 0.1em;
}
select {
width: 100%;
background: var(--bg-primary);
border: 1px solid var(--border-color);
color: var(--text-primary);
padding: 8px;
font-family: var(--mono);
font-size: 13px;
cursor: pointer;
}
select:focus {
outline: none;
border-color: var(--accent-red);
}
select:disabled {
opacity: 0.5;
cursor: not-allowed;
}
.btn {
width: 100%;
padding: 10px;
font-family: var(--mono);
font-size: 11px;
text-transform: uppercase;
letter-spacing: 0.1em;
border: 1px solid var(--border-color);
background: var(--bg-primary);
color: var(--text-primary);
cursor: pointer;
transition: all 0.2s ease;
}
.btn:hover:not(:disabled) {
border-color: var(--accent-red);
background: var(--accent-red);
color: var(--bg-primary);
}
.btn:disabled {
opacity: 0.4;
cursor: not-allowed;
}
.btn-primary {
border-color: var(--accent-red);
background: rgba(255, 51, 102, 0.1);
}
.input-row {
display: flex;
gap: 8px;
margin-bottom: 8px;
}
input[type="text"] {
flex: 1;
background: var(--bg-primary);
border: 1px solid var(--border-color);
color: var(--text-primary);
padding: 8px 10px;
font-family: var(--mono);
font-size: 12px;
}
input[type="text"]:focus {
outline: none;
border-color: var(--accent-red);
}
input[type="file"] {
display: none;
}
.file-label {
display: block;
padding: 10px;
text-align: center;
border: 1px dashed var(--border-color);
color: var(--text-secondary);
cursor: pointer;
font-size: 11px;
transition: all 0.2s ease;
}
.file-label:hover {
border-color: var(--accent-red);
color: var(--accent-red);
}
.file-label.has-file {
border-style: solid;
border-color: var(--accent-green);
color: var(--accent-green);
}
.divider {
text-align: center;
color: var(--text-secondary);
font-size: 10px;
margin: 8px 0;
position: relative;
}
.divider::before, .divider::after {
content: '';
position: absolute;
top: 50%;
width: 40%;
height: 1px;
background: var(--border-color);
}
.divider::before { left: 0; }
.divider::after { right: 0; }
.status {
padding: 8px 10px;
font-size: 11px;
border-left: 3px solid var(--accent-blue);
background: rgba(0, 212, 255, 0.05);
display: none;
}
.status.show { display: block; }
.status.error {
border-color: var(--accent-red);
background: rgba(255, 51, 102, 0.05);
color: var(--accent-red);
}
.status.success {
border-color: var(--accent-green);
background: rgba(0, 255, 136, 0.05);
color: var(--accent-green);
}
.canvas-area {
flex: 1;
display: flex;
flex-direction: column;
background: var(--bg-secondary);
border: 1px solid var(--border-color);
min-width: 0;
}
.canvas-header {
display: flex;
justify-content: space-between;
align-items: center;
padding: 12px 16px;
border-bottom: 1px solid var(--border-color);
flex-shrink: 0;
flex-wrap: wrap;
gap: 12px;
}
.header-left {
display: flex;
align-items: center;
gap: 20px;
}
.header-right {
display: flex;
align-items: center;
gap: 16px;
}
.graph-info {
display: flex;
gap: 20px;
}
.info-item {
text-align: center;
}
.info-value {
font-size: 18px;
font-weight: 700;
color: var(--accent-red);
}
.info-label {
font-size: 9px;
text-transform: uppercase;
letter-spacing: 0.1em;
color: var(--text-secondary);
}
.toggle-group {
display: flex;
gap: 4px;
}
.toggle-btn {
padding: 6px 12px;
font-size: 10px;
text-transform: uppercase;
border: 1px solid var(--border-color);
background: transparent;
color: var(--text-secondary);
cursor: pointer;
font-family: var(--mono);
}
.toggle-btn.active {
border-color: var(--accent-red);
background: var(--accent-red);
color: var(--bg-primary);
}
.toggle-btn:hover:not(.active) {
border-color: var(--accent-red);
color: var(--accent-red);
}
#canvas {
flex: 1;
position: relative;
overflow: hidden;
}
#canvas svg {
width: 100%;
height: 100%;
}
.empty-state {
position: absolute;
top: 50%;
left: 50%;
transform: translate(-50%, -50%);
text-align: center;
color: var(--text-secondary);
}
.empty-icon {
font-size: 48px;
opacity: 0.3;
margin-bottom: 8px;
font-family: var(--serif);
}
.pagination {
display: flex;
align-items: center;
justify-content: center;
gap: 8px;
padding: 10px;
border-top: 1px solid var(--border-color);
flex-shrink: 0;
}
.pagination button {
padding: 6px 12px;
font-family: var(--mono);
font-size: 11px;
border: 1px solid var(--border-color);
background: transparent;
color: var(--text-secondary);
cursor: pointer;
}
.pagination button:hover:not(:disabled) {
border-color: var(--accent-red);
color: var(--accent-red);
}
.pagination button:disabled {
opacity: 0.3;
cursor: not-allowed;
}
.page-info {
min-width: 100px;
text-align: center;
color: var(--text-secondary);
font-size: 12px;
}
.page-info span {
color: var(--accent-red);
font-weight: 700;
}
.node { cursor: pointer; }
.node:hover { filter: brightness(1.3); }
.link { stroke-opacity: 0.6; }
.node-label {
font-family: var(--mono);
font-size: 10px;
fill: var(--text-primary);
text-anchor: middle;
pointer-events: none;
}
.legend {
display: flex;
gap: 16px;
font-size: 10px;
color: var(--text-secondary);
}
.legend-item {
display: flex;
align-items: center;
gap: 6px;
}
.legend-dot {
width: 10px;
height: 10px;
border-radius: 50%;
}
.legend-dot.red { background: var(--accent-red); }
.legend-dot.blue { background: var(--accent-blue); }
.loading {
position: absolute;
top: 50%;
left: 50%;
transform: translate(-50%, -50%);
color: var(--text-secondary);
}
.loading::after {
content: '';
display: inline-block;
width: 16px;
height: 16px;
border: 2px solid var(--border-color);
border-top-color: var(--accent-red);
border-radius: 50%;
animation: spin 0.8s linear infinite;
margin-left: 8px;
vertical-align: middle;
}
@keyframes spin {
to { transform: rotate(360deg); }
}
/* Matrix styles */
.matrix-container {
position: absolute;
top: 0;
left: 0;
right: 0;
bottom: 0;
display: flex;
align-items: center;
justify-content: center;
overflow: auto;
padding: 20px;
}
.matrix-wrapper {
display: flex;
flex-direction: column;
align-items: center;
}
.matrix-labels-top {
display: flex;
margin-left: 30px;
}
.matrix-label {
width: var(--cell-size, 24px);
height: 20px;
display: flex;
align-items: center;
justify-content: center;
font-size: 10px;
color: var(--text-secondary);
}
.matrix-row {
display: flex;
align-items: center;
}
.matrix-row-label {
width: 30px;
height: var(--cell-size, 24px);
display: flex;
align-items: center;
justify-content: center;
font-size: 10px;
color: var(--text-secondary);
}
.matrix-cell {
width: var(--cell-size, 24px);
height: var(--cell-size, 24px);
border: 1px solid var(--border-color);
display: flex;
align-items: center;
justify-content: center;
font-size: 10px;
transition: all 0.15s ease;
}
.matrix-cell.edge {
background: var(--accent-red);
color: var(--bg-primary);
font-weight: 700;
}
.matrix-cell.complement {
background: var(--accent-blue);
color: var(--bg-primary);
font-weight: 700;
}
.matrix-cell.diagonal {
background: var(--bg-primary);
color: var(--text-secondary);
}
.matrix-cell.empty {
background: transparent;
color: var(--text-secondary);
}
.matrix-cell:hover:not(.diagonal) {
transform: scale(1.1);
z-index: 10;
box-shadow: 0 0 10px rgba(255, 51, 102, 0.5);
}
/* Modal styles */
.modal {
display: none;
position: fixed;
top: 0;
left: 0;
right: 0;
bottom: 0;
z-index: 1000;
align-items: center;
justify-content: center;
}
.modal.show {
display: flex;
}
.modal-overlay {
position: absolute;
top: 0;
left: 0;
right: 0;
bottom: 0;
background: rgba(0, 0, 0, 0.8);
}
.modal-content {
position: relative;
background: var(--bg-secondary);
border: 1px solid var(--border-color);
max-width: 600px;
max-height: 80vh;
width: 90%;
display: flex;
flex-direction: column;
}
.modal-content.modal-large {
max-width: 900px;
}
.modal-header {
display: flex;
justify-content: space-between;
align-items: center;
padding: 16px 20px;
border-bottom: 1px solid var(--border-color);
}
.modal-header h2 {
font-family: var(--serif);
font-size: 20px;
font-weight: 600;
color: var(--text-primary);
}
.modal-close {
width: 32px;
height: 32px;
display: flex;
align-items: center;
justify-content: center;
border: 1px solid var(--border-color);
background: transparent;
color: var(--text-secondary);
font-size: 20px;
cursor: pointer;
transition: all 0.2s ease;
}
.modal-close:hover {
border-color: var(--accent-red);
color: var(--accent-red);
}
.modal-body {
padding: 20px;
overflow-y: auto;
font-size: 13px;
line-height: 1.7;
color: var(--text-secondary);
}
.modal-body p {
margin-bottom: 12px;
}
.modal-body strong {
color: var(--text-primary);
}
.modal-body .highlight {
color: var(--accent-red);
font-weight: 700;
}
.modal-body .challenge {
padding: 16px;
margin: 16px 0;
background: rgba(255, 51, 102, 0.1);
border-left: 3px solid var(--accent-red);
}
.modal-body .significance {
padding: 16px;
margin: 16px 0;
background: rgba(0, 212, 255, 0.1);
border-left: 3px solid var(--accent-blue);
}
/* Progress table */
.ramsey-table {
width: 100%;
border-collapse: collapse;
font-size: 11px;
margin-top: 12px;
}
.ramsey-table th,
.ramsey-table td {
padding: 8px 6px;
border: 1px solid var(--border-color);
text-align: center;
}
.ramsey-table th {
background: var(--bg-primary);
color: var(--accent-red);
font-weight: 700;
}
.ramsey-table td.exact {
background: rgba(0, 255, 136, 0.1);
color: var(--accent-green);
}
.ramsey-table td.range {
background: rgba(0, 212, 255, 0.1);
color: var(--accent-blue);
}
.ramsey-table td.trivial {
color: var(--text-secondary);
}
.table-legend {
display: flex;
gap: 20px;
margin-top: 16px;
font-size: 11px;
}
.table-legend-item {
display: flex;
align-items: center;
gap: 8px;
}
.legend-box {
width: 16px;
height: 16px;
}
.legend-box.exact {
background: rgba(0, 255, 136, 0.1);
border: 1px solid var(--accent-green);
}
.legend-box.range {
background: rgba(0, 212, 255, 0.1);
border: 1px solid var(--accent-blue);
}
/* Links panel */
.panel-links {
margin-top: auto;
}
.link-list {
display: flex;
flex-direction: column;
gap: 6px;
}
.link-list a {
display: flex;
align-items: center;
gap: 10px;
padding: 8px 10px;
background: var(--bg-primary);
border: 1px solid var(--border-color);
color: var(--text-secondary);
text-decoration: none;
font-size: 11px;
transition: all 0.2s ease;
}
.link-list a:hover {
border-color: var(--accent-red);
color: var(--text-primary);
}
.link-icon {
width: 28px;
height: 28px;
display: flex;
align-items: center;
justify-content: center;
background: var(--border-color);
color: var(--text-primary);
flex-shrink: 0;
padding: 5px;
}
.link-icon svg {
width: 100%;
height: 100%;
}
.link-list a:hover .link-icon {
background: var(--accent-red);
color: var(--bg-primary);
}
.link-text {
overflow: hidden;
text-overflow: ellipsis;
white-space: nowrap;
}
@media (max-width: 900px) {
.main-content {
flex-direction: column;
}
.sidebar {
width: 100%;
flex-direction: row;
flex-wrap: wrap;
}
.sidebar .panel {
flex: 1;
min-width: 200px;
}
.panel-links {
margin-top: 0;
}
.canvas-header {
flex-direction: column;
align-items: flex-start;
}
}
</style>
</head>
<body>
<div class="app">
<header>
<div class="title-area">
<h1>Ramsey Graph</h1>
<span class="subtitle" data-i18n="subtitle">Interactive Visualizer</span>
</div>
<div class="header-actions">
<button class="action-btn" id="introBtn">
<svg class="btn-icon" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2">
<path d="M4 19.5A2.5 2.5 0 0 1 6.5 17H20"></path>
<path d="M6.5 2H20v20H6.5A2.5 2.5 0 0 1 4 19.5v-15A2.5 2.5 0 0 1 6.5 2z"></path>
</svg>
<span data-i18n="introduction">Introduction</span>
</button>
<button class="action-btn" id="progressBtn">
<svg class="btn-icon" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2">
<path d="M18 20V10"></path>
<path d="M12 20V4"></path>
<path d="M6 20v-6"></path>
</svg>
<span data-i18n="progress">Progress</span>
</button>
<div class="lang-toggle">
<button class="lang-btn active" data-lang="en">
<svg class="lang-icon" viewBox="0 0 24 24" fill="currentColor">
<circle cx="12" cy="12" r="10" fill="none" stroke="currentColor" stroke-width="1.5"/>
<path d="M2 12h20M12 2a15.3 15.3 0 0 1 4 10 15.3 15.3 0 0 1-4 10 15.3 15.3 0 0 1-4-10 15.3 15.3 0 0 1 4-10z" fill="none" stroke="currentColor" stroke-width="1.5"/>
</svg>
EN
</button>
<button class="lang-btn" data-lang="zh">
<svg class="lang-icon" viewBox="0 0 24 24" fill="currentColor">
<circle cx="12" cy="12" r="10" fill="none" stroke="currentColor" stroke-width="1.5"/>
<path d="M2 12h20M12 2a15.3 15.3 0 0 1 4 10 15.3 15.3 0 0 1-4 10 15.3 15.3 0 0 1-4-10 15.3 15.3 0 0 1 4-10z" fill="none" stroke="currentColor" stroke-width="1.5"/>
</svg>
中文
</button>
</div>
</div>
</header>
<div class="main-content">
<div class="sidebar">
<div class="panel">
<div class="panel-title" data-i18n="selectDataset">Select Dataset</div>
<div class="selector-grid">
<div class="selector-item">
<label>s</label>
<select id="selectS"></select>
</div>
<div class="selector-item">
<label>t</label>
<select id="selectT"></select>
</div>
<div class="selector-item">
<label>n</label>
<select id="selectN"></select>
</div>
</div>
<button class="btn btn-primary" id="loadDatasetBtn" data-i18n="loadDataset">Load Ramsey(s,t,n)</button>
<div id="datasetInfo" style="margin-top: 8px; font-size: 10px; color: var(--text-secondary);"></div>
</div>
<div class="panel">
<div class="panel-title" data-i18n="customSource">Custom Source</div>
<div class="input-row">
<input type="text" id="urlInput" data-i18n-placeholder="urlPlaceholder" placeholder="Enter .g6 file URL...">
</div>
<button class="btn" id="loadUrlBtn" data-i18n="loadUrl">Load URL</button>
<div class="divider" data-i18n="or">or</div>
<input type="file" id="fileInput" accept=".g6">
<label class="file-label" id="fileLabel" for="fileInput" data-i18n="uploadFile">
Drop or click to upload .g6 file
</label>
</div>
<div id="status" class="status"></div>
<div class="panel panel-links">
<div class="panel-title" data-i18n="links">Links</div>
<div class="link-list">
<a href="https://huggingface.co/datasets/linxy/RamseyGraph" target="_blank">
<span class="link-icon">
<svg viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2">
<path d="M21 16V8a2 2 0 0 0-1-1.73l-7-4a2 2 0 0 0-2 0l-7 4A2 2 0 0 0 3 8v8a2 2 0 0 0 1 1.73l7 4a2 2 0 0 0 2 0l7-4A2 2 0 0 0 21 16z"></path>
<polyline points="3.27 6.96 12 12.01 20.73 6.96"></polyline>
<line x1="12" y1="22.08" x2="12" y2="12"></line>
</svg>
</span>
<span class="link-text" data-i18n="hfDataset">HuggingFace Dataset</span>
</a>
<a href="https://github.com/LinXueyuanStdio/RamseyGraph" target="_blank">
<span class="link-icon">
<svg viewBox="0 0 24 24" fill="currentColor">
<path d="M12 0c-6.626 0-12 5.373-12 12 0 5.302 3.438 9.8 8.207 11.387.599.111.793-.261.793-.577v-2.234c-3.338.726-4.033-1.416-4.033-1.416-.546-1.387-1.333-1.756-1.333-1.756-1.089-.745.083-.729.083-.729 1.205.084 1.839 1.237 1.839 1.237 1.07 1.834 2.807 1.304 3.492.997.107-.775.418-1.305.762-1.604-2.665-.305-5.467-1.334-5.467-5.931 0-1.311.469-2.381 1.236-3.221-.124-.303-.535-1.524.117-3.176 0 0 1.008-.322 3.301 1.23.957-.266 1.983-.399 3.003-.404 1.02.005 2.047.138 3.006.404 2.291-1.552 3.297-1.23 3.297-1.23.653 1.653.242 2.874.118 3.176.77.84 1.235 1.911 1.235 3.221 0 4.609-2.807 5.624-5.479 5.921.43.372.823 1.102.823 2.222v3.293c0 .319.192.694.801.576 4.765-1.589 8.199-6.086 8.199-11.386 0-6.627-5.373-12-12-12z"/>
</svg>
</span>
<span class="link-text" data-i18n="ghRepo">GitHub Repository</span>
</a>
<a href="https://users.cecs.anu.edu.au/~bdm/data/ramsey.html" target="_blank">
<span class="link-icon">
<svg viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2">
<ellipse cx="12" cy="5" rx="9" ry="3"></ellipse>
<path d="M21 12c0 1.66-4 3-9 3s-9-1.34-9-3"></path>
<path d="M3 5v14c0 1.66 4 3 9 3s9-1.34 9-3V5"></path>
</svg>
</span>
<span class="link-text" data-i18n="originDb">Origin Database</span>
</a>
<a href="mailto:linxy59@mail2.sysu.edu.cn">
<span class="link-icon">
<svg viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2">
<path d="M4 4h16c1.1 0 2 .9 2 2v12c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V6c0-1.1.9-2 2-2z"></path>
<polyline points="22,6 12,13 2,6"></polyline>
</svg>
</span>
<span class="link-text" data-i18n="contact">Contact</span>
</a>
<a href="https://www.combinatorics.org" target="_blank">
<span class="link-icon">
<svg viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2">
<path d="M2 3h6a4 4 0 0 1 4 4v14a3 3 0 0 0-3-3H2z"></path>
<path d="M22 3h-6a4 4 0 0 0-4 4v14a3 3 0 0 1 3-3h7z"></path>
</svg>
</span>
<span class="link-text" data-i18n="wiki">E-JC Survey</span>
</a>
<a href="https://en.wikipedia.org/wiki/Ramsey%27s_theorem" target="_blank" id="wikiLink">
<span class="link-icon">
<svg viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2">
<circle cx="12" cy="12" r="10"></circle>
<path d="M12 16v-4"></path>
<path d="M12 8h.01"></path>
</svg>
</span>
<span class="link-text" data-i18n="wikiLink">Wikipedia</span>
</a>
</div>
</div>
</div>
<div class="canvas-area">
<div class="canvas-header">
<div class="header-left">
<div class="graph-info">
<div class="info-item">
<div class="info-value" id="nodeCount">-</div>
<div class="info-label" data-i18n="nodes">Nodes</div>
</div>
<div class="info-item">
<div class="info-value" id="edgeCount">-</div>
<div class="info-label" data-i18n="edges">Edges</div>
</div>
</div>
<div class="legend">
<div class="legend-item"><div class="legend-dot red"></div><span data-i18n="graphG">Graph G</span></div>
<div class="legend-item"><div class="legend-dot blue"></div><span data-i18n="complement">Complement</span></div>
</div>
</div>
<div class="header-right">
<div class="toggle-group" id="displayToggle">
<button class="toggle-btn active" data-display="force" data-i18n="force">Force</button>
<button class="toggle-btn" data-display="matrix" data-i18n="matrix">Matrix</button>
</div>
<div class="toggle-group" id="viewToggle">
<button class="toggle-btn active" data-mode="graph">G</button>
<button class="toggle-btn" data-mode="complement">G'</button>
<button class="toggle-btn" data-mode="both" data-i18n="both">Both</button>
</div>
</div>
</div>
<div id="canvas">
<div class="empty-state">
<div class="empty-icon">R</div>
<div data-i18n="emptyState">Select a dataset or upload a file</div>
</div>
</div>
<div class="pagination" id="pagination" style="display: none;">
<button id="prevBtn" data-i18n="prev">< Prev</button>
<div class="page-info">
<span data-i18n="graph">Graph</span> <span id="currentPage">1</span> / <span id="totalPages">1</span>
</div>
<button id="nextBtn" data-i18n="next">Next ></button>
</div>
</div>
</div>
<!-- Introduction Modal -->
<div class="modal" id="introModal">
<div class="modal-overlay"></div>
<div class="modal-content">
<div class="modal-header">
<h2 data-i18n="introTitle">What is a Ramsey Graph?</h2>
<button class="modal-close">×</button>
</div>
<div class="modal-body" id="introBody">
</div>
</div>
</div>
<!-- Progress Modal -->
<div class="modal" id="progressModal">
<div class="modal-overlay"></div>
<div class="modal-content modal-large">
<div class="modal-header">
<h2 data-i18n="progressTitle">Known Ramsey Numbers</h2>
<button class="modal-close">×</button>
</div>
<div class="modal-body" id="progressBody">
</div>
</div>
</div>
</div>
<script>
// i18n translations
const i18n = {
en: {
subtitle: 'Interactive Visualizer',
selectDataset: 'Select Dataset',
loadDataset: 'Load Ramsey(s,t,n)',
customSource: 'Custom Source',
urlPlaceholder: 'Enter .g6 file URL...',
loadUrl: 'Load URL',
or: 'or',
uploadFile: 'Drop or click to upload .g6 file',
links: 'Links',
hfDataset: 'HuggingFace Dataset',
ghRepo: 'GitHub Repository',
originDb: 'Origin Database',
contact: 'Contact',
wiki: 'E-JC Survey',
nodes: 'Nodes',
edges: 'Edges',
graphG: 'Graph G',
complement: 'Complement',
force: 'Force',
matrix: 'Matrix',
both: 'Both',
emptyState: 'Select a dataset or upload a file',
prev: '< Prev',
next: 'Next >',
graph: 'Graph',
loading: 'Loading',
loadedGraphs: 'Loaded {0} graph(s)',
noValidGraphs: 'No valid graphs found',
errorLoading: 'Error: {0}',
failedToLoad: 'Failed to load',
graphCount: '{0} graph(s)',
compressed: '(compressed)',
introduction: 'Introduction',
progress: 'Progress',
introTitle: 'What is a Ramsey Graph?',
progressTitle: 'Known Ramsey Numbers',
exactValue: 'Exact value known',
rangeValue: 'Only bounds known',
wikiLink: 'Wikipedia'
},
zh: {
subtitle: '交互式可视化工具',
selectDataset: '选择数据集',
loadDataset: '加载 Ramsey(s,t,n)',
customSource: '自定义来源',
urlPlaceholder: '输入 .g6 文件 URL...',
loadUrl: '加载 URL',
or: '或',
uploadFile: '拖放或点击上传 .g6 文件',
links: '链接',
hfDataset: 'HuggingFace 数据集',
ghRepo: 'GitHub 仓库',
originDb: '原始数据库',
contact: '联系方式',
wiki: '电子组合学期刊',
nodes: '节点',
edges: '边',
graphG: '图 G',
complement: '补图',
force: '力导向',
matrix: '矩阵',
both: '两者',
emptyState: '选择数据集或上传文件',
prev: '< 上一个',
next: '下一个 >',
graph: '图',
loading: '加载中',
loadedGraphs: '已加载 {0} 个图',
noValidGraphs: '未找到有效的图',
errorLoading: '错误: {0}',
failedToLoad: '加载失败',
graphCount: '{0} 个图',
compressed: '(压缩)',
introduction: '介绍',
progress: '进展',
introTitle: '什么是拉姆齐图？',
progressTitle: '已知拉姆齐数',
exactValue: '精确值已知',
rangeValue: '仅知道上下界',
wikiLink: '维基百科'
}
};
const wikiUrls = {
en: 'https://en.wikipedia.org/wiki/Ramsey%27s_theorem',
zh: 'https://zh.wikipedia.org/wiki/%E6%8B%89%E5%A7%86%E9%BD%90%E5%AE%9A%E7%90%86'
};
let currentLang = localStorage.getItem('lang') || 'en';
function t(key, ...args) {
let text = i18n[currentLang][key] || i18n['en'][key] || key;
args.forEach((arg, i) => {
text = text.replace(`{${i}}`, arg);
});
return text;
}
function applyLanguage() {
document.querySelectorAll('[data-i18n]').forEach(el => {
const key = el.getAttribute('data-i18n');
el.textContent = t(key);
});
document.querySelectorAll('[data-i18n-placeholder]').forEach(el => {
const key = el.getAttribute('data-i18n-placeholder');
el.placeholder = t(key);
});
// Update wiki link URL based on language
const wikiLink = document.getElementById('wikiLink');
if (wikiLink) {
wikiLink.href = wikiUrls[currentLang] || wikiUrls.en;
}
// Update dataset info if loaded
if (selectS.value) updateDatasetInfo();
}
function setLanguage(lang) {
currentLang = lang;
localStorage.setItem('lang', lang);
document.querySelectorAll('.lang-btn').forEach(btn => {
btn.classList.toggle('active', btn.dataset.lang === lang);
});
applyLanguage();
}
// Dataset configuration based on data/ folder
const DATASETS = {
'3,4': [1,2,3,4,5,6,7,8],
'3,5': [1,2,3,4,5,6,7,8,9,10,11,12,13],
'3,6': [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],
'3,7': [21,22],
'3,8': [27],
'3,9': [35],
'4,4': [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],
'4,5': [24],
'4,6': [35],
'5,5': [42]
};
// Files that are compressed (gzipped)
const COMPRESSED = new Set([
'r36_11', 'r36_12', 'r36_13', 'r36_14', 'r36_15', 'r36_16',
'r37_21', 'r38_27',
'r44_10', 'r44_11', 'r44_12', 'r44_13', 'r44_14'
]);
// Approximate graph counts for info display
const GRAPH_COUNTS = {
'r34_1':1,'r34_2':2,'r34_3':3,'r34_4':6,'r34_5':9,'r34_6':15,'r34_7':9,'r34_8':3,
'r35_1':1,'r35_2':2,'r35_3':3,'r35_4':7,'r35_5':13,'r35_6':32,'r35_7':71,'r35_8':179,'r35_9':290,'r35_10':313,'r35_11':105,'r35_12':12,'r35_13':1,
'r36_1':1,'r36_2':2,'r36_3':3,'r36_4':7,'r36_5':14,'r36_6':37,'r36_7':100,'r36_8':356,'r36_9':1407,'r36_10':6657,'r36_11':30395,'r36_12':116792,'r36_13':275086,'r36_14':263520,'r36_15':64732,'r36_16':2576,'r36_17':7,
'r37_21':1118436,'r37_22':191,
'r38_27':477142,
'r39_35':1,
'r44_1':1,'r44_2':2,'r44_3':4,'r44_4':9,'r44_5':24,'r44_6':84,'r44_7':362,'r44_8':2079,'r44_9':14701,'r44_10':103706,'r44_11':546356,'r44_12':1449166,'r44_13':1184231,'r44_14':130816,'r44_15':640,'r44_16':2,'r44_17':1,
'r45_24':352366,
'r46_35some':37,
'r55_42some':328
};
// State
let graphs = [];
let currentIndex = 0;
let viewMode = 'graph';
let displayMode = 'force';
let simulation = null;
// DOM
const selectS = document.getElementById('selectS');
const selectT = document.getElementById('selectT');
const selectN = document.getElementById('selectN');
const loadDatasetBtn = document.getElementById('loadDatasetBtn');
const datasetInfo = document.getElementById('datasetInfo');
const urlInput = document.getElementById('urlInput');
const loadUrlBtn = document.getElementById('loadUrlBtn');
const fileInput = document.getElementById('fileInput');
const fileLabel = document.getElementById('fileLabel');
const status = document.getElementById('status');
const canvas = document.getElementById('canvas');
const pagination = document.getElementById('pagination');
const prevBtn = document.getElementById('prevBtn');
const nextBtn = document.getElementById('nextBtn');
const currentPage = document.getElementById('currentPage');
const totalPages = document.getElementById('totalPages');
const nodeCount = document.getElementById('nodeCount');
const edgeCount = document.getElementById('edgeCount');
// Initialize selectors
function initSelectors() {
const sValues = [...new Set(Object.keys(DATASETS).map(k => k.split(',')[0]))].sort((a,b) => a-b);
selectS.innerHTML = sValues.map(s => `<option value="${s}">${s}</option>`).join('');
updateTOptions();
}
function updateTOptions() {
const s = selectS.value;
const tValues = [...new Set(Object.keys(DATASETS).filter(k => k.startsWith(s+',')).map(k => k.split(',')[1]))].sort((a,b) => a-b);
selectT.innerHTML = tValues.map(t => `<option value="${t}">${t}</option>`).join('');
updateNOptions();
}
function updateNOptions() {
const key = `${selectS.value},${selectT.value}`;
const nValues = DATASETS[key] || [];
selectN.innerHTML = nValues.map(n => `<option value="${n}">${n}</option>`).join('');
updateDatasetInfo();
}
function updateDatasetInfo() {
const s = selectS.value, tVal = selectT.value, n = selectN.value;
const fileKey = `r${s}${tVal}_${n}`;
const count = GRAPH_COUNTS[fileKey] || GRAPH_COUNTS[fileKey + 'some'] || '?';
const isCompressed = COMPRESSED.has(fileKey);
const countText = t('graphCount', count.toLocaleString());
datasetInfo.innerHTML = `${countText}${isCompressed ? ` <span style="color:var(--accent-blue)">${t('compressed')}</span>` : ''}`;
}
function getDatasetUrl() {
const s = selectS.value, t = selectT.value, n = selectN.value;
let fileKey = `r${s}${t}_${n}`;
if (['4,6', '5,5'].includes(`${s},${t}`)) {
fileKey += 'some';
}
const ext = COMPRESSED.has(fileKey.replace('some','')) ? '.g6.gz' : '.g6';
return `https://huggingface.co/datasets/linxy/RamseyGraph/resolve/main/data/${fileKey}${ext}?download=true`;
}
selectS.addEventListener('change', updateTOptions);
selectT.addEventListener('change', updateNOptions);
selectN.addEventListener('change', updateDatasetInfo);
// Status helper
function showStatus(msg, type = 'info') {
status.textContent = msg;
status.className = `status show ${type}`;
if (type !== 'error') {
setTimeout(() => status.className = 'status', 3000);
}
}
// Parse graph6
function parseGraph6(line) {
line = line.trim();
if (!line) return null;
let pos = 0;
let n;
const firstByte = line.charCodeAt(pos) - 63;
if (firstByte < 63) {
n = firstByte;
pos++;
} else if (line.charCodeAt(pos + 1) - 63 < 63) {
n = ((line.charCodeAt(pos + 1) - 63) << 12) |
((line.charCodeAt(pos + 2) - 63) << 6) |
(line.charCodeAt(pos + 3) - 63);
pos += 4;
} else {
n = ((line.charCodeAt(pos + 2) - 63) << 30) |
((line.charCodeAt(pos + 3) - 63) << 24) |
((line.charCodeAt(pos + 4) - 63) << 18) |
((line.charCodeAt(pos + 5) - 63) << 12) |
((line.charCodeAt(pos + 6) - 63) << 6) |
(line.charCodeAt(pos + 7) - 63);
pos += 8;
}
const edges = [];
let bitPos = 0;
let currentByte = 0;
for (let j = 1; j < n; j++) {
for (let i = 0; i < j; i++) {
if (bitPos === 0) {
if (pos >= line.length) break;
currentByte = line.charCodeAt(pos) - 63;
pos++;
}
const bit = (currentByte >> (5 - bitPos)) & 1;
bitPos = (bitPos + 1) % 6;
if (bit === 1) edges.push([i, j]);
}
}
return { nodes: n, edges };
}
// Load functions
async function loadFromUrl(url) {
showStatus(t('loading') + '...', 'info');
canvas.innerHTML = `<div class="loading">${t('loading')}</div>`;
try {
const response = await fetch(url);
if (!response.ok) throw new Error(`HTTP ${response.status}`);
let text;
if (url.includes('.gz')) {
const buffer = await response.arrayBuffer();
const decompressed = await decompress(buffer);
text = new TextDecoder().decode(decompressed);
} else {
text = await response.text();
}
parseAndDisplay(text);
showStatus(t('loadedGraphs', graphs.length), 'success');
} catch (err) {
showStatus(t('errorLoading', err.message), 'error');
canvas.innerHTML = `<div class="empty-state"><div class="empty-icon">!</div><div>${t('failedToLoad')}</div></div>`;
}
}
async function decompress(buffer) {
const ds = new DecompressionStream('gzip');
const decompressedStream = new Response(new Blob([buffer]).stream().pipeThrough(ds)).arrayBuffer();
return new Uint8Array(await decompressedStream);
}
function loadFromFile(file) {
showStatus(t('loading') + '...', 'info');
const reader = new FileReader();
reader.onload = async (e) => {
let text;
if (file.name.endsWith('.gz')) {
const decompressed = await decompress(e.target.result);
text = new TextDecoder().decode(decompressed);
} else {
text = e.target.result;
}
parseAndDisplay(text);
showStatus(t('loadedGraphs', graphs.length), 'success');
};
reader.onerror = () => showStatus(t('errorLoading', 'File read error'), 'error');
if (file.name.endsWith('.gz')) {
reader.readAsArrayBuffer(file);
} else {
reader.readAsText(file);
}
}
function parseAndDisplay(text) {
graphs = [];
const lines = text.split('\n');
for (const line of lines) {
const g = parseGraph6(line);
if (g) graphs.push(g);
}
if (graphs.length > 0) {
currentIndex = 0;
updatePagination();
visualize(0);
} else {
showStatus(t('noValidGraphs'), 'error');
}
}
function updatePagination() {
pagination.style.display = graphs.length > 1 ? 'flex' : 'none';
currentPage.textContent = currentIndex + 1;
totalPages.textContent = graphs.length;
prevBtn.disabled = currentIndex === 0;
nextBtn.disabled = currentIndex === graphs.length - 1;
}
function getComplement(n, edges) {
const set = new Set(edges.map(e => `${e[0]}-${e[1]}`));
const comp = [];
for (let i = 0; i < n; i++) {
for (let j = i + 1; j < n; j++) {
if (!set.has(`${i}-${j}`)) comp.push([i, j]);
}
}
return comp;
}
// Build adjacency matrix
function buildAdjMatrix(n, edges) {
const matrix = Array.from({ length: n }, () => Array(n).fill(0));
for (const [i, j] of edges) {
matrix[i][j] = 1;
matrix[j][i] = 1;
}
return matrix;
}
// Main visualization dispatcher
function visualize(index) {
if (index < 0 || index >= graphs.length) return;
currentIndex = index;
const g = graphs[index];
nodeCount.textContent = g.nodes;
edgeCount.textContent = g.edges.length;
updatePagination();
if (displayMode === 'force') {
visualizeForce(g);
} else {
visualizeMatrix(g);
}
}
// Force-directed graph visualization
function visualizeForce(g) {
canvas.innerHTML = '';
const nodes = Array.from({ length: g.nodes }, (_, i) => ({ id: i }));
let links = [];
if (viewMode === 'graph') {
links = g.edges.map(e => ({ source: e[0], target: e[1], type: 'graph' }));
} else if (viewMode === 'complement') {
links = getComplement(g.nodes, g.edges).map(e => ({ source: e[0], target: e[1], type: 'complement' }));
} else {
links = g.edges.map(e => ({ source: e[0], target: e[1], type: 'graph' }));
links = links.concat(getComplement(g.nodes, g.edges).map(e => ({ source: e[0], target: e[1], type: 'complement' })));
}
const rect = canvas.getBoundingClientRect();
const width = rect.width;
const height = rect.height;
const svg = d3.select('#canvas').append('svg').attr('width', width).attr('height', height);
simulation = d3.forceSimulation(nodes)
.force('link', d3.forceLink(links).id(d => d.id).distance(60))
.force('charge', d3.forceManyBody().strength(-150))
.force('center', d3.forceCenter(width / 2, height / 2))
.force('collision', d3.forceCollide().radius(16));
const link = svg.append('g')
.selectAll('line')
.data(links)
.join('line')
.attr('class', 'link')
.attr('stroke', d => d.type === 'graph' ? '#ff3366' : '#00d4ff')
.attr('stroke-width', 2);
const node = svg.append('g')
.selectAll('circle')
.data(nodes)
.join('circle')
.attr('class', 'node')
.attr('r', 8)
.attr('fill', '#e8e8e8')
.call(drag(simulation));
const label = svg.append('g')
.selectAll('text')
.data(nodes)
.join('text')
.attr('class', 'node-label')
.text(d => d.id);
simulation.on('tick', () => {
link.attr('x1', d => d.source.x).attr('y1', d => d.source.y)
.attr('x2', d => d.target.x).attr('y2', d => d.target.y);
node.attr('cx', d => d.x).attr('cy', d => d.y);
label.attr('x', d => d.x).attr('y', d => d.y + 20);
});
}
// Matrix visualization
function visualizeMatrix(g) {
canvas.innerHTML = '';
const n = g.nodes;
const edgeMatrix = buildAdjMatrix(n, g.edges);
const compMatrix = buildAdjMatrix(n, getComplement(n, g.edges));
// Calculate cell size based on available space
const rect = canvas.getBoundingClientRect();
const availableSize = Math.min(rect.width - 80, rect.height - 60);
const cellSize = Math.max(16, Math.min(32, Math.floor(availableSize / n)));
const container = document.createElement('div');
container.className = 'matrix-container';
const wrapper = document.createElement('div');
wrapper.className = 'matrix-wrapper';
wrapper.style.setProperty('--cell-size', `${cellSize}px`);
// Top labels
const topLabels = document.createElement('div');
topLabels.className = 'matrix-labels-top';
for (let j = 0; j < n; j++) {
const label = document.createElement('div');
label.className = 'matrix-label';
label.textContent = j;
topLabels.appendChild(label);
}
wrapper.appendChild(topLabels);
// Matrix rows
for (let i = 0; i < n; i++) {
const row = document.createElement('div');
row.className = 'matrix-row';
// Row label
const rowLabel = document.createElement('div');
rowLabel.className = 'matrix-row-label';
rowLabel.textContent = i;
row.appendChild(rowLabel);
// Cells
for (let j = 0; j < n; j++) {
const cell = document.createElement('div');
cell.className = 'matrix-cell';
if (i === j) {
cell.classList.add('diagonal');
cell.textContent = '-';
} else {
const isEdge = edgeMatrix[i][j] === 1;
const isComp = compMatrix[i][j] === 1;
if (viewMode === 'graph') {
if (isEdge) {
cell.classList.add('edge');
cell.textContent = '1';
} else {
cell.classList.add('empty');
cell.textContent = '0';
}
} else if (viewMode === 'complement') {
if (isComp) {
cell.classList.add('complement');
cell.textContent = '1';
} else {
cell.classList.add('empty');
cell.textContent = '0';
}
} else { // both
if (isEdge) {
cell.classList.add('edge');
cell.textContent = '1';
} else if (isComp) {
cell.classList.add('complement');
cell.textContent = '1';
} else {
cell.classList.add('empty');
cell.textContent = '0';
}
}
}
cell.title = `(${i}, ${j})`;
row.appendChild(cell);
}
wrapper.appendChild(row);
}
container.appendChild(wrapper);
canvas.appendChild(container);
}
function drag(sim) {
return d3.drag()
.on('start', e => { if (!e.active) sim.alphaTarget(0.3).restart(); e.subject.fx = e.subject.x; e.subject.fy = e.subject.y; })
.on('drag', e => { e.subject.fx = e.x; e.subject.fy = e.y; })
.on('end', e => { if (!e.active) sim.alphaTarget(0); e.subject.fx = null; e.subject.fy = null; });
}
// Event listeners
loadDatasetBtn.addEventListener('click', () => loadFromUrl(getDatasetUrl()));
loadUrlBtn.addEventListener('click', () => {
const url = urlInput.value.trim();
if (url) loadFromUrl(url);
});
urlInput.addEventListener('keypress', e => {
if (e.key === 'Enter') loadUrlBtn.click();
});
fileInput.addEventListener('change', e => {
if (e.target.files[0]) {
fileLabel.textContent = e.target.files[0].name;
fileLabel.classList.add('has-file');
loadFromFile(e.target.files[0]);
}
});
prevBtn.addEventListener('click', () => { if (currentIndex > 0) visualize(currentIndex - 1); });
nextBtn.addEventListener('click', () => { if (currentIndex < graphs.length - 1) visualize(currentIndex + 1); });
// Display mode toggle (Force / Matrix)
document.querySelectorAll('#displayToggle .toggle-btn').forEach(btn => {
btn.addEventListener('click', e => {
document.querySelectorAll('#displayToggle .toggle-btn').forEach(b => b.classList.remove('active'));
e.target.classList.add('active');
displayMode = e.target.dataset.display;
if (graphs.length > 0) visualize(currentIndex);
});
});
// View mode toggle (G / G' / Both)
document.querySelectorAll('#viewToggle .toggle-btn').forEach(btn => {
btn.addEventListener('click', e => {
document.querySelectorAll('#viewToggle .toggle-btn').forEach(b => b.classList.remove('active'));
e.target.classList.add('active');
viewMode = e.target.dataset.mode;
if (graphs.length > 0) visualize(currentIndex);
});
});
// Keyboard navigation
document.addEventListener('keydown', e => {
if (graphs.length === 0) return;
if (e.key === 'ArrowLeft' || e.key === 'a') prevBtn.click();
if (e.key === 'ArrowRight' || e.key === 'd') nextBtn.click();
if (e.key === 'm') {
displayMode = displayMode === 'force' ? 'matrix' : 'force';
document.querySelectorAll('#displayToggle .toggle-btn').forEach(b => {
b.classList.toggle('active', b.dataset.display === displayMode);
});
visualize(currentIndex);
}
});
// Language toggle
document.querySelectorAll('.lang-btn').forEach(btn => {
btn.addEventListener('click', () => setLanguage(btn.dataset.lang));
});
// Modal content
const trophyIcon = '<svg style="width:16px;height:16px;vertical-align:middle;margin-right:4px;" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2"><path d="M6 9H4.5a2.5 2.5 0 0 1 0-5H6"></path><path d="M18 9h1.5a2.5 2.5 0 0 0 0-5H18"></path><path d="M4 22h16"></path><path d="M10 14.66V17c0 .55-.47.98-.97 1.21C7.85 18.75 7 20.24 7 22"></path><path d="M14 14.66V17c0 .55.47.98.97 1.21C16.15 18.75 17 20.24 17 22"></path><path d="M18 2H6v7a6 6 0 0 0 12 0V2Z"></path></svg>';
const lightbulbIcon = '<svg style="width:16px;height:16px;vertical-align:middle;margin-right:4px;" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2"><path d="M15 14c.2-1 .7-1.7 1.5-2.5 1-.9 1.5-2.2 1.5-3.5A6 6 0 0 0 6 8c0 1 .2 2.2 1.5 3.5.7.7 1.3 1.5 1.5 2.5"></path><path d="M9 18h6"></path><path d="M10 22h4"></path></svg>';
const introContent = {
en: `
<p><strong>A Ramsey(s,t,n) graph</strong> is a graph with <span class="highlight">n vertices</span> that contains no clique of size s and no independent set of size t.</p>
<p>The <strong>Ramsey Theorem</strong> states that for given s and t, the number of Ramsey(s,t) graphs is finite. The minimum number of vertices for which no such graph exists is called the <strong>Ramsey Number R(s,t)</strong>.</p>
<p>For given s and t, as the number of vertices n increases, there exists a <span class="highlight">critical threshold</span>—once n exceeds this threshold, a clique of size s or an independent set of size t <strong>must</strong> exist in any graph. Finding Ramsey graphs means finding this critical vertex count: the exact point where we can still find at least one special graph that contains neither a clique of size s nor an independent set of size t.</p>
<div class="significance">
<strong>${lightbulbIcon}Why It Matters:</strong> If we had an algorithm to determine the exact Ramsey number in advance, we would know precisely when certain substructures <strong>must</strong> appear in a system. This knowledge could help avoid maintaining excess nodes, potentially saving significant costs in network design, distributed systems, and other applications.
</div>
<p>Finding all such graphs, or even determining the maximum n for which they exist, is a famous problem in combinatorics. Most Ramsey numbers are still unknown—we only know upper and lower bounds.</p>
<div class="challenge">
<strong>${trophyIcon}Open Challenge:</strong> Find a <span class="highlight">Ramsey(5,5) graph with 43 vertices</span>!<br><br>
All 42-vertex Ramsey(5,5) graphs have been found, but it's unknown if a 43-vertex one exists. The lower bound of R(5,5) hasn't been improved since <strong>1989</strong>. Finding just one such graph would be a major breakthrough—${new Date().getFullYear() - 1989} years in the making!
</div>
<p>For the latest research on Ramsey graphs, see <strong>Radziszowski's</strong> dynamic survey published in the <a href="https://www.combinatorics.org" target="_blank" style="color: var(--accent-blue);">Electronic Journal of Combinatorics</a>.</p>
`,
zh: `
<p><strong>Ramsey(s,t,n) 图</strong>是具有 <span class="highlight">n 个顶点</span>的图，它不包含大小为 s 的团，也不包含大小为 t 的独立集。</p>
<p><strong>拉姆齐定理</strong>表明，对于给定的 s 和 t，Ramsey(s,t) 图的数量是有限的。满足这种图存在的最小顶点数称为<strong>拉姆齐数 R(s,t)</strong>。</p>
<p>对于给定的 s 和 t，当节点数量 n 增加时，存在一个<span class="highlight">临界数量</span>——一旦节点数超过这个临界值，大小为 s 的团或大小为 t 的独立集就<strong>一定</strong>存在于任意图中。寻找 Ramsey 图就是在寻找这个临界节点数：在这个节点数量下，我们恰好至少能找到一个很特殊的图，它既不包含大小为 s 的团，也不包含大小为 t 的独立集。</p>
<div class="significance">
<strong>${lightbulbIcon}重要意义：</strong>如果我们能有一种算法提前知道拉姆齐数的具体值，就相当于知道系统中某种子结构在什么时候<strong>必然</strong>开始存在。这样就不用保持过量的节点，从而在网络设计、分布式系统等应用中节省成本。
</div>
<p>找到所有这样的图，甚至确定它们存在的最大 n，都是组合数学中的著名难题。大多数拉姆齐数仍然未知——我们只知道它们的上界和下界。</p>
<div class="challenge">
<strong>${trophyIcon}开放挑战：</strong>找到一个 <span class="highlight">43 顶点的 Ramsey(5,5) 图</span>！<br><br>
目前所有 42 顶点的 Ramsey(5,5) 图都已被找到，但不确定是否存在 43 顶点的图。R(5,5) 的下界自 <strong>1989 年</strong>以来就没有被改进过。只要找到一个这样的图，就是这个领域 ${new Date().getFullYear() - 1989} 年来的重大突破！
</div>
<p>有关 Ramsey 图的最新研究，请参见 <strong>Radziszowski</strong> 的动态综述，持续更新刊登于<a href="https://www.combinatorics.org" target="_blank" style="color: var(--accent-blue);">电子组合学期刊</a>。</p>
`
};
const ramseyTable = [
['s\\t', '1', '2', '3', '4', '5', '6', '7', '8', '9', '10'],
['1', '1', '1', '1', '1', '1', '1', '1', '1', '1', '1'],
['2', '-', '2', '3', '4', '5', '6', '7', '8', '9', '10'],
['3', '-', '-', '6', '9', '14', '18', '23', '28', '36', '40-41'],
['4', '-', '-', '-', '18', '25', '36-40', '49-58', '59-79', '73-106', '92-136'],
['5', '-', '-', '-', '-', '43-48', '59-85', '80-133', '101-194', '133-282', '149-381'],
['6', '-', '-', '-', '-', '-', '102-161', '115-273', '134-427', '183-656', '204-949'],
['7', '-', '-', '-', '-', '-', '-', '205-497', '219-840', '252-1379', '292-2134'],
['8', '-', '-', '-', '-', '-', '-', '-', '282-1532', '329-2683', '343-4432'],
['9', '-', '-', '-', '-', '-', '-', '-', '-', '565-5366', '581-9797'],
['10', '-', '-', '-', '-', '-', '-', '-', '-', '-', '798-17730']
];
function generateProgressTable() {
let html = '<table class="ramsey-table"><thead><tr>';
ramseyTable[0].forEach(h => html += `<th>${h}</th>`);
html += '</tr></thead><tbody>';
for (let i = 1; i < ramseyTable.length; i++) {
html += '<tr>';
ramseyTable[i].forEach((cell, j) => {
if (j === 0) {
html += `<th>${cell}</th>`;
} else if (cell === '-') {
html += `<td class="trivial">-</td>`;
} else if (cell.includes('-')) {
html += `<td class="range">${cell}</td>`;
} else {
html += `<td class="exact">${cell}</td>`;
}
});
html += '</tr>';
}
html += '</tbody></table>';
html += `<div class="table-legend">
<div class="table-legend-item"><div class="legend-box exact"></div><span data-i18n="exactValue">${t('exactValue')}</span></div>
<div class="table-legend-item"><div class="legend-box range"></div><span data-i18n="rangeValue">${t('rangeValue')}</span></div>
</div>`;
return html;
}
function openModal(modalId) {
const modal = document.getElementById(modalId);
if (modalId === 'introModal') {
document.getElementById('introBody').innerHTML = introContent[currentLang];
} else if (modalId === 'progressModal') {
document.getElementById('progressBody').innerHTML = generateProgressTable();
}
modal.classList.add('show');
}
function closeModal(modal) {
modal.classList.remove('show');
}
// Modal event listeners
document.getElementById('introBtn').addEventListener('click', () => openModal('introModal'));
document.getElementById('progressBtn').addEventListener('click', () => openModal('progressModal'));
document.querySelectorAll('.modal-overlay, .modal-close').forEach(el => {
el.addEventListener('click', (e) => {
const modal = e.target.closest('.modal');
if (modal) closeModal(modal);
});
});
document.addEventListener('keydown', e => {
if (e.key === 'Escape') {
document.querySelectorAll('.modal.show').forEach(m => closeModal(m));
}
});
// Init
initSelectors();
// Apply saved language
setLanguage(currentLang);
</script>
</body>
</html>
|