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<!DOCTYPE html>
<html>
<head>
<title>MathJax Example</title>
<script>
MathJax = {
tex: {
inlineMath: [['$', '$'], ['\(', '\)']]
},
svg: {
fontCache: 'global'
}
};
</script>
<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
</head>
<body>
<p> $x=a$ </p>
<p> $C_{1},\ldots,C_{k}\cup(C\setminus\{v\})$ </p>
<p> $z^{v}$ </p>
<p> $\{2,\dots,s-1\}$ </p>
<p> $S\cap(A\cup C)$ </p>
<p> $H:=G[A\cup B\cup S]$ </p>
<p> $z\in V(C)$ </p>
<p> $N_{G}(p_{s})\cap V(H)=\{b_{2}\}$ </p>
<p> $H\setminus C$ </p>
<p> $k\geq\chi(\overline{G})\geq 2$ </p>
<p> $H_{1},H_{2}\in\mathcal{M}_{\mathcal{C}}$ </p>
<p> $\{p_{0},\dots,p_{s-1}\}$ </p>
<p> $(x,c)$ </p>
<p> ${\cal G}_{1}$ </p>
<p> $q_{t}=y$ </p>
<p> $q_{2},\dots,q_{t}\in B)$ </p>
<p> $G\in\mathcal{G}_{k}$ </p>
<p> $S=(S^{\prime}\setminus\{x,y\})\cup\{v^{xy}\}$ </p>
<p> $X_{v}$ </p>
<p> $\mathcal{M}_{\mathcal{G}_{2}}=\{\overline{K_{2}\cup C_{2k+1}}\mid k\in\mathbb{%
N}\}$ </p>
<p> $\{a_{i},b_{j}\}$ </p>
<p> $\mathcal{O}(n^{\omega}\log n)$ </p>
<p> $|V(H)|\geq 2$ </p>
<p> $V(C)$ </p>
<p> $q_{i},\ldots,q_{t},b_{1},b_{2},a_{2},q_{i}$ </p>
<p> $N_{G}(v)\cap V(H)\subseteq A$ </p>
<p> $G[N_{G}(v)]$ </p>
<p> $G_{A}\setminus S^{\prime}$ </p>
<p> $\mathcal{O}(n^{2k})$ </p>
<p> $\mathbb{Z}_{k}$ </p>
<p> $\{X_{v}\}_{v\in V(H)}$ </p>
<p> $2K_{1}\vee K_{2}$ </p>
<p> $G[\{a_{1},a_{2},b_{1},b_{2}\}\cup V(Q)]$ </p>
<p> $v^{xy}\in S$ </p>
<p> $S\cap A$ </p>
<p> $(S^{\prime}\setminus\{x,y\})\cup\{v^{xy}\}\subseteq S$ </p>
<p> $X_{w}\subseteq V(D)$ </p>
<p> $\mathcal{G}_{k}=\mathcal{G}_{\mathcal{C}_{k}}$ </p>
<p> $N_{G}[u]=V(G)$ </p>
<p> $\mathcal{O}(n^{2.373}(n+m))$ </p>
<p> $F\in{\cal F}$ </p>
<p> $r_{i}\in C$ </p>
<p> $G\setminus x$ </p>
<p> $G\setminus N_{G}[v]$ </p>
<p> $S^{*}:=(S\setminus\{v^{xy}\})\cup\{x,y\}$ </p>
<p> $U:=\{v\in V(H)\mid X_{v}\cap V(C)\neq\emptyset\}$ </p>
<p> $N_{A}\cap N_{B}=\emptyset$ </p>
<p> $G\setminus(A\cup B)$ </p>
<p> $N_{G}(q_{t})\cap V(H)=\{a_{1},b_{1}\}$ </p>
<p> $S\subseteq S^{*}$ </p>
<p> $K_{\ell+1}\in\mathcal{G}_{\mathcal{C}}$ </p>
<p> ${\mathcal{C}_{k}}$ </p>
<p> $V(H)=A\cup B$ </p>
<p> $K_{\ell}$ </p>
<p> $N_{G}(v)\cap V(H)=B$ </p>
<p> $X_{w}$ </p>
<p> $H\setminus a$ </p>
<p> $H[A]$ </p>
<p> $G^{\prime}[S]$ </p>
<p> $G_{B}:=G[B\cup C]$ </p>
<p> $S^{*}\subseteq S\cup(V(G)\setminus V(H))$ </p>
<p> $G^{\prime}:=G/xy$ </p>
<p> $p_{i},\dots,p_{s},b_{1},b_{3},a_{3},a_{2},q_{t},\dots,q_{0},p_{i}$ </p>
<p> $q_{2},\dots,q_{t}\in Y$ </p>
<p> $a_{1},q_{i}$ </p>
<p> $\{2K_{1}\vee H\mid H\in\mathcal{M}_{\mathcal{C}}\}$ </p>
<p> $p_{1},\dots,p_{i-1}\in A$ </p>
<p> $v^{xy}$ </p>
<p> $\mathcal{C}\subseteq\mathcal{G}_{\mathcal{C}}$ </p>
<p> $S^{\prime}\setminus\{x,y\}$ </p>
<p> $p_{1}=x$ </p>
<p> $N_{G}(q_{t})\cap V(H)=\{a_{2}\}$ </p>
<p> $G\setminus N_{G}[x]$ </p>
<p> $\overline{\overline{G}}=G$ </p>
<p> $H[S]\in\mathcal{C}$ </p>
<p> $S^{\prime}=S$ </p>
<p> $\bigcup_{v\in V(H)}X_{v}\not\subseteq V(H_{2})$ </p>
<p> $c\in C\setminus S$ </p>
<p> $N_{G}(p_{s})\cap V(H)=\{b_{1}\}$ </p>
<p> $\{2K_{1}\vee H\mid H\in\mathcal{M}_{\mathcal{C}_{0}}\}=\{2K_{1}\vee K_{1}\}=\{%
P_{3}\}$ </p>
<p> $K_{\ell+1}$ </p>
<p> $H\in\mathcal{H}$ </p>
<p> $A=C\cup\{v\}$ </p>
<p> $U=\{v\in V(H)\mid X_{v}\subseteq V(C)\}$ </p>
<p> $S_{A}:=S\setminus B$ </p>
<p> $2K_{1}\vee 3K_{1}$ </p>
<p> $q_{j}\in C$ </p>
<p> $p_{i-1},p_{j+1}\in C$ </p>
<p> $\{a_{1},b_{1}\}$ </p>
<p> $Y\subseteq V(G)\setminus\{x\}$ </p>
<p> $\{a,b\}=\{x,y\}$ </p>
<p> $\{X_{v}\}_{v\in\{a,b\}\cup V(H)}$ </p>
<p> $|V(H)|=2k$ </p>
<p> $(x,b)$ </p>
<p> $C\cap S$ </p>
<p> $\mathcal{O}(|V(G)|^{2})$ </p>
<p> $G[a_{j},a_{k},b_{j},b_{k},q_{i},q_{i+1},\dots,q_{t}]$ </p>
<p> $2K_{1}$ </p>
<p> $a_{i},a_{j}$ </p>
<p> $p_{i}\in B$ </p>
</body>
</html>