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تسجيل مستخدم جديدChi-boundedness of graph classes excluding wheel vertex-minors
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A class of graphs is $chi$-bounded if there exists a function $f:mathbb Nrightarrow mathbb N$ such that for every graph $G$ in the class and an induced subgraph $H$ of $G$, if $H$ has no clique of size $q+1$, then the chromatic number of $H$ is less than or equal to $f(q)$. We denote by $W_n$ the wheel graph on $n+1$ vertices. We show that the class of graphs having no vertex-minor isomorphic to $W_n$ is $chi$-bounded. This generalizes several previous results; $chi$-boundedness for circle graphs, for graphs having no $W_5$ vertex-minors, and for graphs having no fan vertex-minors.
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