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arXiv · 1702.07851

Chi-boundedness of graph classes excluding wheel vertex-minors

Hojin Choi·O-joung Kwon·Sang-il Oum·Paul Wollan
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Abstract

A class of graphs is $\chi$-bounded if there exists a function $f:\mathbb N\rightarrow \mathbb N$ 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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Hojin Choi, O-joung Kwon, Sang-il Oum, Paul Wollan. 2017-02-25. Chi-boundedness of graph classes excluding wheel vertex-minors. https://doi.org/10.1016/j.jctb.2018.08.009

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