Chi-boundedness of graph classes excluding wheel vertex-minors

Abstract

A class of graphs is $\chi$-bounded if there exists a function $f:\mathbb{N}\to \mathbb{N}$ 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.

27 pages, 9 figures (revised version)

References in corpus (1)

• Coloring graphs without fan vertex-minors and graphs without cycle pivot-minors

Cited by in corpus (1)

• Classes of graphs with no long cycle as a vertex-minor are polynomially $\chi$-bounded