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arXiv · 2305.01927

The robust chromatic number of certain graph classes

Gábor Bacsó·Csilla Bujtás·Balázs Patkós·Zsolt Tuza·Máté Vizer
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Abstract

A 1-selection $f$ of a graph $G$ is a function $f: V(G)\rightarrow E(G)$ such that $f(v)$ is incident to $v$ for every vertex $v$. The 1-removed $G_f$ is the graph $(V(G),E(G)\setminus f[V(G)])$. The (1-)robust chromatic number $\chi_1(G)$ is the minimum of $\chi(G_f)$ over all 1-selections $f$ of $G$. We determine the robust chromatic number of complete multipartite graphs and Kneser graphs and prove tight lower and upper bounds on the robust chromatic number of chordal graphs and some of their extensively studied subclasses, with respect to their ordinary chromatic number.

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Gábor Bacsó, Csilla Bujtás, Balázs Patkós, Zsolt Tuza, Máté Vizer. 2023-05-03. The robust chromatic number of certain graph classes. https://arxiv.org/abs/2305.01927

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