Work

The robust chromatic number of certain graph classes

Year: 2023

Type: article

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 $χ_1(G)$ is the minimum of $χ(G_f)$ 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.

Source: DiRROS repository (University of Maribor)

DOI: 10.48550/arxiv.2305.01927

Authors: Bacsó, Gábor, Bujtás, Csilla, Patkós, Balázs, Tuza, Zsolt, Vizer, Máté

Institutions: HUN-REN Alfréd Rényi Institute of Mathematics, University of Pannonia, Budapest University of Technology and Economics

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Javna Agencija za Raziskovalno Dejavnost RS, Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, National Research, Development and Innovation Office