Optimal chromatic bound for (Formula presented.)-free graphs

Article Type

Research Article

Publication Title

Journal of Graph Theory

Abstract

For a graph (Formula presented.), let (Formula presented.) ((Formula presented.)) denote its chromatic (clique) number. A (Formula presented.) is the graph obtained by taking the disjoint union of a two-vertex path (Formula presented.) and a three-vertex path (Formula presented.). A (Formula presented.) is the complement graph of a (Formula presented.). In this paper, we study the class of ((Formula presented.))-free graphs and show that every such graph (Formula presented.) with (Formula presented.) satisfies (Formula presented.). Moreover, the bound is tight. Indeed, for any (Formula presented.) and (Formula presented.), there is a ((Formula presented.))-free graph (Formula presented.) with (Formula presented.) and (Formula presented.).

First Page

149

Last Page

178

DOI

10.1002/jgt.23009

Publication Date

2-1-2024

Comments

Open Access; Bronze Open Access

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