Optimal chromatic bound for (P2+P3,P2+P3¯ ${P}_{2}+{P}_{3},\bar{{P}_{2}+{P}_{3}}$)‐free graphs

Abstract

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