Colouring of (P3UP2)-free graphs

TL;DR

This paper investigates the chromatic number bounds of (P3UP2)-free graphs and related subclasses, providing polynomial upper bounds and identifying conditions under which these classes are perfect.

Contribution

It establishes new polynomial bounds for the chromatic number of (P3UP2)-free graphs and subclasses, extending understanding of graph coloring in these classes.

Findings

O(w^3) upper bound for (P3UP2)-free graphs

Sharper bounds for (P3UP2, diamond)-free graphs

Certain subclasses are perfect for w >= 4 or 5

Abstract

The class of 2K2-free graphs and its various subclasses have been studied in a variety of contexts. In this paper, we are concerned with the colouring of (P3UP2)-free graphs, a super class of 2K2-free graphs. We derive a O(w^3) upper bound for the chromatic number of (P3UP2)-free graphs, and sharper bounds for (P3UP2), diamond)-free graphs, where w denotes the clique number. By applying similar proof techniques we obtain chromatic bounds for (2K2, diamond)-free graphs. The last two classes are perfect if w >=5 and >= 4 respectively.