Improvement on Brook theorem for 2K2-free Graphs

TL;DR

This paper proves a new bound on the chromatic number of 2K2-free graphs with maximum degree at least 5, confirming the Borodin & Kostochka Conjecture for this class.

Contribution

It establishes an improved upper bound on the chromatic number for 2K2-free graphs, advancing the understanding of graph coloring in this class.

Findings

Chromatic number ≤ max{Δ-1, ω} for 2K2-free graphs with Δ ≥ 5

Borodin & Kostochka Conjecture holds for 2K2-free graphs

Provides a tighter bound on graph coloring in specific graph classes

Abstract

Here we prove that for a 2K2-free graph G with maximum degree greater than or equal to 5, the chromatic number is less than or equal to max{maximum degree-1, maximum clique size}. This implies that Borodin & Kostochka Conjecture is true for 2K2-free graphs.