On the chromatic number of 2K2-free graphs

In this paper, we study the chromatic number of 2K(2)-free graphs. We show linear chi-binding functions for several subclasses of 2K(2)-free graphs, namely (2K(2),H)-free graphs where H is an element of {house, gem, 2K(1) + K-p, (K-1 boolean OR K-2) + K-p}. We will also discuss chi-binding functions for (2K(2), claw)-free graphs. Finally, we will present extensions of our results to subclasses of P-5-free graphs. (C) 2018 Elsevier B.V. All rights reserved.