Linear χ -binding functions for some classes of ( P 3 ∪ P 2 )-free graphs
Athmakoori Prashant, P. Francis, S. Francis Raj · AKCE International Journal of Graphs and Combinatorics · 2024
The class of 2K2-free graphs has been well studied in the past. In the paper “On the chromatic number of 2K2-free graphs, Discrete Applied Mathematics, 253 (2019), 14–24”, it was shown that the class of {2K2,2K1+Kp}-free graphs and {2K2,(K1∪K2)+Kp}-free graphs admit a linear χ-binding function. In this paper, we study some subclasses of (P3∪P2)-free graphs which is a superclass of 2K2-free graphs. We show that {P3∪P2,2K1+Kp}-free graphs and {P3∪P2,(K1∪K2)+Kp}-free graphs also admit linear χ-binding functions. In addition, we give a tight χ-binding function for {P3∪P2,HVN}-free graphs and improve the χ-bound for {P3∪P2,diamond}-free graphs with ω = 4.