Tight Chromatic Upper Bound for {3K1, C5}-free Graphs

Abstract

Problem of finding an optimal upper bound for a chromatic no. of 3K1-free graphs is still open and pretty hard. Here we find a tight chromatic upper bound for {3K1, C5}-free graphs. We prove that if G is {3K1, C5}-free, then the chromatic no. <= (3{\omega}-1)/2 where {\omega} is the size of a maximum clique in G and show with examples that the bound is tight.