  Problem of finding an optimal upper bound for the chromatic no. of 3K1-free
graphs is still open and pretty hard. It was proved by Choudum et al that an
upper bound on the chromatic no. of {3K1, K1+C4}-free graphs, is 2{\omega}. We
improve this by proving that if G is {3K1, K1+C4}-free, then its chromatic no.
is less than or equal to 3{\omega} divided by 2, where {\omega} is the size of
a maximum clique in G. Also we give examples to show that this bound is tight.
