A Note Related to Graph Theory

Abstract

This article foucuses on $(P_3\cup P_2,K_4)$-free graph. In this paper, we prove that if G is $(P_3\cup P_2,K_4)$-free, then $\chi (G)\le 7$. We then use our result to obtain the upper bound of order and chromatic number of $(4K_1,\overline{P_3\cup P_2},K_{\omega })$-free graph .

12 pages,8 figures