The coloring problem for $\{P_5,\bar{P_5}\}$-free graphs and $\{P_5,K_p-e\}$-free graphs is polynomial

Abstract

We show that determining the chromatic number of a $\{P_5,\bar{P_5}\}$-free graph or a $\{P_5,K_p-e\}$-free graph can be done in polynomial time