On $\omega \psi$-Perfect Graphs

Abstract

In this paper, we generalize the concept of {\it{perfect graphs}} to other parameters related to graph vertex coloring. This idea was introduced by Christen and Selkow in 1979 and Yegnanarayanan in 2001. Let $ a,b \in \{ \omega, \chi, \Gamma, \alpha, \psi \} $ where $ \omega $ is the clique number, $ \chi $ is the chromatic number, $ \Gamma $ is the Grundy number, $ \alpha $ is the achromatic number and $ \psi $ is the pseudoachromatic number. A graph $ G $ is \emph{$ ab $-perfect}, if for every induced subgraph $ H $ of $G$, $ a(H)$ equals $b(H) $. In this paper, we characterize the $ab$-perfect graphs when $a=\omega$ and $b=\psi$.