Perfectly colorable graphs

Abstract

We define a perfect coloring of a graph G as a proper coloring of G such that every connected induced subgraph H of G uses exactly ω ( H ) many colors where ω ( H ) is the clique number of H. A graph is perfectly colorable if it admits a perfect coloring. We show that the class of perfectly colorable graphs is exactly the class of perfect paw-free graphs. It follows that perfectly colorable graphs can be recognized and colored in linear time.