On a Class of P5-Free Graphs

A graph G is perfect in the sense of Berge if for every induced subgraph G′ of G, the chromatic number χ(G′) equals the largest number ω(G′) of pairwise adjacent vertices in G′. The Strong Perfect Graph Conjecture asserts that a graph G is perfect if, and only if, neither G nor its complement ? contains an odd chordless cycle of length at least five. We prove that the conjecture is true for a class of P₅-free graphs.