On the P4-structure of perfect graphs v. overlap graphs

Abstract

Given a graph G we define its k-overlap graph as the graph whose vertices are the induced P4's of G and two vertices in the overlap graph are adjacent if the corresponding P4's in G have exactly k vertices in common. For k = 1, 2, 3 we prove that if the k-overlap graph of G is bipartite then G is perfect. © 1996 Academic Press, Inc.