A Description of Claw-Free Perfect Graphs

Abstract

It is known that all claw-free perfect graphs can be decomposed via clique-cutsets into two types of indecomposable graphs respectively called elementary and peculiar (1988, V. Chvátal and N. Sbihi,J. Combin. Theory Ser. B44, 154-176). We show here that every elementary graph is made up in a well-defined way of a line-graph of bipartite graph and some local augments consisting of complements of bipartite graphs. This yields a complete description of the structure of claw-free Berge graphs and a new proof of their perfectness. © 1999 Academic Press.