A description of claw-free perfect graphs

It is known that all claw-free perfect graphs can be decomposed via clique- cutsets into two types of indecomposable graphs respectively called element ary and peculiar (1988, V. Chvatal and N. Sbihi, J. Combin. Theory Set. B 4 4, 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 cons isting of complements of bipartite graphs. This yields a complete descripti on of the structure of claw-free Berge graphs and a new proof of their perf ectness. (C) 1999 Academic Press.