THE RANK FACETS OF THE STABLE SET POLYTOPE FOR CLAW-FREE GRAPHS

This paper provides a complete characterization of the rank facets of the stable set polytope STAB(G) associated with a claw-free graph G. I n particular, it is shown that a claw-free graph G produces a rank fac et of STAB(G) if and only if it can be obtained by means of two simple lifting procedures from three basic classes of graphs: (i) cliques, ( ii) line graphs of minimal 2-connected hypomatchable graphs, and (iii) circulant graphs C-alpha omega+1(omega-1). As a by-product, a charact erization of the rank facets of STAB(G) having right-hand side 2 is gi ven. (C) 1997 Academic Press.