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 graphG. In particular, it is shown that a claw-free graphGproduces a rank facet 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 graphsCω−1αω+1. As a by-product, a characterization of the rank facets of STAB(G) having right-hand side 2 is given.