The rank facets of the stable set polytope for claw-free graphs (Q1354111)

This paper provides a complete characterization of the rank facets of the stable set polytope \(\text{STAB}(G)\) associated with a claw-free graph \(G\). In particular, it is shown that a claw-free graph \(G\) produces a rank facet of \(\text{STAB}(G)\) 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 \(C^{\omega-1}_{\alpha\omega+1}\). As a by-product, a characterization of the rank facets of \(\text{STAB}(G)\) having right-hand side 2 is given.