on Non-Rank Facets of the Stable Set Polytope of Claw-Free Graphs and Circulant Graphs

We deal with non-rank facets of the stable set polytope of claw-free graphs. We extend results of Gilles and Trotter (7) by (i) showing that for any nonnegative integer a there exists a circulant graph whose stable set polytope has a facet-inducing inequality with (a,a+1) valued coefficinets (rank facets have onnly coefficients 0, 1), and (ii) providing new facets of the stable set polytope with up to five different non-zero coefficients for claw-free graphs. We prove that coefficients have to be consecutive in any facet with exactly two different non-zero coefficients (assuming they are relatively prime). Last but not least, we present a complete description of the stable set polytope for graphs with stability number 2, already obseerved by Cook (3) and Shepperd (18)