On non-rank facets of the stable set polytope of claw-free graphs and circulant graphs

Thomas M. Liebling (), Gianpaolo Oriolo (), Bianca Spille () and Gautier Stauffer ()

Mathematical Methods of Operations Research, 2004, vol. 59, issue 1, 25-35

Abstract: We deal with non-rank facets of the stable set polytope of claw-free graphs. We extend results of Giles 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 coefficients (rank facets have only 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 observed by Cook [3] and Shepherd [18]. Copyright Springer-Verlag 2004

Keywords: Stable sets; Claw-free graphs; Quasi-line graphs; Circulant graphs; Clique family inequalities (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/s001860300317

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