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

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

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Article ID: iaor20051032
Country: Germany
Volume: 59
Issue: 1
Start Page Number: 25
End Page Number: 35
Publication Date: Jan 2004
Journal: Mathematical Methods of Operations Research (Heidelberg)
Authors: , , ,
Keywords: sets
Abstract:

We deal with non-rank facets of the stable set polytope of claw-free graphs. We extend results of Giles and Trotter by (i) showing that for any non-negative 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 and Shepherd.

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