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

Author

Listed:
  • Thomas M. Liebling
  • Gianpaolo Oriolo
  • Bianca Spille
  • Gautier Stauffer

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

Suggested Citation

  • Thomas M. Liebling & Gianpaolo Oriolo & Bianca Spille & Gautier Stauffer, 2004. "On non-rank facets of the stable set polytope of claw-free graphs and circulant graphs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(1), pages 25-35, February.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:1:p:25-35
    DOI: 10.1007/s001860300317
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    Citations

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    Cited by:

    1. Anna Galluccio & Claudio Gentile & Paolo Ventura, 2009. "Gear Composition of Stable Set Polytopes and (G-script)-Perfection," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 813-836, November.
    2. Gianpaolo Oriolo & Gautier Stauffer, 2022. "On the facets of stable set polytopes of circular interval graphs," Annals of Operations Research, Springer, vol. 312(2), pages 1007-1029, May.

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