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].
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Acknowledgements. Much of this work was carried out while the second and the third authors held Postdoctoral Fellowships at EPFL, funded by the European Union as part of the TMR program on Discrete Optimisation (DONET), FMRX-CT98-0202. The authors gratefully acknowledge the support of DONET for this research.
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Liebling, T., Oriolo, G., Spille, B. et al. On non-rank facets of the stable set polytope of claw-free graphs and circulant graphs. Math Meth Oper Res 59, 25–35 (2004). https://doi.org/10.1007/s001860300317
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DOI: https://doi.org/10.1007/s001860300317