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Article Dans Une Revue Discrete Applied Mathematics Année : 2023

Lovász–Schrijver PSD-operator and the stable set polytope of claw-free graphs

Résumé

The subject of this work is the study of LS+-perfect graphs defined as those graphs G for which the stable set polytope STAB(G) is achieved in one iteration of Lovász-Schrijver PSD-operator LS+, applied to its edge relaxation ESTAB(G). In particular, we look for a polyhedral relaxation of STAB(G) that coincides with LS+(ESTAB(G)) and STAB(G) if and only if G is LS+-perfect. An according conjecture has been recently formulated (LS+-Perfect Graph Conjecture); here we verify it for the wellstudied class of claw-free graphs.
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Dates et versions

hal-04404041 , version 1 (18-01-2024)

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Silvia M Bianchi, Mariana Escalante, Graciela Nasini, Annegret K Wagler. Lovász–Schrijver PSD-operator and the stable set polytope of claw-free graphs. Discrete Applied Mathematics, 2023, 332, pp.70-86. ⟨10.1016/j.dam.2023.01.012⟩. ⟨hal-04404041⟩
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