Lov\'asz-Schrijver PSD-operator on Claw-Free Graphs
Silvia Bianchi, Mariana Escalante, Graciela Nasini, Annegret Wagler

TL;DR
This paper investigates the properties of -perfect graphs, focusing on claw-free graphs, and verifies a conjecture relating the Love1sz-Schrijver PSD-operator to stable set polytopes within this class.
Contribution
It confirms the -perfect graph conjecture for claw-free graphs, advancing understanding of polyhedral relaxations in graph theory.
Findings
Verification of the -perfect graph conjecture for claw-free graphs
Characterization of -perfect graphs in relation to the Love1sz-Schrijver PSD-operator
Enhanced understanding of stable set polytopes in claw-free graphs
Abstract
The subject of this work is the study of -perfect graphs defined as those graphs for which the stable set polytope is achieved in one iteration of Lov\'asz-Schrijver PSD-operator , applied to its edge relaxation . In particular, we look for a polyhedral relaxation of that coincides with and if and only if is -perfect. An according conjecture has been recently formulated (-Perfect Graph Conjecture); here we verify it for the well-studied class of claw-free graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Complexity and Algorithms in Graphs
