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Lovász-Schrijver PSD-Operator on Claw-Free Graphs

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Combinatorial Optimization (ISCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9849))

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Abstract

The subject of this work is the study of the Lovász-Schrijver PSD-operator \(LS_+\) applied to the edge relaxation \(\mathrm{ESTAB}(G)\) of the stable set polytope \(\mathrm{STAB}(G)\) of a graph G. We are interested in the problem of characterizing the graphs G for which \(\mathrm{STAB}(G)\) is achieved in one iteration of the \(LS_+\)-operator, called \(LS_+\)-perfect graphs, and to find a polyhedral relaxation of \(\mathrm{STAB}(G)\) that coincides with \(LS_+(\mathrm{ESTAB}(G))\) and \(\mathrm{STAB}(G)\) 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 well-studied class of claw-free graphs.

This work was supported by an ECOS-MINCyT cooperation (A12E01), a MATH-AmSud cooperation (PACK-COVER), PID-CONICET 0277, PICT-ANPCyT 0586.

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Author information

Authors and Affiliations

  1. FCEIA, Universidad Nacional de Rosario, Rosario, Argentina

    Silvia Bianchi, Mariana Escalante & Graciela Nasini

  2. LIMOS (UMR 6158 CNRS), University Blaise Pascal, Clermont-Ferrand, France

    Annegret Wagler

Authors
  1. Silvia Bianchi
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  2. Mariana Escalante
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  3. Graciela Nasini
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  4. Annegret Wagler
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Correspondence to Annegret Wagler .

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Editors and Affiliations

  1. University of Salerno , Fisciano, Italy

    Raffaele Cerulli

  2. Kyoto University , Kyoto, Japan

    Satoru Fujishige

  3. LAMSADE, Université Paris-Dauphine , Paris , France

    A. Ridha Mahjoub

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Bianchi, S., Escalante, M., Nasini, G., Wagler, A. (2016). Lovász-Schrijver PSD-Operator on Claw-Free Graphs. In: Cerulli, R., Fujishige, S., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2016. Lecture Notes in Computer Science(), vol 9849. Springer, Cham. https://doi.org/10.1007/978-3-319-45587-7_6

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  • DOI: https://doi.org/10.1007/978-3-319-45587-7_6

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