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Lovász and Schrijver \(N_+\)-Relaxation on Web Graphs

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Combinatorial Optimization (ISCO 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8596))

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Abstract

In this contribution we continue the study of the Lovász-Schrijver PSD-operator applied to the edge relaxation of the stable set polytope of a graph. The problem of obtaining a combinatorial characterization of graphs for which the PSD-operator generates the stable set polytope in one step has been open since 1990. In an earlier publication, we named these graphs \(N_+\)-perfect. In the current work, we prove that the only imperfect web graphs that are \(N_+\)-perfect are the odd-cycles and their complements. This result adds evidence for the validity of the conjecture stating that the only graphs which are \(N_+\)-perfect are those whose stable set polytope is described by inequalities with near-bipartite support. Finally, we make some progress on identifying some minimal forbidden structures on \(N_+\)-perfect graphs which are also rank-perfect.

Partially supported by grants PIP-CONICET 241, PICT-ANPCyT 0361, PID UNR 415, PID UNR 416.

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Authors and Affiliations

  1. CONICET and FCEIA - Universidad Nacional de Rosario, Rosario, Argentina

    Mariana Escalante & Graciela Nasini

Authors
  1. Mariana Escalante
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  2. Graciela Nasini
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Correspondence to Mariana Escalante .

Editor information

Editors and Affiliations

  1. Univ Pierre et Marie Curie LIP6, Paris, France

    Pierre Fouilhoux

  2. Universidade de Lisboa, Lisbon, Portugal

    Luis Eduardo Neves Gouveia

  3. LAMSADE, Université Paris-Dauphine, Paris Cedex 16, France

    A. Ridha Mahjoub

  4. LAMSADE, Université Paris-Dauphine, Paris Cedex 16, France

    Vangelis T. Paschos

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Escalante, M., Nasini, G. (2014). Lovász and Schrijver \(N_+\)-Relaxation on Web Graphs. In: Fouilhoux, P., Gouveia, L., Mahjoub, A., Paschos, V. (eds) Combinatorial Optimization. ISCO 2014. Lecture Notes in Computer Science(), vol 8596. Springer, Cham. https://doi.org/10.1007/978-3-319-09174-7_19

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  • DOI: https://doi.org/10.1007/978-3-319-09174-7_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09173-0

  • Online ISBN: 978-3-319-09174-7

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