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Stable sets and graphs with no even holes

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Abstract

We develop decomposition/composition tools for efficiently solving maximum weight stable sets problems as well as for describing them as polynomially sized linear programs (using “compact systems”). Some of these are well-known but need some extra work to yield polynomial “decomposition schemes”. We apply the tools to graphs with no even hole and no cap. A hole is a chordless cycle of length greater than three and a cap is a hole together with an additional node that is adjacent to two adjacent nodes of the hole and that has no other neighbors on the hole.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste 63, 35121, Padua, Italy

    Michele Conforti & Kanstantsin Pashkovich

  2. Centrum Wiskunde & Informatica, Science Park 123, 1098 XG, Amsterdam, The Netherlands

    Bert Gerards

  3. Department of Combinatorics and Optimization, University of Waterloo, University Avenue West 200, Waterloo, ON, N2L 3G1, Canada

    Kanstantsin Pashkovich

Authors
  1. Michele Conforti
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  2. Bert Gerards
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  3. Kanstantsin Pashkovich
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Corresponding author

Correspondence to Bert Gerards.

Additional information

Michele Conforti supported by “Progetto di Eccellenza 2008–2009” of “Fondazione Cassa di Risparmio di Padova e Rovigo”.

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Conforti, M., Gerards, B. & Pashkovich, K. Stable sets and graphs with no even holes. Math. Program. 153, 13–39 (2015). https://doi.org/10.1007/s10107-015-0912-3

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  • DOI: https://doi.org/10.1007/s10107-015-0912-3

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