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Algorithms for square-3PC(.,.)-free Berge graphs

Author

Listed:
  • Frédéric Maffray

    (Leibniz - IMAG - Laboratoire Leibniz - UJF - Université Joseph Fourier - Grenoble 1 - INPG - Institut National Polytechnique de Grenoble - CNRS - Centre National de la Recherche Scientifique)

  • Nicolas Trotignon

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Kristina Vuskovic

    (School of Computing [Leeds] - University of Leeds)

Abstract

We consider the class of graphs containing no odd hole, no odd antihole and no configuration consisting of three paths between two nodes such that any two of the paths induce a hole and at least two of the paths are of length 2. This class generalizes claw-free Berge graphs and square-free Berge graphs. We give a combinatorial algorithm of complexity O(n7) to find a clique of maximum weight in such a graph. We also consider several subgraph-detection problems related to this class.

Suggested Citation

  • Frédéric Maffray & Nicolas Trotignon & Kristina Vuskovic, 2006. "Algorithms for square-3PC(.,.)-free Berge graphs," Post-Print halshs-00130439, HAL.
    • Handle: RePEc:hal:journl:halshs-00130439
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00130439
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    References listed on IDEAS

    as
    1. HSU, Wen-Lian & NEMHAUSER, George L., 1984. "Algorithms for maximum weight cliques, minimum weighted clique covers and minimum colorings of claw-free perfect graphs," LIDAM Reprints CORE 595, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Xueliang Li & Wenan Zang, 2005. "A Combinatorial Algorithm for Minimum Weighted Colorings of Claw-Free Perfect Graphs," Journal of Combinatorial Optimization, Springer, vol. 9(4), pages 331-347, June.
    Full references (including those not matched with items on IDEAS)

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    1. Frédéric Maffray & Nicolas Trotignon & Kristina Vuskovic, 2006. "Algorithms for square-3PC(.,.)-free Berge graphs," Cahiers de la Maison des Sciences Economiques b06085, Université Panthéon-Sorbonne (Paris 1).
    2. Xueliang Li & Wenan Zang, 2005. "A Combinatorial Algorithm for Minimum Weighted Colorings of Claw-Free Perfect Graphs," Journal of Combinatorial Optimization, Springer, vol. 9(4), pages 331-347, June.
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