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Decomposing Berge graphs

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Abstract

A hole in a graph is an induceed cycle on at least four vertices. A graph is Berge if it has no old hole and if its complement has no odd hole. In 2002, Chudnovsky, Robertson, Seymour and Thomas proved a decomposition theorem for Berge graphs saying that every Berge graph either is in a well understood basic class or has some kind of decomposition. Then, Chudnovsky proved a stronger theorem by restricting the allowed decompositions and another theorem where some decompositions were restricted while other decompositions were extended. We prove here a theorem stronger than all those previously known results. Our proof uses at an essential step one of the theorems of Chudnovsky

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  • Nicolas Trotignon, 2006. "Decomposing Berge graphs," Cahiers de la Maison des Sciences Economiques b06002, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:mse:wpsorb:b06002
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    File URL: https://halshs.archives-ouvertes.fr/halshs-00082823
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    Keywords

    Perfect graph; Berge graph; 2-join; even skew partition; decomposition;
    All these keywords.

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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