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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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    File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2006/B06002.pdf
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    Bibliographic Info

    Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b06002.

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    Length: 50 pages
    Date of creation: Jan 2006
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    Handle: RePEc:mse:wpsorb:b06002

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    Keywords: Perfect graph; Berge graph; 2-join; even skew partition; decomposition.;

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