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A new decomposition theorem for Berge graphs

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Abstract

A hole in a graph is an induced cycle on at least four vertices. A graph is Berge if it has no odd 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. We prove here a stronger theorem by restricting again the allowed decompositions. Motivation for this new theorem will be given in a work in preparation.

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  • Nicolas Trotignon, 2005. "A new decomposition theorem for Berge graphs," Cahiers de la Maison des Sciences Economiques b05079, Université Panthéon-Sorbonne (Paris 1).
  • Handle: RePEc:mse:wpsorb:b05079
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    File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2005/B05079.pdf
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    Keywords

    Graph; Berge; decomposition; 2-join; skew partition.;

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