Decomposing Berge graphs

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

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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 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.

Keywords: even skew partition; 2-join; Berge graph; Perfect graph; decomposition (search for similar items in EconPapers)
Date: 2006-01
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Published in 2006

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