Decomposing Berge graphs
AbstractA 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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Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b06002.
Length: 50 pages
Date of creation: Jan 2006
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Perfect graph; Berge graph; 2-join; even skew partition; decomposition.;
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- C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-03-05 (All new papers)
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