A new decomposition theorem for Berge graphs
AbstractA 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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Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b05079.
Length: 26 pages
Date of creation: Nov 2005
Date of revision:
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Graph; Berge; decomposition; 2-join; skew partition.;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-12-09 (All new papers)
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