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Decomposing Berge graphs

Author

Listed:
  • Nicolas Trotignon

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

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.

Suggested Citation

  • Nicolas Trotignon, 2006. "Decomposing Berge graphs," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00082823, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00082823
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00082823
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