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A new decomposition theorem for Berge graphs

Author

Listed:
  • Nicolas Trotignon

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - 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 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.

Suggested Citation

  • Nicolas Trotignon, 2005. "A new decomposition theorem for Berge graphs," Post-Print halshs-00196448, HAL.
    • Handle: RePEc:hal:journl:halshs-00196448
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00196448
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