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Norms and perfect graphs

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Abstract

The weak Berge hypothesis states that a graph is perfect if and only if its complement is perfect. Previous proofs of this hypothesis have used combinatorial or polyhedral methods.

In this paper, the concept of norms related to graphs is used to provide an alternative proof for the weak Berge hypothesis.

Zusammenfassung

Die schwache Berge Vermutung sagt aus, daß ein Graph genau dann perfekt ist, wenn dies auch für sein Komplement gilt. Frühere Beweise dieser Vermutung benutzten kombinatorische oder polyedrische Methoden.

In dieser Arbeit wird das Konzept einer Norm bezüglich eines Graphen benutzt, um einen alternativen Beweis der schwachen Berge Vermutung zu liefern.

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Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 137, PL-00-950, Warszawa

    S. Perz & S. Rolewicz

Authors
  1. S. Perz
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  2. S. Rolewicz
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Additional information

This is a written account of an invited lecture delivered by the second author on occasion of the 12. Symposium on Operations Research, Passau, 9.–11. 9. 1987.

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Perz, S., Rolewicz, S. Norms and perfect graphs. ZOR - Methods and Models of Operations Research 34, 13–27 (1990). https://doi.org/10.1007/BF01415946

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  • DOI: https://doi.org/10.1007/BF01415946

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