Graphs and Combinatorics

, Volume 3, Issue 1, pp 127–139 | Cite as

Bull-free Berge graphs are perfect

  • Vašek Chvátal
  • Najiba Sbihi
Article

Abstract

Abull is the (self-complementary) graph with verticesa, b, c, d, e and edgesab, ac, bc, bd, ce; a graphG is calledBerge if neitherG not its complement contains a chordless cycle whose length is odd and at least five. We prove that bull-free Berge graphs are perfect; a part of our argument relies on a new property of minimal imperfect graphs.

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References

  1. 1.
    Chvátal, V.: Star-cutsets and perfect graphs. J. Comb. Theory (B)39, 189–199 (1985)Google Scholar
  2. 2.
    Lovász, L.: Normal hypergraphs and the perfect graph conjecture. Discrete Math.2, 253–267 (1972)Google Scholar
  3. 3.
    Olariu, S.: No antitwins in minimal imperfect graphs. J. Comb. Theory (B) (to appear)Google Scholar
  4. 4.
    Seinsche, D.: On a property of the class ofn-colorable graphs. J. Comb. Theory (B)16, 191–193 (1974)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Vašek Chvátal
    • 1
  • Najiba Sbihi
    • 2
  1. 1.Department of Computer ScienceRutgers UniversityNew BrunswickUSA
  2. 2.Centre National de Coordination et de Planification de la Recherche Scientifique et TechniqueRabatMorocco

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