Article

Graphs and Combinatorics

, Volume 3, Issue 1, pp 127-139

Bull-free Berge graphs are perfect

  • Vašek ChvátalAffiliated withDepartment of Computer Science, Rutgers University
  • , Najiba SbihiAffiliated withCentre National de Coordination et de Planification de la Recherche Scientifique et Technique

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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.