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