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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.

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References

  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)

  4. Seinsche, D.: On a property of the class ofn-colorable graphs. J. Comb. Theory (B)16, 191–193 (1974)

    Google Scholar 

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This work was done while both authors were at the School of Computer Science, McGill University; support by NSERC is gratefully acknowledged.

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Chvátal, V., Sbihi, N. Bull-free Berge graphs are perfect. Graphs and Combinatorics 3, 127–139 (1987). https://doi.org/10.1007/BF01788536

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  • DOI: https://doi.org/10.1007/BF01788536

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