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On the structure of bull-free perfect graphs

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Abstract

A bull is a graph obtained by adding a pendant vertex at two vertices of a triangle. Chvátal and Sbihi showed that the Strong Perfect Graph Conjecture holds for bull-free graphs. We show that bull-free perfect graphs are quasi-parity graphs, and that bull-free perfect graphs with no antihole are perfectly contractile. Our proof yields a polynomial algorithm for coloring bull-free strict quasi-parity graphs

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Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21944, Rio de Janeiro, RJ, Brasil

    Celina M. H. de Figueiredo

  2. LSD2-IMAG, BP 53, 38041, Grenoble Cedex 9, France

    Frédéric Maffray

  3. Dept. de Engenharia Elétrica, PUC-Rio, Rua Marquês de São Vicente 225, Predio Cardeal Leme, Sala 401, CEP 22453, Rio de Janeiro, RJ, Brasil

    Oscar Porto

Authors
  1. Celina M. H. de Figueiredo
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  2. Frédéric Maffray
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  3. Oscar Porto
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Partially supported by CNPq, grant 30 1160/91.0

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de Figueiredo, C.M.H., Maffray, F. & Porto, O. On the structure of bull-free perfect graphs. Graphs and Combinatorics 13, 31–55 (1997). https://doi.org/10.1007/BF01202235

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  • DOI: https://doi.org/10.1007/BF01202235

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