Preperfect graphs

Abstract

We say that a vertexx of a graph is predominant if there exists another vertexy ofG such that either every maximum clique ofG containingy containsx or every maximum stable set containingx containsy. A graph is then called preperfect if every induced subgraph has a predominant vertex. We show that preperfect graphs are perfect, and that several well-known classes of perfect graphs are preperfect. We also derive a new characterization of perfect graphs.

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Hammer, P.L., Maffray, F. Preperfect graphs. Combinatorica 13, 199–208 (1993). https://doi.org/10.1007/BF01303204

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AMS subject classification code (1991)

  • 05 C 15
  • 05 C 70
  • 05 C 75