Perfect couples of graphs

Abstract

We generalize the concept of perfect graphs in terms of additivity of a functional called graph entropy. The latter is an information theoretic functional on a graphG with a probability distributionP on its vertex set. For any fixedP it is sub-additive with respect to graph union. The entropy of the complete graph equals the sum of those ofG and its complement G iffG is perfect. We generalize this recent result to characterize all the cases when the sub-additivity of graph entropy holds with equality.

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The research of the authors is partially supported by the Hungarian National Foundation for Scientific Research (OTKA), grant No. 1806 resp. No. 1812.

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Körner, J., Simonyi, G. & Tuza, Z. Perfect couples of graphs. Combinatorica 12, 179–192 (1992). https://doi.org/10.1007/BF01204721

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AMS subject classification code (1991)

  • 05 C 75
  • 94 A 17
  • 05 C 15
  • 94 A 15