Entropy splitting for antiblocking corners and perfect graphs

Abstract

We characterize pairs of convex setsA, B in thek-dimensional space with the property that every probability distribution (p 1,...,p k ) has a repsesentationp i =a l .b i , a∃A, b∃B.

Minimal pairs with this property are antiblocking pairs of convex corners. This result is closely related to a new entropy concept. The main application is an information theoretic characterization of perfect graphs.

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Research was partially sponsored by the Hungarian National Foundation, Scientific Research Grants No 1806 and 1812.

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Csiszár, I., Körner, J., Lovász, L. et al. Entropy splitting for antiblocking corners and perfect graphs. Combinatorica 10, 27–40 (1990). https://doi.org/10.1007/BF02122693

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AMS subject classification (1980)

  • 05C15