Cones of alternating and cut submodular set functions


We describe facets of the cones of alternating set functions and cut submodular set functions generated by directed and undirected graphs and by uniform even hypergraphs. This answers a question asked by L. Lovász at the Bonn Mathematical Programming Conference in 1982. We show that there is a network flow algorithm for minimizing a hypergraph cut set function.

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Grishuhin, V.P. Cones of alternating and cut submodular set functions. Combinatorica 9, 21–32 (1989).

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AMS subject classification (1980)

  • 52 A 25
  • 05 B 35
  • 05 C 99