Directed cut transversal packing for source-sink connected graphs

Abstract

Concerning the conjecture that in every directed graph, a maximum packing of directed cut transversals is equal in cardinality to a minimum directed cut, a proof is given for the side coboundaries of a graph. This case includes, and is essentially equivalent to, all source-sink connected graphs, for which Schrijver has given a proof. The method used here first reduces the assertion to a packing theorem for bi-transversals. A packing of bi-transversals of the required size is constructed one edge at a time, by maintaining a Hall-like feasibility condition as each edge is added.

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Feofiloff, P., Younger, D.H. Directed cut transversal packing for source-sink connected graphs. Combinatorica 7, 255–263 (1987). https://doi.org/10.1007/BF02579302

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AMS subject classification (1980)

  • 05 C 20