Evolutionary trees: An integer multicommodity max-flow-min-cut theorem

Authors:
Péter L Erdös;Lászlóa Székely
Affiliations:
Department of Applied Mathematics, University of Twente, Enschede, The Netherlands and Hungarian Academy of Sciences, H-1364 Budapest, P.O.B 127, Hungary;Department of Computer Science, Eötvös Loránd University, H-1088 Budapest, Hungary
Venue:
Advances in Applied Mathematics
Year:
1992

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Abstract

In biomathematics, the extensions of a leaf-colouration of a binary tree to the whole vertex set with minimum number of colour-changing edges are extensively studied. Our paper generalizes the problem for trees; algorithms and a Menger-type theorem are presented. The LP dual of the problem is a multicommodity flow problem, for which a max-flow-min-cut theorem holds. The problem that we solve is an instance of the NP-hard multiway cut problem.