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- Published 1994 in SIAM J. Comput.

In the Multiterminal Cut problem we are given an edge-weighted graph and a subset of the vertices called terminals, and asked for a minimum weight set of edges that separates each terminal from all the others. When the number k of terminals is two, this is simply the mincut, max-flow problem, and can be solved in polynomial time. We show that the problem becomes NP-hard as soon as k = 3, but can be solved in polynomial time for planar graphs for any fixed k. The planar problem is NP-hard, however, if k is not fixed. We also describe a simple approximation algorithm for arbitrary graphs that is guaranteed to come within a factor of 2 − 2/ k of the optimal cut weight.

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@article{Dahlhaus1994TheCO,
title={The Complexity of Multiterminal Cuts},
author={Elias Dahlhaus and David S. Johnson and Christos H. Papadimitriou and Paul D. Seymour and Mihalis Yannakakis},
journal={SIAM J. Comput.},
year={1994},
volume={23},
pages={864-894}
}