The Complexity of Multiterminal Cuts

@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}
}
In the multiterminal cut problem one is given an edge-weighted graph and a subset of the vertices called terminals, and is 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. It is shown 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… Expand
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