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The k-cut problem is to find a partition of an edge weighted graph into k nonempty components, such that the total edge weight between components is minimum. This problem is NP-complete for an arbitrary k and its version involving fixing a vertex in each component is NP-hard even for k = 3. We present a polynomial algorithm for k fixed, that runs in O(n k ²/2−3k/2+4 T(n, m)) steps, where T(n, m) is the running time required to find the minimum (s, t)-cut on a graph with n vertices and m edges.
Goldschmidt et al. (Tue,) studied this question.
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