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 . The authors present a polynomial algorithm for k fixed, that runs in steps, where is the running time required to find the minimum -cut on a graph with n vertices and m edges.
