Generating partitions of a graph into a fixed number of minimum weight cuts

In this paper, we present an algorithm for the generation of all partitions of a graph G with positive edge weights into k mincuts. The algorithm is an enumeration procedure based on the cactus representation of the mincuts of G. We report computational results demonstrating the efficiency of the algorithm in practice and describe in more detail a specific application for generating cuts in branch-and-cut algorithms for the traveling salesman problem.