On finding the maximum number of disjoint cuts in seymour graphs

Abstract

In the CUT PACKING problem, given an undirected connected graph G, it is required to find the maximum number of pairwise edge disjoint cuts in G. It is an open question if CUT PACKING is NP-hard on general graphs. In this paper we prove that the problem is polynomially solvable on Seymour graphs which include both all bipartite and all series-parallel graphs. We also consider the weighted version of the problem in which each edge of the graph G has a nonnegative weight and the weight of a cut D is equal to the maximum weight of edges in D. We show that the weighted version is NP-hard even on cubic planar graphs.