On the integral 4-packing of T-cuts Original Research Article

Let G = (V, E) be an undirected graph, w: E → Z+ a weight function and T ⊆ V an even subset of vertices from G. A T-cut is an edge-cut set which divides T into two odd sets. For |T| = 4 Seymour gave a good characterization of the graphs for which there exists a maximum packing of T-cuts that is integral. Based on Seymourʹs characterization we provide a simple O(n3m + n4 log n) algorithm for increasing minimally the weight function on the edge-set of a graph so that the value of the maximum integral packing of T-cuts with respect to the increased weights is equal to the original value of a minimum weight T-join.