Good characterization for path packing in a subclass of Karzanov networks

The path packing problem is stated finding the maximum number of edge-disjoint paths between predefined pairs of nodes in an undirected multigraph. Such a multigraph together with predefined node pairs is often called a network. While in general the path packing problem is NP-hard, there exists a class of networks for which the hope of better solution for the path packing problem exists. In this paper we prove a combinatorial max-min theorem (also called a good characterization) for a wide class of such networks, thus showing that the path packing problem for this class of networks is in co-NP.