On Two Commodity Network Flows

The paper considers the problem of two-commodity network flows and generalizes a result of Hu on integral flows in networks with integral capacities. The main result of the paper is a max-flow min-cut theorem for two commodity networks. The method of proof involves a particular type of separation process. This leads to an algorithm for finding the maximal flows. Several counterexamples to certain possible generalizations are given at the end of the paper.