Abstract
A network is a set of nodes Nı connected by arcs with nonnegative arc capacities bıj which indicates the maximum amount of flow that can pass through the arc from Nı to Nj. Given all bıj, there is a maximum flow from Nı to Nj using all arcs. Under the assumption that bıj = bjı, the present paper generalizes the max-flow min-cut theorem of Ford and Fulkerson to the problem of finding the maximum simultaneous flows of two commodities and gives an algorithm similar to the labelling method for constructing the two flows.
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