An Approximation for a Continuous Max-Flow Problem

We consider an approximation for the continuous max-flow problem stated in [2] by a sequence of max-flow problems in finite networks. The used approximation scheme was introduced by Gomory and Hu in [6, Chapter 12]. But in [6] there is no definition of a continuous flow and therefore also no proof of a convergence of network flows to continuous flows. In this sense this paper solves the central open problem of Chapter 12 in [6].