On Gale's feasibility theorem for certain infinite networks (Q1323136)

The authors extend Gale's feasibility theorem to infinite, but locally finite networks. The result is different from the extensions of Fuchssteiner and Lusky or from that of Neumann, either by relaxing hypotheses or by the fact that the obtained flows are functions, not measures. Lemma 2, the central part of the paper, that gives conditions for a feasible flow bounded from below by zero, seems to be new, even in the case of a finite network. As an application of their result the authors prove a generalization of the max-flow min-cut theorem of Ford and Fulkerson.