Characterizations of Max-Balanced Flows

Rothblum, U.G., H. Schneider and M.H. Schneider, Characterizations of max-balanced flows, Discrete Applied Mathematics 39 (1992) 241-26!. Let G=( V, A) be a graph with vertex set V and arc set A. Aflow for G is an arbitrary real-valued function defined on the arcs A. A flow f is called max-balanced if for every cut W, 0f WC V, the maximum flow over arcs leaving W equals the maximum flow over arcs entering W. We describe ten characterizations of max-balanced flows using properties of graph contractions, maximum cycle means, flow maxima, level sets of flows, cycle covers, and minimality with respect to order structure in the set of flows derived from a given flow by reweighting. We also give a linear programming based proof for an existence result of Schneider and Schneider. Correspondence to: Professor M.H. Schneider, Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD 21218, USA. * Research supported in part by Israel-United States BSF grant 87-00194. ** Research supported in part by NSF grants DMS-8521521 and ECS 87-18971, and BSF granl 87-00194. *** Research supported in part by NSF grant ECS 87-18971. 0166-218X/92/$05.00