TY - JOUR
AU - Seymour, P. D.
AB - Let T be an even subset of the vertices of a graph G. A T‐cut is an edge‐cutset of the graph which divides T into two odd sets. We prove that if G is bipartite, then the maximum number of disjoint T‐cuts is equal to the minimum cardinality of a set of edges which meets every T‐cut. (A weaker form of this was proved by Edmonds and Johnson.) We deduce a solution to the real‐valued multi‐commodity flow problem for a class of planar graphs; and we also solve the integral 2‐commodity flow problem for the same class of graphs, by a further analysis of the T‐cut problem when|T| = 4.
TI - On Odd Cuts and Plane Multicommodity Flows
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s3-42.1.178
DA - 1981-01-01
UR - https://www.deepdyve.com/lp/wiley/on-odd-cuts-and-plane-multicommodity-flows-SDkTFPiyHO
SP - 178
EP - 192
VL - s3-42
IS - 1
DP - DeepDyve
ER -