|Title:||ON SEYMOUR'S AND LOMONOSOV'S PLANE INTEGRAL TWO COMMODITY FLOW RESULTS
|Authors:||E. Korach and M. Penn
|Abstract:||We consider the maximum integral tWo-Commodity flow problem in augmented planar graphs (i.e., with both source-sink edges added) and provide an o(IVI21ogIVI) algorithm for that problem. Let G =(V, E) be a graph and w : E -t Z+ a weight function. Let T C V be an even subset of the vertices of G. A T-cut is an edge-cutset of the graph which divides T into two odd sets. Lomonosov gave a good characterization of augmented, planar graphs for which the maximum two-commodity flow is integral. We derive Lomonosov's characterization by using results of Seymour on integral packing of T-cuts in the case ITI = 4, and on the correspondence between plane integral multicommodity flow and integral packing of T-cuts.|
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