On the planar integer two-flow problem


We consider the two-commodity flow problem and give a good characterization of the optimum flow if the augmented network (with both source-sink edges added) is planar. We show that max flow ≧ min cut −1, and describe the structure of those networks for which equality holds.

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Lomonosov, M.V. On the planar integer two-flow problem. Combinatorica 3, 207–218 (1983). https://doi.org/10.1007/BF02579295

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AMS subject classification (1980)

  • 90 B 10
  • 90 C 10