A node-capacitated Okamura–Seymour theorem

  title={A node-capacitated Okamura–Seymour theorem},
  author={James R. Lee and M. Mendel and Mohammadreza Moharrami},
  journal={Mathematical Programming},
The classical Okamura–Seymour theorem states that for an edge-capacitated, multi-commodity flow instance in which all terminals lie on a single face of a planar graph, there exists a feasible concurrent flow if and only if the cut conditions are satisfied. Simple examples show that a similar theorem is impossible in the node-capacitated setting. Nevertheless, we prove that an approximate flow/cut theorem does hold: For some universal $$\varepsilon > 0$$ε>0, if the node cut conditions are… Expand
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