The Klein bottle and multicommodity flows


LetG be an eulerian graph embedded on the Klein bottle. Then the maximum number of pairwise edge-disjoint orientation-reversing circuits inG is equal to the minimum number of edges intersecting all orientation-reversing circuits. This generalizes a theorem of Lins for the projective plane. As consequences we derive results on disjoint paths in planar graphs, including theorems of Okamura and of Okamura and Seymour.

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Schrijver, A. The Klein bottle and multicommodity flows. Combinatorica 9, 375–384 (1989).

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AMS subject classification (1980)

  • 05C10
  • 98CXX