Abstract
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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References
A. Lehman, On the width-length inequality,Mathematical Programming,17 (1979) 403–417.
S. Lins, A minimax theorem on circuits in projective graphs,Journal of Combinatorial Theory (B),30 (1981) 253–262.
H. Okamura, Multicommodity flows in graphs,Discrete Applied Mathematics.6 (1983) 55–62.
H. Okamura andP. D. Seymour, Multicommodity flows in planar graphs,Journal of Combinatorial Theory (B),31 (1981) 75–81.
A. Schrijver, Distances and cuts in planar graphs,Journal of Combinatorial Theory (B),46 (1989), 46–57.
P. D. Seymour, The matroids with the max-flow min-cut property,Journal of Combinatorial Theory (B),23 (1977) 189–222.