Packings of cuts realizing distances between certain vertices in a planar graph

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Abstract

Recently A. Schrijver proved the following theorem. Suppose that G=(V, E) is a connected planar graph embedded in the euclidean plane, that O and I are two of its faces, and that the edges e∈E have nonnegative integer-valued lengths l(e) such that the length of each circuit in G is even. Then there exist cuts B1,..., Bk in G weighted by nonnegative integer-valued weights λ1,...,λk so that: (i) for each eε{lunate}E, the sum of the weights of the cuts containing e does not exceed l(e), and (ii) for each two vertices s and t both in the boundary of O or in the boundary of I, the sum of the weights of the cuts 'separatingh' s and t is equal to the distance between s and t. We given another proof of this theorem which provides a strongly polynomial-time algorithm for finding such cuts and weights. © 1990.

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APA

Karzanov, A. V. (1990). Packings of cuts realizing distances between certain vertices in a planar graph. Discrete Mathematics, 85(1), 73–87. https://doi.org/10.1016/0012-365X(90)90164-D

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