Distances and cuts in planar graphs
نویسنده
چکیده
We prove the following theorem. Let G = (V, E) be a planar bipartite graph, embedded in the etrclidean plane. Let 0 and I be two of its faces. Then there exist pairwise edge-disjoint cuts C,, . . . . C, so that for each two vertices u, w with U, w E 0 or V, WE I, the distance from u to w in G is equal to the number of cuts C, separating u and w. This theorem is dual to a theorem of Okamura on plane multicommodity flows, in the same way as a theorem of Karzanov is dual to one of Lomonosov.
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عنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 46 شماره
صفحات -
تاریخ انتشار 1989