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A linear time algorithm for finding the maximum number of vertex-disjoint paths between vertices s and t in a planar graph is presented. For general undirected graphs this problem is usually solved by applying flow techniques. These lead to an O(n*) resp. 0(En) algorithm for planar graphs, where k is the maximum number of (s, t)-paths. (In this paper k is… (More)

In this paper we present a linear-time algorithm for the vertex-disjoint Two-Face Paths Problem in planar graphs, i.e., the problem of nding k vertex-disjoint paths between pairs of terminals which lie on two face boundaries. The algorithm is based on the idea of nding rightmost paths with a certain property in planar graphs. Using this method, a… (More)

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