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Computing Vertex-Disjoint Paths using MAOs (1609.06522v1)
Published 21 Sep 2016 in cs.DM and cs.DS
Abstract: Let G be a graph with minimum degree $\delta$. It is well-known that maximal adjacency orderings (MAOs) compute a vertex set S such that every pair of S is connected by at least $\delta$ internally vertex-disjoint paths in G. We present an algorithm that, given any pair of S, computes these $\delta$ paths in linear time O(n+m). This improves the previously best solutions for these special vertex pairs, which were flow-based. Our algorithm simplifies a proof about pendant pairs of Mader and makes a purely existential proof of Nagamochi algorithmic.