A linear-time algorithm for finding a one-to-many 3-disjoint path cover in the cube of a connected graph

초록

Given two disjoint vertex sets S = {s} and T = {t(1), t(2), t(3)} of a connected graph, a one-to many 3-disjoint path cover joining s and T is a vertex-disjoint path cover {P-1, P-2, P-3} such that each path P1 joins s and ti. In this paper, we present an efficient algorithm that builds, if exists, a one-to-many 3-disjoint path cover in the cube of a connected graph G joining the two terminal sets. Interestingly enough, we show that a carefully selected spanning tree or spanning unicyclic subgraph of G is all we need to find the desired disjoint path cover in time linear to the size of G. (C) 2018 Elsevier B.V. All rights reserved.

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