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

Abstract

Given two disjoint vertex sets S={s} and T={t1,t2,t3} of a connected graph, a one-to-many 3-disjoint path cover joining S and T is a vertex-disjoint path cover {P1,P2,P3} such that each path Pi 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.