Single-source three-disjoint path covers in cubes of connected graphs

초록

A k-disjoint path cover (k-DPC for short) of a graph is a set of k internally vertex-disjoint paths from given sources to sinks that collectively cover every vertex in the graph. In this paper, we establish a necessary and sufficient condition for the cube of a connected graph to have a 3-DPC joining a single source to three sinks. We also show that the cube of a connected graph always has a 3-DPC joining arbitrary two vertices. (C) 2013 Elsevier B.V. All rights reserved.

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