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

Authors:
Jung-Heum Park;Insung Ihm
Affiliations:
School of Computer Science and Information Engineering, The Catholic University of Korea, Bucheon, Republic of Korea;Department of Computer Science and Engineering, Sogang University, Seoul, Republic of Korea
Venue:
Information Processing Letters
Year:
2013

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Abstract

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.