| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 427481 | Information Processing Letters | 2013 | 6 Pages |
•To establish the exact condition for the cube of a connected graph to have a 3-DPC joining a single source to three sinks (Theorem 1).•To show that the cube of a connected graph always has a 3-DPC joining arbitrary two vertices (Theorem 2).•To provide constructive proofs for the above two problems so that the respective 3-DPC finding algorithms may easily be constructed.
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.
