Single-source three-disjoint path covers in cubes of connected graphs
نویسندگان
چکیده
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.
منابع مشابه
A linear-time algorithm for finding a paired 2-disjoint path cover in the cube of a connected graph
For a connected graph G = (V (G), E(G)) and two disjoint subsets of V (G) A = {α1, . . . , αk} and B = {β1, . . . , βk}, a paired (many-to-many) k-disjoint path cover of G joining A and B is a vertex-disjoint path cover {P1, . . . , Pk} such that Pi is a path from αi to βi for 1 ≤ i ≤ k. In the recent paper [Disjoint Path Covers in Cubes of Connected Graphs, Discrete Mathematics 325 (2014) 65–7...
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ورودعنوان ژورنال:
- Inf. Process. Lett.
دوره 113 شماره
صفحات -
تاریخ انتشار 2013