| |
[摘要]：A many-to-many k-disjoint path cover (k-DPC) of a graph G is a set of k disjoint paths joining k sources and k sinks in which each vertex of G is covered by a path. It is called a paired many-to-many disjoint path cover when each source should be joined to a specific sink, and it is called an unpaired many-to-many disjoint path cover when each source can be joined to an arbitrary sink. In this paper, we discuss about paired and unpaired many-to-many disjoint path covers including their relationships, application to strong Hamiltonicity, and necessary conditions. And then, we give a construction scheme for paired many-to-many disjoint path covers in the graph H-0 circle plus H-1 obtained from connecting two graphs H-0 and H-1 with |V(H-0)| = |V(H-1)| by |V(H-0)| pairwise nonadjacent edges joining vertices in H-0 and vertices in H-1, where H-0=G(0) circle plus G(1) and H-1=G(2) circle plus G(3) for some graphs G(j). Using the construction, we show that every m-dimensional restricted HL-graph and recursive circulant G(2(m); 4) with f or less faulty elements have a paired k-DPC for any f and k >= 2 with f + 2k <= m. |
|
