One-To-Many Disjoint Path Covers In A Graph With Faulty Elements
COCOON(2004)
摘要
In a graph G, k disjoint paths joining a single source and k distinct sinks that cover all the vertices in the graph are called a one-to-many k-disjoint path cover of G. We consider a k-disjoint path cover in a graph with faulty vertices and/or edges obtained by merging two graphs H-0 and H-1, \V(H-0)\ = \V(H-1)\ = n, with n pairwise nonadjacent edges joining vertices in Ho and vertices in H-1. We present a sufficient condition for such a graph to have a k-disjoint path cover and give the construction scheme. Applying our main result to interconnection graphs, we observe that when there are f or less faulty elements, all of recursive circulant G(2(m), 4), twisted cube TQ(m), and crossed cube CQ(m) of degree M have k-disjoint path covers for any f greater than or equal to 0 and k greater than or equal to 2 such that f + k less than or equal to m - 1.
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