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Published in:
20-03-2019
One-to-one disjoint path covers in hypercubes with faulty edges
Published in: The Journal of Supercomputing | Issue 8/2019
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Abstract
A one-to-one k-disjoint path cover \(\{P_1,P_2,\ldots ,P_k\}\) of a graph G is a collection of k internally vertex disjoint paths joining source with sink that cover all vertices of G. In this paper, we investigate the problem of one-to-one disjoint path cover in hypercubes with faulty edges and obtain the following results: Let u, v ∈ V(Qn) be such that \(p(u)\ne p(v)\) and \(1\le k\le n\). Then there exists a one-to-one k-disjoint path cover \(\{P_1,P_2,\ldots ,P_k\}\) joining vertices u and v in \(Q_n\). Moreover, when \(1\le k\le n-2\), the result still holds even if removing \(n-2-k\) edges from \(Q_n\).