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One-to-one disjoint path covers in hypercubes with faulty edges

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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 \(Q_n\).

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Acknowledgements

The authors would like to express their gratitude to the anonymous reviewers for their kind suggestions on the original manuscript.

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Authors and Affiliations

  1. School of Sciences, Nanchang University, Nanchang, 330000, Jiangxi, People’s Republic of China

    Fan Wang

  2. Institute for Interdisciplinary Research, Jianghan University, Wuhan, 430056, Hubei, People’s Republic of China

    Weisheng Zhao

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  1. Fan Wang
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  2. Weisheng Zhao
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Correspondence to Fan Wang.

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This work is supported by NSFC (Grant Nos. 11501282 and 11861032).

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Wang, F., Zhao, W. One-to-one disjoint path covers in hypercubes with faulty edges. J Supercomput 75, 5583–5595 (2019). https://doi.org/10.1007/s11227-019-02817-6

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