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Small Matchings Extend to Hamiltonian Cycles in Hypercubes

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Abstract

Ruskey and Savage asked the following question: does every matching of a hypercube \(Q_{n}\) for \(n\ge 2\) extend to a Hamiltonian cycle of \(Q_{n}\)? Fink confirmed that the question is true for every perfect matching, thus solved Kreweras’ conjecture. In this paper we prove that every matching of at most \(3n-10\) edges can be extended to a Hamiltonian cycle of \(Q_{n}\) for \(n\ge 4\).

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Acknowledgments

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

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, Gansu, People’s Republic of China

    Fan Wang & Heping Zhang

  2. Department of Mathematics, Nanchang University, Nanchang, 330000, Jiangxi, People’s Republic of China

    Fan Wang

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  1. Fan Wang
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  2. Heping Zhang
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Correspondence to Heping Zhang.

Additional information

This work is supported by NSFC (grant nos. 11371180 and 61073046).

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Wang, F., Zhang, H. Small Matchings Extend to Hamiltonian Cycles in Hypercubes. Graphs and Combinatorics 32, 363–376 (2016). https://doi.org/10.1007/s00373-015-1533-6

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  • DOI: https://doi.org/10.1007/s00373-015-1533-6

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