Geodesic
Matchings Extend to Hamiltonian Cycles in 5-Cube
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 217-231

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Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Qn for n ∈ 2, 3, 4. In this paper, we prove that every matching in Q5 can be extended to a Hamiltonian cycle of Q5.
Keywords: hypercube, Hamiltonian cycle, matching 
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     author = {Wang, Fan and Zhao, Weisheng},
     title = {Matchings {Extend} to {Hamiltonian} {Cycles} in {5-Cube}},
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Wang, Fan; Zhao, Weisheng. Matchings Extend to Hamiltonian Cycles in 5-Cube. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 1, pp. 217-231. http://geodesic.mathdoc.fr/item/DMGT_2018_38_1_a17/