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.
@article{bwmeta1.element.doi-10_7151_dmgt_2010,
author = {Fan Wang and Weisheng Zhao},
title = {Matchings Extend to Hamiltonian Cycles in 5-Cube},
journal = {Discussiones Mathematicae Graph Theory},
volume = {38},
year = {2018},
pages = {217-231},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_2010}
}
Fan Wang; Weisheng Zhao. Matchings Extend to Hamiltonian Cycles in 5-Cube. Discussiones Mathematicae Graph Theory, Tome 38 (2018) pp. 217-231. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_2010/