Perfect matchings extend to two or more hamiltonian cycles in hypercubes

Abstract

Kreweras conjectured that every perfect matching of a hypercube Qn for n≥2 can be extended to a hamiltonian cycle of Qn. Fink confirmed the conjecture to be true. It is more general to ask whether every perfect matching of Qn for n≥2 can be extended to two or more hamiltonian cycles of Qn. In this paper, we prove that every perfect matching of Qn for n≥4 can be extended to at least 22n−4 different hamiltonian cycles of Qn.