Matchings extend to Hamiltonian cycles in 5-cube

Ruskey and Savage asked the following question: Does every matching in a hypercube Q n for n 2 extend to a Hamiltonian cycle of Q n ? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Q n , thus solved Kreweras' conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Q n for n {2, 3, 4}. In this paper, we prove that every matching in Q 5 can be extended to a Hamiltonian cycle of Q 5 .