Ruskey–Savage matching-extension conjecture

Prove that every matching of the n-dimensional hypercube Q_n, for n ≥ 2, can be extended to a Hamilton cycle.

Background

The Ruskey–Savage conjecture is the paper’s principal longstanding open problem. It asks whether an arbitrary matching in a hypercube can be completed by additional hypercube edges to form a Hamilton cycle. The paper proves this assertion for matchings whose edges span at most five directions, but does not resolve the unrestricted case.