Perfect matchings extend to Hamilton cycles in hypercubes

Krewerasʹ conjecture [G. Kreweras, Matchings and Hamiltonian cycles on hypercubes, Bull. Inst. Combin. Appl. 16 (1996) 87–91] asserts that any perfect matching of the hypercube Q d , d ⩾ 2 , can be extended to a Hamilton cycle. We prove this conjecture.