Perfect matchings extend to Hamilton cycles in hypercubes

Kreweras' 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.

[1]  Carla Savage,et al.  A Survey of Combinatorial Gray Codes , 1997, SIAM Rev..

[2]  Tomás Dvorák,et al.  Hamiltonian Cycles with Prescribed Edges in Hypercubes , 2005, SIAM J. Discret. Math..