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Perfect matchings extend to Hamilton cycles in hypercubes. (English) Zbl 1126.05080
Summary: Kreweras’ conjecture [{\it G. Kreweras}, Bull. Inst. Comb. Appl. 16, 87--91 (1996; Zbl 0855.05089)] asserts that any perfect matching of the hypercube $Q_{d}$, $d\geqslant 2$, can be extended to a Hamilton cycle. We prove this conjecture.

MSC:
05C70Factorization, etc.
05C45Eulerian and Hamiltonian graphs
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References:
[1] Kreweras, G.: Matchings and Hamiltonian cycles on hypercubes. Bull. inst. Combin. appl. 16, 87-91 (1996) · Zbl 0855.05089
[2] Savage, C.: A survey of combinatorial gray codes. SIAM rev. 39, 605-629 (1997) · Zbl 1049.94513
[3] Gros, L.: Théorie du baguenodier. (1872)
[4] Dvořák, T.: Hamiltonian cycles with prescribed edges in hypercubes. SIAM J. Discrete math. 19, 135-144 (2005) · Zbl 1082.05056
[5] D. Dimitrov, R. Škrekovski, T. Dvořák, P. Gregor, Gray Codes Faulting Matchings, manuscript
[6] R. Škrekovski, private communication