Hamilton cycles that extend transposition matchings in Cayley graphs of Sn
SIAM Journal on Discrete Mathematics
A Survey of Combinatorial Gray Codes
SIAM Review
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
Hamiltonian Cycles with Prescribed Edges in Hypercubes
SIAM Journal on Discrete Mathematics
Note: Perfect matchings extend to Hamilton cycles in hypercubes
Journal of Combinatorial Theory Series B
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Kreweras' conjecture [G. Kreweras, Matchings and hamiltonian cycles on hypercubes, Bull. Inst. Combin. Appl. 16 (1996) 87-91] asserts that every perfect matching of the hypercube Q"d can be extended to a Hamiltonian cycle of Q"d. We [Jiri Fink, Perfect matchings extend to hamilton cycles in hypercubes, J. Combin. Theory Ser. B, 97 (6) (2007) 1074-1076] proved this conjecture but here we present a simplified proof. The matching graphM(G) of a graph G has a vertex set of all perfect matchings of G, with two vertices being adjacent whenever the union of the corresponding perfect matchings forms a Hamiltonian cycle of G. We show that the matching graph M(K"n","n) of a complete bipartite graph is bipartite if and only if n is even or n=1. We prove that M(K"n","n) is connected for n even and M(K"n","n) has two components for n odd, n=3. We also compute distances between perfect matchings in M(K"n","n).