Matching graphs of Hypercubes and Complete Bipartite Graphs

Kreweras’ conjecture [9] asserts that every perfect matching of the hypercube Qd can be extended to a Hamiltonian cycle of Qd. We [5] proved this conjecture but here we present a simplified proof. The matching graph M(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(Kn,n) of a complete

• Type: Journal
• Year: 2007
• Where: ENDM
• Authors: Jirí Fink
• Keywords: Conjecture, ENDM 2007, Hamiltonian Cycle, Perfect Matchings