Index of Talk Titles

Kreweras’ conjecture [1] asserts that any perfect matching of the hypercubeQd, d ≥ 2, can be extended to a Hamiltonian cycle. We proved this conjec-ture in [2] but here we present an idea of a simplified proof. The matchinggraph M(G) of a graph G is a graph whose vertex set consists of all per-fect matchings of G, with two vertices being adjacent whenever the unionof the corresponding perfect matchings is a Hamiltonian cycle. We showthatM(Qd) is bipartite. We proved that the matching graph of completebipartite graph Kn,n, n ≥ 2, is connected and bipartite if and only if n iseven.