Hamilton cycles in 2-connected regular bipartite graphs

Abstract

Häggkvist conjectured in 1976 that every 2-connected k-regular bipartite graph G on at most 6k vertices is hamiltonian. Chetwynd and Häggkvist have shown that G is hamiltonian if G has at most 4.2k vertices. The upper bound on |V(G)| was subsequently improved to 5k - 12 and then 5k - 8 by Ash and Min Aung, respectively. We shall essentially verify Häggkvist’s conjecture by showing that every 2-connected k-regular bipartite graph on at most 6k - 38 vertices is hamiltonian. © 1994 by Academic Press, Inc.