Abstract
Häggkvist conjectured in 1976 that every 2-connected k-regular bipartite graph G on at most 6 k vertices is hamiltonian. Chetwynd and Häggkvist have shown that G is hamiltonian if G has at most 4.2 k vertices. The upper bound on | V( G)| was subsequently improved to 5 k − 12 and then 5 k − 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 6 k − 38 vertices is hamiltonian.
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