A bicubic graph is a bipartite cubic graph. Tutte conjectured that all 3-connected bicubic graphs are Hamiltonian (the Tutte conjecture), but a number of bicubic nonhamiltonian graphs have subsequently been discovered. The numbers of simple bicubic graphs on n = 2, 4, ... nodes are 0, 0, 1, 1, 2, 5, 13, 38, 149, ... (OEIS A006823), the first few of which are illustrated above. The following table summarizes some named bicubic graphs.
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