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.

bipartite graph | cubic graph | Tutte conjecture