A bicubic graph is a bipartite cubic graph.
Tutte (1971) 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 
, 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.
