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.
See also
Bipartite Graph, Cubic Graph, Tutte Conjecture
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References
Sloane, N. J. A. Sequences A006823/M1450 in "The On-Line Encyclopedia of Integer Sequences."
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Cite this as:
Weisstein, Eric W. "Bicubic Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BicubicGraph.html