Bicubic Graph

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 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.

See also

Bipartite Graph, Cubic Graph, Tutte Conjecture

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Sloane, N. J. A. Sequences A006823/M1450 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Bicubic Graph

Cite this as:

Weisstein, Eric W. "Bicubic Graph." From MathWorld--A Wolfram Web Resource.

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