Similarly, Barnette conjectured that all cubic, 3-connected, planar graphs with a face size of at most 6 are Hamiltonian.
Aldred et al. (2000) have verified this conjecture for all graphs with fewer
than 177 vertices.
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D.; Manvel, B.; and McKay, B. "Hamiltonian Cycles in Cubic 3-Connected Bipartite
Planar Graphs." J. Combin. Th. Ser. B38, 279-297, 1985.Owens,
P. J. "Bipartite Cubic Graphs and a Shortness Exponent." Disc.
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