Tutte (1971/72) conjectured that there are no 3-connected nonhamiltonian bicubic graphs. However, a counterexample was found by J. D. Horton in 1976, and several smaller counterexamples are now known. Known small counterexamples are summarized in the following table and illustrated above.

bicubic graph | bicubic nonhamiltonian graph | cubic graph | Ellingham-Horton graphs | Georges graph | Horton graphs | nonhamiltonian graph | Tait's Hamiltonian graph conjecture