There are (at least) two graphs associated with Horton, illustrated above. The first is a graph on 96 nodes providing a counterexample to the Tutte
conjecture that every 3-regular 3-connected bipartite graph is Hamiltonian
(left figure above). The second is a smaller counterexample on 92 nodes (right figure
above). (A number of even smaller counterexamples have subsequently been found.)
Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, pp. 61 and 242, 1976.Ellingham,
M. N. "Non-Hamiltonian 3-Connected Cubic Partite Graphs." Research
Report No. 28, Dept. of Math., Univ. Melbourne, Melbourne, 1981.Ellingham,
M. N. "Constructing Certain Cubic Graphs." In Combinatorial Mathematics,
IX: Proceedings of the Ninth Australian Conference held at the University of Queensland,
Brisbane, August 24-28, 1981 (Ed. E. J. Billington, S. Oates-Williams,
and A. P. Street). Berlin: Springer-Verlag, pp. 252-274, 1982.Ellingham,
M. N. and Horton, J. D. "Non-Hamiltonian 3-Connected Cubic Bipartite
Graphs." J. Combin. Th. Ser. B34, 350-353, 1983.Horton,
J. D. "On Two-Factors of Bipartite Regular Graphs." Disc. Math.41,
35-41, 1982.Owens, P. J. "Bipartite Cubic Graphs and a Shortness
Exponent." Disc. Math.44, 327-330, 1983.
