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Ellingham-Horton Graphs

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Ellingham-HortonGraphs

There are (at least) two graphs associated with Ellingham and Horton. These graphs on 54 and 78 nodes respectively, illustrated above, are examples of 3-connected bicubic nonhamiltonian graphs, and therefore provide counterexamples to the Tutte conjecture.

See also

Bicubic Nonhamiltonian Graph, Horton Graphs, Tutte Conjecture

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References

Ellingham, M. N. "Non-Hamiltonian 3-Connected Cubic Partite Graphs." Research Report No. 28, Dept. of Math., Univ. Melbourne, Melbourne, 1981.Ellingham, M. N. Cycles in 3-Connected Cubics Graphs. M.Sc. thesis. Melbourne, Australia: University of Melbourne, June 1982a.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, 1982b.Ellingham, M. N. and Horton, J. D. "Non-Hamiltonian 3-Connected Cubic Bipartite Graphs." J. Combin. Th. Ser. B 34, 350-353, 1983.

Cite this as:

Weisstein, Eric W. "Ellingham-Horton Graphs." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Ellingham-HortonGraphs.html

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