The Georges graph, also called the Georges-Kel'mans graph, is the 50-node graph illustrated above that is the smallest 3-connected bicubic
nonhamiltonian graph. It was independently discovered by Georges (1989) and Kelmans
(1988) as the smallest known such example. It was subsequently proved to be the smallest
possible by Brinkmann et al. (2022).
Bondy, J. A. and Murty, U. S. R. Graph Theory. Berlin: Springer-Verlag, pp. 487-488, 2008.Brinkmann,
G.; Goedgebeur, J.; and McKay, B. D. "the Minimality of the Georges-Kelmans
Graph." Math. Comput.91, 1483-1500, 2022.Georges,
J. P. "Non-Hamiltonian Bicubic Graphs." J. Combin. Th. B46,
121-124, 1989.Grünbaum, B. "3-Connected Configurations with No Hamiltonian Circuit."
Bull. Inst. Combin. Appl.46, 15-26, 2006.Grünbaum,
B. Configurations
of Points and Lines. Providence, RI: Amer. Math. Soc., p. 311, 2009.Kel'mans,
A. K. "Cubic Bipartite Cyclically-Connected Graphs With No Hamiltonian
Cycles." Uspekhi Mat. Nauk43, 181-182, 1988. English transl.
in Russian Math. Surveys43, 205-206, 1988.
with No Hamiltonian Circuit."
Bull. Inst. Combin. Appl. 46, 15-26, 2006.Grünbaum,
B.