Geodesic
A conjecture on the prevalence of cubic bridge graphs
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 1, pp. 175-179

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Almost all d-regular graphs are Hamiltonian, for d ≥ 3 [8]. In this note we conjecture that in a similar, yet somewhat different, sense almost all cubic non-Hamiltonian graphs are bridge graphs, and present supporting empirical results for this prevalence of the latter among all connected cubic non-Hamiltonian graphs.
Keywords: Hamiltonian graph, non-Hamiltonian graph, cubic bridge graph 
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Filar, Jerzy; Haythorpe, Michael; Nguyen, Giang. A conjecture on the prevalence of cubic bridge graphs. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 1, pp. 175-179. http://geodesic.mathdoc.fr/item/DMGT_2010_30_1_a13/