Geodesic
Hamiltonicity in multitriangular graphs
Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 1, pp. 77-88

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The family of 5-valent polyhedral graphs whose faces are all triangles or 3s-gons, s ≥ 9, is shown to contain non-hamiltonian graphs and to have a shortness exponent smaller than one.
Keywords: polyhedral graphs, longest cycles, shortness exponent 
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Owens, Peter; Walther, Hansjoachim. Hamiltonicity in multitriangular graphs. Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 1, pp. 77-88. http://geodesic.mathdoc.fr/item/DMGT_1995_15_1_a8/