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/

[1] E. J. Grinberg, Planehomogeneous graphs of degree three without Hamiltonian circuits, Latvian Math. Yearbook 4 (1968) 51-58 (in Russian).

[2] B. Grünbaum and H. Walther, Shortness exponents of families of graphs, J. Combin. Theory (A) 14 (1973) 364-385, doi: 10.1016/0097-3165(73)90012-5.

[3] J. Harant, Über den Shortness Exponent regulärer Polyedergraphen mit genau zwei Typen von Elementarflächen, Thesis A, Ilmenau Institute of Technology (1982).

[4] D. A. Holton and B. D. McKay, The smallest non-hamiltonian 3-connected cubic planar graphs have 38 vertices, J. Combin. Theory (B) 45 (1988) 305-319, with correction, J. Combin. Theory (B) 47 (1989) 248.

[5] P. J. Owens, Non-hamiltonian simple 3-polytopes whose faces are all 5-gons or 7-gons, Discrete Math. 33 (1981) 107-109.

[6] P. J. Owens, Regular planar graphs with faces of only two types and shortness parameters, J. Graph Theory 8 (1984) 253-275, doi: 10.1002/jgt.3190080207.

[7] P. J. Owens, Simple 3-polytopal graphs with edges of only two types and shortness coefficients, Discrete Math. 59 (1986) 107-114, doi: 10.1016/0012-365X(86)90074-9.

[8] P. J. Owens, Shortness exponents, simple polyhedral graphs and large bridges, unpublished.

[9] M. Tkáč, Shortness coefficients of simple 3-polytopal graphs with edges of only two types, Discrete Math. 103 (1992) 103-110, doi: 10.1016/0012-365X(92)90045-H.

[10] M. Tkáč, Simple 3-polytopal graphs with edges of only two types and shortness coefficients, Math. Slovaca 42 (1992) 147-152.

[11] M. Tkáč, On shortness coefficients of simple 3-polytopal graphs with edges of only one type of face besides triangles, Discrete Math. 128 (1994) 407-413, doi: 10.1016/0012-365X(94)90133-3.

[12] W. T. Tutte, On Hamiltonian circuits, J. London Math. Soc. 21 (1946) 98-101, doi: 10.1112/jlms/s1-21.2.98.

[13] H. Walther, Über das Problem der Existenz von Hamiltonkreisen in planaren regulären Graphen, Math. Nachr. 39 (1969) 277-296, doi: 10.1002/mana.19690390407.

[14] H. Walther, Note on the problems of J.Zaks concerning Hamiltonian 3-polytopes, Discrete Math. 33 (1981) 107-109, doi: 10.1016/0012-365X(81)90265-X.

[15] H. Walther, A non-hamiltonian five-regular multitriangular polyhedral graph (to appear).

[16] J. Zaks, Non-Hamiltonian non-Grinbergian graphs, Discrete Math. 17 (1977) 317-321, doi: 10.1016/0012-365X(77)90165-0.

[17] J. Zaks, Non-Hamiltonian simple 3-polytopes having just two types of faces, Discrete Math. 29 (1980) 87-101, doi: 10.1016/0012-365X(90)90289-T.

[18] J. Zaks, Non-hamiltonian simple planar graphs, in: Annals of Discrete Math. 12 (North - Holland, 1982) 255-263.