Geodesic
Cubic graphs having only k-cycles in each 2-factor
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 1, pp. 281-296

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We consider the class of 2-connected cubic graphs having only k-cycles in each 2-factor, and obtain the following two results: (i) every 2-connected cubic graph having only 8-cycles in each 2-factor is isomorphic to a unique Hamiltonian graph of order 8; and (ii) a 2-connected cubic planar graph G has only k-cycles in each 2-factor if and only if k=4 and G is the complete graph of order 4.
Keywords: cubic graph, $2$-factor, Hamiltonian cycle, $2$-factor Hamiltonian 
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Matsumoto, Naoki; Noguchi, Kenta; Yashima, Takamasa. Cubic graphs having only k-cycles in each 2-factor. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 1, pp. 281-296. http://geodesic.mathdoc.fr/item/DMGT_2024_44_1_a13/