Geodesic
Decomposing 10-Regular Graphs into Paths of Length 5
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 4, pp. 1089-1097

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Let G be a 10-regular graph which does not contain any 4-cycles. In this paper, we prove that G can be decomposed into paths of length 5, such that every vertex is a terminal of exactly two paths.
Keywords: 10-regular graph, decomposition, path 
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Xie, Mengmeng; Zhou, Chuixiang. Decomposing 10-Regular Graphs into Paths of Length 5. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 4, pp. 1089-1097. http://geodesic.mathdoc.fr/item/DMGT_2022_42_4_a4/