Geodesic
Decomposing the Complete Graph Into Hamiltonian Paths (Cycles) and 3-Stars
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 3, pp. 823-839

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Let H be a graph. A decomposition of H is a set of edge-disjoint subgraphs of H whose union is H. A Hamiltonian path (respectively, cycle) of H is a path (respectively, cycle) that contains every vertex of H exactly once. A k-star, denoted by Sk, is a star with k edges. In this paper, we give necessary and sufficient conditions for decomposing the complete graph into α copies of Hamiltonian path (cycle) and β copies of S3.
Keywords: decomposition, complete graph, Hamiltonian path, Hamiltonian cycle, star 
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Lee, Hung-Chih; Chen, Zhen-Chun. Decomposing the Complete Graph Into Hamiltonian Paths (Cycles) and 3-Stars. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 3, pp. 823-839. http://geodesic.mathdoc.fr/item/DMGT_2020_40_3_a8/