Geodesic
On Double-Star Decomposition of Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 835-840

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A tree containing exactly two non-pendant vertices is called a double-star. A double-star with degree sequence (k_1 + 1, k_2 + 1, 1, . . ., 1) is denoted by S_k_1,k_2. We study the edge-decomposition of graphs into double-stars. It was proved that every double-star of size k decomposes every 2k-regular graph. In this paper, we extend this result by showing that every graph in which every vertex has degree 2k + 1 or 2k + 2 and containing a 2-factor is decomposed into S_k_1,k_2 and S_k_1−1,k_2, for all positive integers k_1 and k_2 such that k_1 + k_2 = k.
Keywords: graph decomposition, double-stars, bipartite graph 
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Akbari, Saieed; Haghi, Shahab; Maimani, Hamidreza; Seify, Abbas. On Double-Star Decomposition of Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 835-840. http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a23/