Geodesic
On Decomposing Regular Graphs Into Isomorphic Double-Stars
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 73-79

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A double-star is a tree with exactly two vertices of degree greater than 1. If T is a double-star where the two vertices of degree greater than one have degrees k_1+1 and k_2+1, then T is denoted by S_k_1,k_2. In this note, we show that every double-star with n edges decomposes every 2n-regular graph. We also show that the double-star S_k,k−1 decomposes every 2k-regular graph that contains a perfect matching.
Keywords: graph decomposition, double-stars 
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El-Zanati, Saad I.; Ermete, Marie; Hasty, James; Plantholt, Michael J.; Tipnis, Shailesh. On Decomposing Regular Graphs Into Isomorphic Double-Stars. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 1, pp. 73-79. http://geodesic.mathdoc.fr/item/DMGT_2015_35_1_a5/