Geodesic
On the Decompositions of Complete Graphs into Cycles and Stars on the Same Number of Edges
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 1, pp. 113-125

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Let C_m and S_m denote a cycle and a star on m edges, respectively. We investigate the decomposition of the complete graphs, K_n, into cycles and stars on the same number of edges. We give an algorithm that determines values of n, for a given value of m, where K_n is C_m, S_m-decomposable. We show that the obvious necessary condition is sufficient for such decompositions to exist for different values of m.
Keywords: cycles, stars, graph-decompositions 
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     title = {On the {Decompositions} of {Complete} {Graphs} into {Cycles} and {Stars} on the {Same} {Number} of {Edges}},
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Abueida, Atif A.; Lian, Chester. On the Decompositions of Complete Graphs into Cycles and Stars on the Same Number of Edges. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 1, pp. 113-125. http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a9/