On the decomposition of a graph into stars

It is known that whenever υ(υ−1) ≡ 0 (mod 2m) and υ⩾2m, the complete graph Kυ can be decomposed into edge disjoint, m-stars [1,2]. In this paper we prove that Kυ can be decomposed into any given sequence of stars Sm1, Sm2,…, Smk if ∑mi=(2υ) and mi⩽1/2υ. Further we generalize this result to the decomposition of not necessarily complete graphs. For example: a graph G = (V, E) can be decomposed into Sm1, Sm2,…, Smk if ∑ mi = ¦E¦ and the degree of every vertex of G is at least 1/2¦V¦ + m−1 where m = maxmi