Factorizing the complete graph into factors with large star number

The graph G has star number n if any n vertices of G belong to a subgraph which is a star. Let f(n, k) be the smallest number m such that the complete graph on m vertices can be factorized into k factors with star number n. In the present paper we prove that $\text{c}{}_1{}^{\mathrm{n}}\text{k ≤ f(n, k) < c}{}_2{}^{\mathrm{n}}\text{k}$.