On the existence of uniformly resolvable decompositions of Kv and Kv − I into paths and kites

In this paper, it is shown that, for every v ≡ 0(mod 12), there exists a uniformly resolvable decomposition of Kv-I, the complete undirected graph minus a 1-factor, into r classes containing only copies of 2-stars and s classes containing only copies of kites if and only if (r, s) ∈ {(3x, 1+ v−4 2 −2x), x = 0, . . . , v−4 4 }. It is also shown that a uniformly resolvable decomposition of Kv into r classes containing only copies of 2-stars and s classes containing only copies of kites ∧ exists if and only if v ≡ 9(mod 12) and s = 0.