On the existence of uniformly resolvable decompositions of [formula omitted] and [formula omitted] into paths and kites

Abstract

In this paper, it is shown that, for every v≡0(mod12), 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−42−2x),x=0,…,v−44}. 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(mod12) and s=0.