On the existence of uniformly resolvable decompositions of and into paths and kites

In this paper, it is shown that, for every v ≡ 0 ( mod 12 ) , there exists a uniformly resolvable decomposition of K v - 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 ) ∈ { ( 3 x , 1 + v − 4 2 − 2 x ) , x = 0 , … , v − 4 4 } . It is also shown that a uniformly resolvable decomposition of K v 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 .