Decomposition of lambda K-nu into kites and 4-cycles

Given a collection of graphs H, an H decomposition of lambda K-v is a decomposition of the edges of lambda K-v into isomorphic copies of graphs in H. A kite is a triangle with a tail consisting of a single edge. In this paper we investigate the decomposition problem when H is the set containing a kite and a 4-cycle, that is; this paper gives a complete solution to the problem of decomposing lambda K-v into r kites and s 4-cycles for every admissible values of v, lambda, r and s.