Uniformly resolvable decompositions of KvKv into K2K2 and K1,3K1,3 graphs

Let KvKv be the complete graph of order vv. A (K2,K1,3)(K2,K1,3)-URD(v;r,s)(v;r,s) is a decomposition of KvKv into a set of subgraphs which can be partitioned into rr parallel classes containing only copies of K2K2 and ss parallel classes containing only copies of K1,3K1,3, such that every point of KvKv  appears exactly once in some subgraphs of each parallel class. S. Küçükçifçi et al. have completely solved the existence of a (K2,K1,3)(K2,K1,3)-URD(v;r,s)(v;r,s) with minimum number of 1-factors and with 14 possible exceptions. In this paper, we shall give some new constructions for (K2,K1,3)(K2,K1,3)-URDs, and completely solve the existence of a (K2,K1,3)(K2,K1,3)-URD(v;r,s)(v;r,s)for any admissible parameters v,rv,r and ss.