Existence of (K4-e)-GDDs of type 2n

Suppose Kv is the complete undirected graph with v vertices. Let K4 − e be the graph obtained from K4 by removing one edge. A (K4 − e) group divisible design (briefly (K4 − e)-GDD) of type h is a triple (X,G,B), where G is a partition of X into groups each of size h, B is an edge-disjoint decomposition of the edge set of Kh,h,...,h, the multipartite complete undirected graph with G as the partition of the vertex set X, into copies of K4 − e. It is proved in this paper that there exists a (K4 − e)-GDD of type 2 if and only if n ≡ 0, 1 (mod 5) and n ≥ 5. Consequently, K2n−F has a (K4 − e)-decomposition if and only if n ≡ 0, 1 (mod 5) and n ≥ 5, where F is a one-factor of K2n.