The spectrum for a class of graph designs - Wang, Lidong (Utilitas Mathematica, 2012)
Let K υ be the complete graph with v vertices. A G-design of K υ, denoted by G-GD(υ), is a partition of K υ into subgraphs so that each subgraph is isomorphic to G. In this paper, we will completely solve the case for G = K 4∪K 2 and prove that the necessary conditions υ ≡ 0,1 (mod 7) and υ ≥ 7 for the existence of G-GD(υ) are also sufficient except for υ ∈ 7,8.