The spectrum of Meta(K4 - e > K3 + e, λ) with any λ1 - Chang, Yanxun,; Lo Faro, Giovanni,; Tripodi, Antoinette, (Utilitas Mathematica, 2007)
Let (X, Β) be a (λKv, G1)-design and G2 a subgraph of G1. Define sets Β(G2) and D(G2\G2) as follows: for each block B ε Β, partition B into copies of G2and G2 \ G 2 and place the copy of G2 in Β(G2) and the edges belonging to the copy of G2\ G2 in D(G2 \ G 2). If the edges belonging to D(G1\ G2) can be assembled into a collection D(G2) of copies of G2, then (X, Β(G2) ∪ D(G2)) is a (λKv, G2)-design, called a metamorphosis of the (λKv, G1)design (X, Β). For brevity we denote such (λK v, G1)-design (X, Β) with a metamorphosis of (λKv,G2)-design (λKv, (G 2) ∪ D(G2)) by (λKv, G1 > G2)-design. Let Meta(G1 > G2, λ) denote the set of all integers v such that there exists a (λK v, G1 > G2)-design. In this paper we completely determine the set M eta(K4 - e > K3 + e, λ) for any λ.