The spectrum of Meta(K4 - e > K3 + e, λ) with any λ1

摘要

Let (X, B) be a (λKv, G1)-design and G2 a subgraph of G1, Define sets B(G2) and D(G1 G2) as follows: for each block B ∈ B, partition B into copies of G2 and G1 G2 and place the copy of G2 in B(G2) and the edges belonging to the copy of G1 G2 in D(G1G2). If the edges belonging to D(G1G2) can be assembled into a collection D(G2) of copies of G2, then (X, B(G2)WD(G2)) is a (λKv, G2)-design, called a metamorphosis of the (λKV, G1)-design (X, B). For brevity we denote such (λKv, G1)-design (X, B) with a metamorphosis of (λKv,G2)-design (X,B(G2) U D(G2)) by (λKv,G1 > G2)-design. Let Meta(G1 > G2,X) denote the set of all integers v such that there exists a (λKv, G1 > G2)-design. In this paper we completely determine the set Me-ta(K4 - e > K3 + e, λ) for any λ.