Decompositions of lambda-Kv
In a series of 2 papers, Kang, Du and Tian solved the existence problem for G-decomposition of lambda K-n when G is any simple graph with 6 vertices and 7 edges, except when G is the graph T = K-4 boolean OR K-2. Notice that a T-decomposition can be considered to be a Pairwise Balanced Design in which each block of size 4 has been matched to a block of size 2. In this paper we remove this exception for all lambda >= 2. The case when lambda = 1 is also addressed.
pairwise balanced designs graph decompositions