The metamorphosis of block designs with block size four into (K4 / e)-designs

Denote K4 / e (= the complete undirected graph K4 with one edge removed) by diagonal inside box sign. A diagonal inside box sign -design of order n is a pair (X, K), where K is a collection of edge disjoint copies of diagonal inside box sign which partitions the edge set of Kn with vertex set X. Let (X, B) be a block design with block size 4. If we remove one edge from each block in B, we obtain a partial diagonal inside box sign -design. If …