The Doyen–Wilson theorem for bull designs

A bull is a graph which is obtained by attaching two edges to two vertices of a triangle. A bull-design of order n is an ordered pair ( X , A ) , where X is the vertex set of K n and A is an edge-disjoint decomposition of K n into copies of bulls. In this paper, it is shown that a bull-design of order n can be embedded in a bull-design of order m if and only if m ≥ 3 n / 2 + 1 or m = n . This produces a generalization of the Doyen–Wilson theorem for bull-designs.