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 nn is an ordered pair (X,A)(X,A), where XX is the vertex set of KnKn and AA is an edge-disjoint decomposition of KnKn into copies of bulls. In this paper, it is shown that a bull-design of order nn can be embedded in a bull-design of order mm if and only if m≥3n/2+1m≥3n/2+1 or m=nm=n. This produces a generalization of the Doyen–Wilson theorem for bull-designs.