Embedding handcuffed designs in D-designs, where D is the triangle with attached edge Original Research Article

Let D be the triangle with attached edge (i.e. D is the graph having vertices {a0,a1,a2,a3} and edges {a0,a1}, {a0,a2}, {a1,a2}, {a0,a3}). Bermond and Schönheim (Discrete Math. 19 (1977) 113) proved that a D-design of order n exists if and only if n≡0 or 1 (mod 8). Let (W,C) be a nontrivial D-design of order n, n⩾8, and let V⊂W, |V|=v