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

Let D be the triangle with attached edge (i.e. D is the graph having vertices {a(0),a(1),a(2),a(3)} and edges {a(0),a(1)}, {a(0),a(2)}, {a(1),a(2)], {a(0),a(3)}). Bermond and Schonheim (Discrete Math. 19 (1977) 113) proved that a D-design of order n exists if and only if n equivalent to 0 or 1 (mod 8). Let (W,C) be a nontrivial D-design of order n, n greater than or equal to 8, and let V subset of W, \V\ = u < n. We say that a handcuffed design (V,P) of order v and block size s (P. Hell, A. Rosa, Discrete Math. 2 (1972) 229 252) is embedded in (W,C) if there is an injective mapping f : P --> C such that B is a subgraph of f (B) for every B is an element of P. For each n equivalent to 0 or 1 (mod 8), we determine the spectrum of all the integers v such that there is a nontrivial handcuffed design of order v and block size s embedded in a D-design of order n. (C) 2002 Elsevier Science B.V. All rights reserved.