Complete sets of disjoint difference families and their applications

Abstract

Let G be an abelian group. A collection of ( G, k, λ) disjoint difference families, { F 0, F 1,…, F s−1} , is a complete set of disjoint difference families if ⋃ 0⩽i⩽s−1⋃ B∈ F i B form a partition of G−{0}. In this paper, several construction methods are provided for complete sets of disjoint difference families. Applications to one-factorizations of complete graphs and to cyclically resolvable cyclic Steiner triple systems are also described.