Complete Sets of Disjoint Difference Families and their Applications

Abstract

Dedicated to the memory of Professor Sumiyasu Yamamoto Let G be an abelian group. A collection of (G, k, λ) disjoint difference families, {F0, F1, · · · , Fs−1}, is a complete set of disjoint difference families if ∪0≤i≤s−1∪B∈FiB 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