Equitable embeddings of steiner triple systems

Abstract

Using an embedding result for pairwise balanced designs, and colourings of small systems, tripling constructions are used to produce equitably coloured Steiner triple systems. It is shown that when the order is v is large enough with respect to the number r of colours, and v ≡ 1, 3 (mod 6), an equitably r -coloured r -chromatic Steiner triple system of order v exists.