Subcubic trades in Steiner triple systems

Abstract

We consider the problem of classifying trades in Steiner triple systems such that each block of the trade contains one of three fixed elements. We show that the fundamental building blocks for such trades are 3-regular graphs that are 1-factorisable. In the process we also generate all possible 2- and 3-way simultaneous edge colourings of graphs with maximum degree 3 using at most 3 colours, where multiple edges but not loops are allowed. Moreover, we generate all possible Latin trades within three rows.