Uniform two‐class regular partial Steiner triple systems

A 2‐class regular partial Steiner triple system is a partial Steiner triple system whose points can be partitioned into 2‐classes such that no triple is contained in either class and any two points belonging to the same class are contained in the same number of triples. It is uniform if the two classes have the same size. We provide necessary and sufficient conditions for the existence of uniform 2‐class regular partial Steiner triple systems.