On uniform partial group divisible designs with block size three. - Zhang, Luchan (2012)
Group divisible designs (GDDs) play a crucial role in the development of combinatorial design theory. We know that GDDs require that each pair of points in distinct groups occurs in exactly $λ$ blocks. If this requirement is relaxed, i.e., each pair of points in distinct groups occurs in at most $λ$ blocks, we can obtain a new of class of designs called partial group divisible designs (PGDDs). In this thesis, we study the uniform PGDDs with block size three. In particular, we determine all possible sizes of uniform PGDDs with block size three and no repeated blocks, where each pair of points in distinct groups occurs either once or twice. The investigation into the sizes of PGDDs with the aforementioned properties are not only practical in design theory, but also applicable to some optimization problems in data replication schemes in computer science.