Class-Uniformly Resolvable Group Divisible Structures II: Frames.

Abstract

We consider Class-Uniformly Resolvable frames (CURFs), which are group divisible designs with partial resolution classes subject to the class-uniform condition. We derive the necessary conditions, including extremal bounds, build the foundation for general CURF constructions, including a frame variant of the $\lambda$ blow-up construction from part I. We also establish a PBD-closure result. For CURFs with blocks of size two and three we determine the existence of CURFs of type $g^u$, completely for $g=3$, with a small list of exceptions for $g=6$, asymptotically for $g=4,5$ and give some other infinite families.