Class-Uniformly Resolvable Group Divisible Structures II: Frames

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 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 gu, completely for g = 3, with a small list of exceptions for g = 6, asymptotically for g = 4, 5 and give some other infinite families.

• Type: Journal
• Year: 2004
• Where: COMBINATORICS
• Authors: Peter Danziger, Brett Stevens
• Keywords: COMBINATORICS 2004, General Curf Constructions, Group Divisible Designs, Partial Resolution Classes