Resolvable group divisible designs with block size 3

Resolvable Modified Group Divisible Designs with Block Size Three

A resolvable modified group divisible design (RMGDD) is an MGDD whose blocks can be partitioned into parallel classes. In this article, we investigate the existence of RMGDDs with block size three and show that the necessary conditions are also sufficient with two exceptions. # 2005 Wiley Periodicals, Inc. J Combin Designs 15: 2–14, 2007

Class-Uniformly Resolvable Group Divisible Structures I: Resolvable Group Divisible Designs

We consider Class-Uniformly Resolvable Group Divisible Designs (CURGDD), which are resolvable group divisible designs in which each of the resolution classes has the same number of blocks of each size. We derive the fully general necessary conditions including a number of extremal bounds. We present some general constructions including a novel construction for shrinking the index of a master de...

Resolvable holey group divisible designs with block size three

Existence of resolvable group divisible designs with block size four I

It is proved in this paper that for m ≡ 0; 2; 6; 10 (mod 12) there exists a resolvable group divisible design of order v, block size 4 and group size m if and only v ≡ 0 (mod 4), v ≡ 0 (modm), v − m ≡ 0 (mod 3), except when (3; 12) and except possibly when (3; 264); (3; 372); (8; 80); (8; 104), (9; 396) (40; 400) or (40; 520). c © 2002 Elsevier Science B.V. All rights reserved.

Odd and even group divisible designs with two groups and block size four

We show the necessary conditions are su6cient for the existence of GDD(n; 2; 4; 1, 2) with two groups and block size four in which every block intersects each group exactly twice (even GDD’s) or in which every block intersects each group in one or three points (odd GDD’s). We give a construction for near 3-resolvable triple systems TS(n; 3; 6) for every n¿ 4, and these are used to provide const...