We prove that the necessary divisibility conditions are sufficient for the existence of resolvable group divisible designs with a fixed number of sufficiently large groups. Our method combines an application of the Rees product construction with a streamlined recursion based on incomplete transversal designs. With similar techniques, we also obtain new results on decompositions of complete multipartite graphs into a prescribed graph.
@article{10_37236_5435,
author = {Peter J. Dukes and Esther R. Lamken and Alan C.H. Ling},
title = {Resolvable group divisible designs with large groups},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {4},
doi = {10.37236/5435},
zbl = {1351.05179},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5435/}
}
TY - JOUR
AU - Peter J. Dukes
AU - Esther R. Lamken
AU - Alan C.H. Ling
TI - Resolvable group divisible designs with large groups
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/5435/
DO - 10.37236/5435
ID - 10_37236_5435
ER -
%0 Journal Article
%A Peter J. Dukes
%A Esther R. Lamken
%A Alan C.H. Ling
%T Resolvable group divisible designs with large groups
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/5435/
%R 10.37236/5435
%F 10_37236_5435
Peter J. Dukes; Esther R. Lamken; Alan C.H. Ling. Resolvable group divisible designs with large groups. The electronic journal of combinatorics, Tome 23 (2016) no. 4. doi: 10.37236/5435
