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Resolvable group divisible designs with large groups. (English) Zbl 1351.05179
Summary: 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.
MSC:
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
05B30 Other designs, configurations
05C51 Graph designs and isomorphic decomposition
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