A new class of group divisible designs with block size three

We present two direct product-type constructions which will prove useful in the construction of resolvable designs. We use our constructions to complete the spectrum for resolvable group-divisible designs with block size three, as well as to give a short proof of the existence of decompositions of K6n into a one-factors and b triangle-factors for any a, b, n with a + 2b = 6n − 1 and a > 1. © 1993 John Wiley & Sons, Inc.

Two new direct product-type constructions for resolvable group-divisible designs

Decompositions of Edge-Colored Complete Graphs

The Hamilton–Waterloo problem seeks a resolvable decomposition of the complete graph Kn, or the complete graph minus a 1-factor as appropriate, into cycles such that each resolution class contains only cycles of specified sizes. We completely solve the case in which the resolution classes are either all 3-cycles or 4-cycles, with a few possible exceptions when n=24 and 48. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 342–352, 2009

http://www.dmi.unict.it/~gquattro/quattrocchigae/Documenti_pdf/34cycles2009.pdf

The Hamilton–Waterloo problem for cycle sizes 3 and 4

Combinatorial constructions for optimal supersaturated designs

Uniformly resolvable pairwise balanced designs with blocksizes two and three

We consider decompositionsK n → H, whereH is eitherP3 (the path with 3 edges) or the complete bipartite graphK1, 3, with the property that upon taking the complement of each graph in the decomposition one obtains a new decompositionK n → H c .

Rolf S. Rees

Papers

Uniformly resolvable pairwise balanced designs with blocksizes two and three

On complementary decompositions of the complete graph