Dr. Rolf Rees has worked in many areas of design theory, including resolvable designs; packings and coverings; graph factorizations and decompositions; frames and group-divisible designs; tournament designs; and applications to cryptography. He is adept at both direct and recursive constructions, using a combination of algebraic and combinatorial techniques. Among the themes that run through his work are the use of frames and other designs with holes, and the use of difference methods for designs and graph factorizations. His research has shown great depth, originality, and diversity.
We describe a few highlights of Professor Rees's work. His paper “The existence of resolvable designs” completed the solution of the existence question for (1,2)-factorizations of the complete graph. His papers “Maximal sets of triangle-factors of graphs” provide an almost complete solution to this problem. “Two new direct product-type constructions for resolvable group-divisible designs” is a landmark paper in design theory; a new use of these construction is seen in “Truncated transversal designs: A new lower bound on the number of idempotent MOLS.” The paper “A new class of group-divisible designs” gives a complete existence proof for group divisible designs of a certain type, and has been frequently referenced. The paper “On the existence of incomplete designs of block size four having one hole” finishes the determination of the spectrum of PBDs with all blocks but one having size four; it uses powerful recursive constructions for designs with holes, and has often been cited.