Research Program |
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July 13 - 18, 2003 Program Chairs: REU Abstracts All week one lectures will be given in the first floor auditorium. |
Combinatorial design theory is that branch of graph theory which deals with partitioning the edges of graphs into special partitions. The graphs most often dealt with are the complete graphs (designs), the complements of complete multipartite graphs (group divisible designs), regular graphs, and trees. For example the partioning of the K_{2n} into one factors can be viewed as a) an edge colouring problem, b) the scheduling of a round robin tournament, c) a commutative idempotent quasigroup, or d) a scheme for testing interactions in the presence of different levels of a disease. Although the class of graphs is restricted the applications are many and varied including error correcting codes, cryptography, redundant storage on arrays of discs, software testing,design of experiments for the agricultural and pharmaceutical fields, and particular applications to genome mapping.
Many other ideas of use to high school teachers such as finite
geometries, latin squares, and "strange" algebras can be brought into
the discussion to enhance some of the concurrent graph theory
course. Although some of the research problems are very difficult,
some -- such block intersection graphs, cyclic and one rotational
designs, isomorphic factorization of trees, and the late WFL
scheduling problem, are easily explained and readily accessible, and
are good ideas from which projects can develop.