报告题目： Chromatic Index of Latin Squares and Steiner Triple Systems
报告人：Wanless Ian Murray
摘要：The chromatic index of a hypergraph is the smallest number of colours with which the edges can be coloured in such a way that no two intersecting edges have the same colour. Latin squares (LSs) and Steiner Triple Systems (STSs) can be viewed as particularly nice 3-uniform hypergraphs. In this viewpoint, the chromatic index of a LS measures how close it is to having an orthogonal mate. Similarly, the chromatic index of an STS measures how close it is to being resolvable. With these thoughts as motivation, we will investigate what is known about the chromatic index of LSs and STSs. Related questions are how few disjoint transversals a LS can have, and how few disjoint parallel classes a STS can have. These are questions that have recently seen some progress, though there is still much that we do not know.