Gábor Sárközy, (WPI)
Title: Rainbow matchings (or transversals in Latin squares)
Abstract: Rainbow matchings (or equivalently transversals in Latin squares) have received a lot of attention. We'll mention some conjectures and results. In particular, we'll prove the following result. If a bipartite multigraph G is the union of (2n-1) matchings of size n, then G contains a rainbow matching (where each edge comes from a different matching) of size n. Alon observed, that this immediately implies the classical Erdos-Ginzburg-Ziv theorem in number theory.
Joint work with J. Barat and A. Gyarfas