## Combinatorics and Probability Seminar

Liana Yepremyan

UIC

Rainbow matchings in equivalence relations

**Abstract:**We show that if a multigraph $G$ with maximum edge-multiplicity of at most $\frac{\sqrt{n}}{\log^2 n}$, is edge-coloured by $n$ colours such that each colour class is a disjoint union of cliques with at least $2n + o(n)$ vertices, then it has a full rainbow matching, that is, a matching where each colour appears exactly once. This asymptotically solves a question raised by Clemens, Ehrenmuller and Pokrovskiy, and is related to problems on algebras of sets studied by Grinblat in [Grinblat 2002]. For the solution we use the differential equation method. This is joint work with David Munhá Correia.

Wednesday March 4, 2020 at 2:00 PM in 612 SEO