The ACO Seminar (2019–2020)

We show that if a multigraph $G$ with maximum edge-multiplicity of at most $\sqrt{n}/\log^2 n$, 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, Ehrenmüller 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.

Before the talk, at 3:10pm, there will be tea and cookies in Wean 6220.