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.
The ACO Seminar (2019–2020)