Full rainbow matchings in equivalence relations
Combinatorics
2020-02-24 v1
Abstract
We show that if a multigraph with maximum edge-multiplicity of at most , is edge-coloured by colours such that each colour class is a disjoint union of cliques with at least 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, Ehrenm\"uller and Pokrovskiy, and is related to problems on algebras of sets studied by Grinblat in [Grinblat 2002].
Cite
@article{arxiv.2002.08974,
title = {Full rainbow matchings in equivalence relations},
author = {David Munhá Correia and Liana Yepremyan},
journal= {arXiv preprint arXiv:2002.08974},
year = {2020}
}