Counterexamples on matchings in hypergraphs and full rainbow matchings in graphs
arXiv:1710.04807
Abstract
A graph whose edges are coloured (not necessarily properly) contains a full rainbow matching if there is a matching that contains exactly one edge of each colour. We refute several conjectures on matchings in hypergraphs and full rainbow matchings in graphs, made by Aharoni and Berger and others.