On some hypergraph problems of paul erdős and the asymptotics of matchings, covers and colorings

Abstract

This article summarizes progress on several old hypergraph problems of Paul Erdős and a few questions to which they led. Quite unexpectedly, there turned out to be substantial connections between the problems under discussion, surely some indication (if any were needed) that Erdős’ questions were the “right” ones. Here’s a quick synopsis.