Upper Bounds on Turán Densities via Extremal Set Theory

Abstract

We exhibit, in a systematic way, connections between hypergraph Turán problems and extremal set theory. More specifically, we construct natural families of uniform hypergraphs for which the upper bounds on their Turán densities reduce to classical problems in extremal set theory, including the Erdős--Ko--Rado theorem, $L$-intersecting families, and the Erdős matching problem.