The Turán Density of the Hypergraph $\{abc,ade,bde,cde\}$

Abstract

Let ${\bf F}_{3,2}$ denote the $3$-graph $\{abc,ade,bde,cde\}$. We show that the maximum size of an ${\bf F}_{3,2}$-free $3$-graph on $n$ vertices is $({4\over9}+o(1)) {n\choose3}$, proving a conjecture of Mubayi and Rödl [J. Comb. Th. A, 100 (2002), 135–152].