On the Tur\'an number of the expansion of the book

Abstract

The book with $t$ pages is the graph on $t+2$ vertices consisting of $t$ triangles which intersect at exactly one common edge. For a given graph $F$, the $r$-expansion $F^r$ of $F$ is the $r$-uniform hypergraph obtained from $F$ by adding $r-2$ distinct new vertices to each edge of $F$. We determine the Tur\'an number of the 3-expansion of the book graph for sufficiently large $n$.