Daniel Gerbner: On the Turán number of the expansion of the t-fan

The $t$-fan is the graph on $2t+1$ vertices consisting of $t$ triangles which intersect at exactly one common vertex. For a given graph $F$, the \textit{$r$-expansion} $F$ is the $r$-graph obtained from $F$ by adding $r-2$ distinct new vertices to each edge of $F$, such that the $(r-2)|E(F)|$ new vertices are distinct from each other and are not in $V(F)$. We determine the Tur\'an number of the 3-expansion of the $t$-fan for $n$ sufficiently large.

Joint work with Xin Cheng, Hilal Hama Karim and Junpeng Zhou.