ChongShangguan

For fixed integers $r\ge 3,e\ge 3$, and $v\ge r+1$, let $f_r(n,v,e)$ denote the maximum number of edges in an $n$-vertex $r$-uniform hypergraph in which the union of arbitrary $e$ distinct edges contains at least $v+1$ vertices. In 1973, Brown, Erdős and Sós initiated the study of the function $f_r(n,v,e)$ and they proved that $\mathrm{\Omega }(n^{\frac{er-v}{e-1}})=f_r(n,v,e)=O(n^{\lceil \frac{er-v}{e-1}\rceil })$. …