Erdős Problem #1178 — The Brown–Erdős–Sós sparse-configuration threshold

For $r,e\geq3$, let $d_r(e)$ be the least integer $d$ such that every $r$-uniform hypergraph on $n$ vertices with no $e$ edges spanning at most $d$ vertices has $o(n^2)$ edges. Is

$$d_r(e)=(r-2)e+3?$$