Kohayakawa–Nagle–Rödl–Schacht forcing conjecture

A graph $G$ is $(p,\delta)$-locally dense if every set $S\subseteq V(G)$ with $|S|\geq\delta|V(G)|$ satisfies $e(S)\geq p|S|^2/2$. A graph $H$ is KNRS-forcing if, for every $p,\alpha\in(0,1)$, there exist $\delta,\varepsilon>0$ such that every $(p,\delta)$-locally dense graph $G$ satisfies $t(H,G)>p^{e(H)}+\varepsilon$, unless $G$ is $(p,\alpha)$-quasirandom.

Kohayakawa–Nagle–Rödl–Schacht forcing conjecture. If $H$ is not a forest, then $H$ is KNRS-forcing.

This strengthens the Kohayakawa–Nagle–Rödl–Schacht conjecture by asserting that the only locally dense graphs asymptotically attaining the lower bound are quasirandom. The source does not state its resolution status.