Erdős problem 180

For every finite family $\mathcal{F}$ of graphs, is there a single $G \in \mathcal{F}$ with $\mathrm{ex}(n;G) \ll_{\mathcal{F}} \mathrm{ex}(n;\mathcal{F})$? A counterexample refutes the Erdős-Simonovits compactness conjecture.