SOLVED - $500
If $H$ is bipartite and is not $r$-degenerate, that is, there exists an induced subgraph of $H$ with minimum degree $>r$ then
\[\mathrm{ex}(n;H) > n^{2-\frac{1}{r}+\epsilon}.\]
Conjectured by Erdős and Simonovits
[ErSi84]. Disproved by Janzer
[Ja21], who constructed, for any $\epsilon>0$, a $3$-regular bipartite graph $H$ such that
\[\mathrm{ex}(n;H)\ll n^{\frac{4}{3}+\epsilon}.\]
See also [113], [146], and [714].
See also the entry in the graphs problem collection.
