If a bipartite graph H has minimum degree r≥3, must there exist varepsilon(H)>0 such that operatornameex(n,H)=Omega(n^2-1/(r-1)+varepsilon(H))?

Erdős Problem #147 — Minimum degree and bipartite Turán exponents

If a bipartite graph $H$ has minimum degree $r\geq3$ , must there exist $\varepsilon(H)>0$ such that

\operatorname{ex}(n,H)=\Omega\left(n^{2-1/(r-1)+\varepsilon(H)}\right)?

References

O. Janzer, Disproof of a conjecture of Erdős and Simonovits on the Turán number of graphs with minimum degree 3, Combinatorica 43 (2023), 105–130.

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