Many Turán exponents via subdivisions

Abstract Given a graph $H$ and positive integer $n$ , the Turán number $\mathrm{ex}(n,H)$ is maximum of edges in an -vertex that does not contain as subgraph. A real $r\in (1,2)$ called exponent if there exists bipartite such $\mathrm{ex}(n,H)=\Theta (n^r)$ . long-standing conjecture Erdős Simonovits states $1+\frac{p}{q}$ for all integers $p$ $q$ with $q\gt p$ In this paper, we show $q \gt p^{2}$ Our result also addresses Janzer [18].