Improved Bounds for the Extremal Number of Subdivisions

Let $H_t$ be the subdivision of $K_t$. Very recently, Conlon and Lee have proved that for any integer $t\geq 3$, there exists a constant $C$ such that $\textrm{ex}(n,H_t)\leq Cn^{3/2-1/6^t}$. In this paper, we prove that there exists a constant $C'$ such that $\textrm{ex}(n,H_t)\leq C'n^{3/2-\frac{1}{4t-6}}$.