A New Upper Bound on Extremal Number of Even Cycles

Abstract

In this paper, we prove $\mathrm{ex}(n, C_{2k})\le (16\sqrt{5}\sqrt{k\log k} + o(1))\cdot n^{1+1/k}$. This improves on a result of Bukh and Jiang from 2017, thereby reducing the best known upper bound by a factor of $\sqrt{5\log k}$.