On the size-Ramsey number of grids

Abstract

We show that the size-Ramsey number of the $\sqrt{n}\times \sqrt{n}$ grid graph is $O(n^{5/4})$, improving a previous bound of $n^{3/2+o(1)}$ by Clemens, Miralaei, Reding, Schacht, and Taraz.

8 pages, 1 figure