Beschreibung:
<jats:title>Abstract</jats:title><jats:p>We show that the size-Ramsey number of the <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0963548323000147_inline1.png" /><jats:tex-math>
$\sqrt{n} \times \sqrt{n}$
</jats:tex-math></jats:alternatives></jats:inline-formula> grid graph is <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0963548323000147_inline2.png" /><jats:tex-math>
$O(n^{5/4})$
</jats:tex-math></jats:alternatives></jats:inline-formula>, improving a previous bound of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0963548323000147_inline3.png" /><jats:tex-math>
$n^{3/2 + o(1)}$
</jats:tex-math></jats:alternatives></jats:inline-formula> by Clemens, Miralaei, Reding, Schacht, and Taraz.</jats:p>