A note on the logarithmic exponent of Ramsey number $r(4,t)$

Abstract

In this short note, we point out that the recent lower bounds for off-diagonal Ramsey numbers $r(s,t)$ with fixed $s\ge 5$, together with the recent proof of the Ajtai--Erd\H{o}s--Koml\'os--Szemer\'edi independence conjecture, imply \[ r(4,t)=\frac{t^3}{(\log t)^{2+o(1)}}. \] This note is solely for informal circulation and will not be submitted for publication.