The asymptotics of $r(4,t)$
For integers $s,t geq 2$, the Ramsey numbers $r(s,t)$ denote the minimum $N$such that every $N$-vertex graph contains either a clique of order $s$ or anindependent set of order $t$. In this paper we prove [ r(4,t) =ΩBigl(frac{t^3}{log^4 ! t}Bigr) quad qua...