Problem 1014

Erdős Problem #1014: declared status 'proved'. Formalized: no. Let $R(k,l)$ be the Ramsey number, so the minimal $n$ such that every graph on at least $n$ vertices contains either a $K_k$ or an independent set on $l$ vertices. Prove, for fixed $k\geq 3$, that$$\lim_{l\to \infty}\frac{R(k,l+1)}{R(k,l)}=1.$$ Prize: no. Tags: graph theory.