Problem Statement
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\[\lim_{l\to \infty}\frac{R(k,l+1)}{R(k,l)}=1.\]
Prove, for fixed $k\geq 3$, that\[\lim_{l\to \infty}\frac{R(k,l+1)}{R(k,l)}=1.\]
Categories:
Graph Theory Ramsey Theory
Progress
This is open even for $k=3$.See also [544] for other behaviour of $R(3,k)$, and [1030] for the diagonal version of this question.
Source: erdosproblems.com/1014 | Last verified: January 19, 2026