Erdős Problem #1014

The problem

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

$$\lim_{l\to \infty}\frac{R(k,l+1)}{R(k,l)}=1.$$

Statement quoted from erdosproblems.com/1014, maintained by Thomas Bloom. Original source: [Er71,p.99]. Current status there: proved (Lean).

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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