The board / graph theory / #1014
Erdős Problem #1014
PROVED LEANdatabase updated 2026-04-24
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
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 \[\lim_{l\to \infty}\frac{R(k,l+1)}{R(k,l)}=1.\] This has been [solved](https://cdn.openai.com/pdf/6dc7175d-d9e7-4b8d-96b8-48fe5798cd5b/Ramsey.pdf) by an internal model at OpenAI.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/1014.Prizenone
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/1014
Attempts
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