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Erdős Problem #716
Ruzsa-Szemerédi problem
PROVED LEANdatabase updated 2026-06-21
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 \(\mathcal{F}\) be the family of all \(3\)-uniform hypergraphs with \(6\) vertices and \(3\) \(3\)-edges. Is it true that \[\mathrm{ex}_3(n,\mathcal{F})=o(n^2)?\] The answer is yes, proved by Ruzsa and Szemerédi [RuSz78] (this is known as the Ruzsa-Szemerédi problem).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/716.Prizenone
Topicsgraph theory, hypergraphs
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/716
Attempts
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