The board / graph theory / #1024
Erdős Problem #1024
SOLVEDdatabase updated 2025-09-12
Resolved in some way other than a straight proof or disproof — usual for open-ended questions, or for multi-part problems whose parts went different ways.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Let \(f(n)\) be such that every \(3\)-uniform linear hypergraph on \(n\) vertices contains an independent set on \(f(n)\) vertices. Estimate \(f(n)\). Phelps and Rödl [PhRo86] proved \(f(n) \asymp (n\log n)^{1/2}\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/1024.Prizenone
Topicsgraph theory, hypergraphs
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1024
Attempts
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