The board / combinatorics / #747
Erdős Problem #747
SOLVEDdatabase updated 2025-08-31
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).
How large should \(\ell(n)\) be such that, almost surely, a random \(3\)-uniform hypergraph on \(3n\) vertices with \(\ell(n)\) edges must contain \(n\) vertex-disjoint edges? The precise asymptotic was given by Kahn [Ka23], proving that the threshold is \(\sim n\log n\) (also for the general problem over \(r\)-uniform hypergraphs).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/747.Prizenone
Topicscombinatorics, hypergraphs
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/747
Attempts
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