The board / combinatorics / #207
Erdős Problem #207
PROVEDdatabase updated 2025-08-31
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
For any \(g\geq 2\), if \(n\) is sufficiently large and \(\equiv 1,3\pmod{6}\) then there exists a 3-uniform hypergraph on \(n\) vertices such that - every pair of vertices is contained in exactly one edge (i.e. the graph is a Steiner triple system) and - for any \(2\leq j\leq g\) any collection of \(j\) edges contains at least \(j+3\) vertices. Proved by Kwan, Sah, Sawhney, and Simkin [KSSS22b].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/207.Prizenone
Topicscombinatorics, hypergraphs
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/207
Attempts
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