The board / graph theory / #1178
Erdős Problem #1178
OPENdatabase updated 2026-01-25
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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For \(r\geq 3\) let \(d_r(e)\) be the minimal \(d\) such that \[\mathrm{ex}_r(n,\mathcal{F})=o(n^2),\] where \(\mathcal{F}\) is the family of \(r\)-uniform hypergraphs on \(d\) vertices with \(e\) edges. Prove that \[d_r(e)=(r-2)e+3\] for all \(r,e\geq 3\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/1178.Prizenone
Topicsgraph theory, hypergraphs
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1178
Attempts
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reduced all uniformities to the exact \(r=3\) core, proved \(f_3(n,7,4)=3,4,6,7,9,12\) for \(7\le n\le12\) with a standalone exhaustive checker, and derived \(f_3(n,7,4)<\frac49n^2+2n\) modulo Gishbol
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