Erdős Problem #209
DISPROVED LEANdatabase updated 2026-06-21
The statement as posed is false. 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).
The number of lines from `A` that pass through the point `p`.
A *Gallai triangle* (or *ordinary triangle*) in a collection `A` of lines: three lines from `A` which intersect in three points, and each of these intersection points only intersects two lines from `A`.
Let \(A\) be a finite collection of \(d\geq 4\) non-parallel lines in \(\mathbb{R}^2\) such that there are no points where at least four lines from \(A\) meet. Must there exist a 'Gallai triangle' (or 'ordinary triangle'): three lines from \(A\) which intersect in three points, and each of these intersection points only intersects two lines from \(A\)? Füredi and Palásti [FuPa84] showed this is false when \(d\geq 4\) is not divisible by \(9\). Escudero [Es16] showed this is false for all \(d\geq 4\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/209.Prizenone
Topicsgeometry
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/209
Attempts
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