The board / graph theory / #905
Erdős Problem #905
PROVED LEANdatabase updated 2026-04-07
The statement as posed is true, and a proof exists. 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).
Every graph with \(n\) vertices and \(>n^2/4\) edges contains an edge which is in at least \(n/6\) triangles. A conjecture of Bollobás and Erdős. This was proved independently by Edwards (unpublished) and Khadzhiivanov and Nikiforov [KhNi79].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/905.Prizenone
Topicsgraph theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/905
Attempts
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