The board / graph theory / #615
Erdős Problem #615
DISPROVED LEANdatabase updated 2026-08-23
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).
Does there exist some constant \(c > 0\) such that for all sufficiently large \(n\), if \(G\) is a graph with \(n\) vertices and at least \((1/8 - c)n^2\) edges then \(G\) must contain either a \(K_4\) or an independent set on at least \(n/\log n\) vertices? The answer is no, as shown by Fox, Loh, and Zhao [FLZ15].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/615.Prizenone
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/615
Attempts
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