The board / graph theory / #22
Erdős Problem #22
PROVED LEANdatabase updated 2026-08-23
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).
Let \(\epsilon > 0\) and let \(n\) be sufficiently large depending on \(\epsilon\). Is there a graph on \(n\) vertices with at least \(n^2/8\) many edges which contains no \(K_4\), such that the largest independent set has size at most \(\epsilon n\)? This is true, as proved by Fox, Loh, and Zhao [FLZ15].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/22.Prizenone
Topicsgraph theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/22
Attempts
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