The board / graph theory / #801
Erdős Problem #801
PROVEDdatabase updated 2025-08-31
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
If \(G\) is a graph on \(n\) vertices containing no independent set on \(>n^{1/2}\) vertices then there is a set of \(\leq n^{1/2}\) vertices containing \(\gg n^{1/2}\log n\) edges. Proved by Alon [Al96b].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/801.Prizenone
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/801
Attempts
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