The board / graph theory / #1008
Erdős Problem #1008
PROVED LEANdatabase updated 2026-01-17
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).
Does every graph with \(m\) edges contain a subgraph with \(\gg m^{2/3}\) edges which contains no \(C_4\)? This problem was first solved in the affirmative by Conlon, Fox, and Sudakov [CFS14b]. A simple proof is given by Hunter in the comments.
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/1008.Prizenone
Topicsgraph theory, cycles
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/1008
Attempts
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