The board / graph theory / #60
Erdős Problem #60
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Does every graph on \(n\) vertices with \(>\mathrm{ex}(n;C_4)\) edges contain \(\gg n^{1/2}\) many copies of \(C_4\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/60.Prizenone
Topicsgraph theory, cycles
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA006855
Original pageerdosproblems.com/60
Attempts
submit one →Read our working report →
Exhaustively verified the new exact cases \(h_{C_4}(n,1)=2\) for every \(14\le n\le18\), with explicit two-cycle witnesses and a 55-second standalone checker; the uniform \(\Omega(\sqrt n)\) problem r
PARTIAL