The board / graph theory / #572
Erdős Problem #572
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).
Show that for \(k\geq 3\) \[\mathrm{ex}(n;C_{2k})\gg n^{1+\frac{1}{k}}.\] This problem is #46 in Extremal Graph Theory in the graphs problem collection.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/572.Prizenone
Topicsgraph theory, turan number, cycles
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/572
Attempts
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Woodall gives the exact all-\(k\) range \(n<2k\) and \(2k\le n\le4k-3\), and an independent exhaustive check verifies the first three \(C_8\) cases, but the required asymptotic construction remains op
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