The board / graph theory / #714
Erdős Problem #714
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).
Is it true that \[\mathrm{ex}(n; K_{r,r}) \gg n^{2-1/r}?\]
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/714.Prizenone
Topicsgraph theory, turan number
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/714
Attempts
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Proved exactly that ex(n;K_{r,r}) equals C(n,2) for n<2r, C(2r,2)-r at n=2r, and C(2r+1,2)-(r+2) at n=2r+1, with exhaustive independent checks through r=4; the asymptotic question remains open.
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