The board / graph theory / #713
Erdős Problem #713
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, for every bipartite graph \(G\), there exists some \(\alpha\in [1,2)\) and \(c>0\) such that \[\mathrm{ex}(n;G)\sim cn^\alpha?\] The condition that \(G\) have at least two edges excludes degenerate forbidden graphs whose extremal number is eventually zero, for which the displayed asymptotic with \(c>0\) is impossible.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/713.Prize$500
Topicsgraph theory, turan number
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/713
Attempts
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The authoritative live statement is literally false for \(G=K_2\) since \(\operatorname{ex}(n,K_2)=0\); for the intended nondegenerate problem, the report proves an explicit infinite \(K_{2,t}\)-core
FOUND