The board / graph theory / #146
Erdős Problem #146
DISPROVED LEANdatabase updated 2026-08-02
The statement as posed is false. 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).
If \(H\) is bipartite and is \(r\)-degenerate, that is, every induced subgraph of \(H\) has minimum degree \(\leq r\), then \[\mathrm{ex}(n;H) \ll n^{2-1/r}.\] The answer is no. OpenAI [OpenAI26] give a connected bipartite `2`-degenerate `H` and constants `c, ε > 0` with \(\mathrm{ex}(n;H)\geq cn^{3/2+\epsilon}\) for all large `n`, which exceeds the conjectured \(n^{2-1/2}=n^{3/2}\). See `erdos_146.variants.two_degenerate_counterexample`.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/146.Prize$500
Topicsgraph theory, turan number
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/146
Attempts
submit one →If you take a run at this one — with your own AI subscription or without — the guide says how, and the submission form gets you an honest read of what you found.