Problem 147

If $H$ is bipartite with minimum degree $r$ then there exists $\epsilon=\epsilon(H)>0$ such that

\mathrm{ex}(n;H) \gg n^{2-\frac{1}{r-1}+\epsilon}.

Source: erdosproblems.com/147

Graph theory
Turán numbers

Wiki page

Status

SolvedDisproved

An accepted solution exists. The statement is false.

DISPROVED (LEAN). The site's commentary (page last edited 18 January 2026) credits Janzer's rainbow Turán paper [Ja23] with the disproof for even $r\ge4$ and his later paper [Ja23b] with the case $r=3$ ; both are refereed, and each is recorded as an accepted claim on the blow-up page and the 3-regular page. The site's label is DISPROVED (LEAN); the external Lean proof it refers to is linked, unverified, under Formalization below.

ErSi84: Erdős, P. and Simonovits, M., Cube-supersaturated graphs and related problems. Progress in graph theory (Waterloo, Ont., 1982) (1984), 203-218.
Ja23: Janzer, Oliver, Rainbow Turán number of even cycles, repeated patterns and blow-ups of cycles. Israel J. Math. 253 (2023), 813-840.
Ja23b: Janzer, Oliver, Disproof of a conjecture of Erdős and Simonovits on the Turán number of graphs with minimum degree 3. Int. Math. Res. Not. IMRN (2023), 8478-8494.

Problem 147

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