The Frankl-Peng-Rodl-Talbot Question on Turan Density Intervals
Frankl, Peng, Rodl and Talbot asked in 2007 whether the set of Turan densities of families of -graphs contains intervals. It does: for every the set contains non-degenerate intervals, including one of the form .
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Construction
- Field
- Extremal combinatorics
- Posed by
- Peter Frankl, Yuejian Peng, Vojtech Rodl, John Talbot
- Year posed
- 2007
- Years open
- 19y
- Solved
- 2026-05-25
- Model
- ChatGPT 5.4 Pro, ChatGPT 5.4 Thinking
- Vendor
- OpenAI
- Collaborators
- Xizhi Liu, Oleg Pikhurko
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 25 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The credit is bounded and precise: the graphs for the internal spectral gadget were suggested by the models, and the authors state the other main ideas and constructions are theirs.
Verification
arXiv preprint; not yet peer-reviewed.