Babai's Minimal Cayley Graph Problem
A Cayley graph is minimal when no proper subset of its connection set generates the group. Babai asked whether minimal Cayley graphs have bounded chromatic number. Resolved negatively: finite minimal Cayley graphs exist with arbitrarily large chromatic number.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Algebraic graph theory
- Posed by
- László Babai
- Year posed
- 1978
- Years open
- 48y
- Solved
- 2026-08-06
- Model
- ChatGPT 5.6 Sol
- Vendor
- OpenAI
- Collaborators
- James Davies, Meike Hatzel, Liana Yepremyan
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 30 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The paper's statement of AI use: "An initial proof was found by ChatGPT 5.6 Sol given [DHY24] in the input. Substantial parts of Section 2 originate from an early draft created in interaction with ChatGPT 5.6 Sol, which was subsequently edited and improved by the authors." The model found the first proof, given one of the authors' own earlier papers as context.
Verification
A preprint days old, with no independent review.