Erdős Problem #130
Erdős problem #130 · erdosproblems.com/130
For an infinite planar set in strong general position, how large can the chromatic and clique numbers of its positive-integer-distance graph be - in particular, can the chromatic number be infinite? Yes: there is such a set, no three collinear and no four concyclic, with infinite chromatic number.
- Result
- Proved(see note)
- Status
- Partial result
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Discrete Geometry, Chromatic Number
- Posed by
- —
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-13
- Model
- GPT-5.6 Star Fleet (Claude Fable 5 referee)
- Vendor
- OpenAI / Anthropic
- Collaborators
- —
- Verification
- Lean-verified
- Publication
- Announced
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
the infinite-chromatic subquestion is proved; the rest of the problem remains open
Verification
Lean-checked end to end; community review pending.