The Chen-Lawrencenko Conjectures on Cyclic Colorations
A cyclic coloration of a triangulation of a closed 2-manifold gives the faces around every vertex distinct colors. Chen and Lawrencenko made two conjectures about the cyclic chromatic number of minimal triangulations in 1999. Their second is proved here and their first disproved.
- Result
- Disproved(see note)
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Topological graph theory
- Posed by
- Beifang Chen, Serge Lawrencenko
- Year posed
- 1999
- Years open
- 27y
- Solved
- 2026-08-07
- Model
- GPT-5.6 Pro
- Vendor
- OpenAI
- Collaborators
- John M. Campbell
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 12 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
One conjecture each way: the second proved, the first disproved. Two further Chen-Lawrencenko conjectures remain open and are flagged as such in the paper.
What the AI did
"We succeed, based on our extensive interactions with GPT-5.6 Pro, in proving and disproving, respectively, Chen and Lawrencenko's second and first conjectures." The acknowledgement places the model in the exploratory and proof-development stages, with all suggestions substantially revised, corrected and independently verified by the author.
Verification
A preprint days old, with no independent review.