Boots-Royle/Cao-Vince Conjecture on Planar Spectral Radius
Boots and Royle, and independently Cao and Vince, conjectured that the join of an edge with a path on vertices is the unique planar graph of maximum adjacency spectral radius for every . Tait and Tobin proved it for sufficiently large in 2017; the conjecture now holds for all .
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Argument
- Field
- Spectral graph theory
- Posed by
- Barry Boots, Gordon Royle; Dasong Cao, Andrew Vince
- Year posed
- 1991
- Years open
- 35y
- Solved
- 2026-07-21
- Model
- ChatGPT
- Vendor
- OpenAI
- Collaborators
- Lele Liu, Bo Ning, Yi Wang
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The declaration credits the model with generating the code that searched for extremal planar graphs, and with assisting in several computations and symbolic derivations, alongside language polishing.
Verification
arXiv preprint; not yet peer-reviewed.
Source
arXiv:2607.19268 - A complete solution to the Boots-Royle/Cao-Vince conjecture