Minimum Edge-Outerplanar Embedding
Can the minimum edge-outerplanarity of a finite loopless planar graph, minimized over all planar embeddings, be computed in polynomial time? Asked by Bentz in 2009.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Graph algorithms
- Posed by
- Cédric Bentz
- Year posed
- 2009
- Years open
- 17y
- Solved
- 2026-07-09
- Model
- GPT-5.5 Pro
- Vendor
- OpenAI
- Collaborators
- Hantao Yu
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 5 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The reduction to computing an embedding of minimum face-depth was initially produced by GPT-5.5 Pro, then verified and polished manually by the author.
Verification
Author-checked and polished arXiv preprint. Not yet peer-reviewed.
Source
arXiv:2607.08110 - Minimum edge-outerplanar embeddings are polynomial-time computable