Sabidussi's Compatibility Conjecture
Can the edges of a finite connected multigraph, given a closed eulerian trail, be partitioned into circuits so that no circuit contains two edges used consecutively in the trail? The proof in fact four-colours the edges to satisfy the constraints.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Graph theory
- Posed by
- Gert Sabidussi
- Year posed
- 1980
- Years open
- 46y
- Solved
- 2026-07-14
- Model
- GPT-5.6 Pro, GPT-5.6 Sol
- Vendor
- OpenAI
- Collaborators
- Nikolay Ulyanov
- Verification
- Lean-verified
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
Developed with GPT-5.6 Pro and GPT-5.6 Sol; the author reviewed the proof.
Verification
Lean 4 formalization available in the author's repository, alongside the arXiv preprint.