Sabidussi's Compatibility Conjecture

Precise statement

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.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

GPT-5.6 Pro, GPT-5.6 Sol

Developed with GPT-5.6 Pro and GPT-5.6 Sol; the author reviewed the proof.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

lean verified statement audited

Lean 4 formalization available in the author's repository, alongside the arXiv preprint.

Correctness: supported · statement fidelity: audited · peer review: none

Timeline

1. 2026-07-14

   arXiv:2607.13225 - A proof of Sabidussi's compatibility conjecture

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.