What was already known
Kotzig’s conjecture asks for all n−1 matchings in a perfect 1-factorisation to have this property. Earlier constructions covered special orders or smaller partial families.
AI involvement
ChatGPT 5.4 generated the rotating-matching construction and an initial proof. Cheng and Sgueglia found a different shorter proof and alone developed the completion to a full factorisation.
The model supplied the retained asymptotic matching construction, while the stronger factorisation theorem and final proofs are human.
Importance
Gives an asymptotically complete pairwise-perfect collection for every large even order.
Limitations
The stronger full factorisation in Theorem 1.2 and its probabilistic completion are human results. The authors replaced the initial model proof with a shorter human proof; the original proof is unavailable for comparison.
Technical verification
The authors call the initial model proof correct and give their own complete proof of the same construction. This checks the assessed construction, though their proof is different from the model's original argument.
Independent checking
Assessment of the initial proof and a separate complete human proof of the retained construction
- Checker
- Yangyang Cheng and Amedeo Sgueglia, authors
- Scope
- Theorem 1.3 pairwise-perfect matching construction
- Basis
- Reported by the linked checker
Human understanding
The authors explain the polygon-and-centre rotation construction, prime condition and how it proves Theorem 1.3.
Correction and publication history
Gives an asymptotically complete pairwise-perfect collection for every large even order.
Read this published revision