A 2-factorization of a graph is a partition of its edges into 2-factors. An ordered 2-factorization assigns labels to the factors, so permuting distinct factors gives a different ordered 2-factorization.
Lee (2026) proved that the number 
of ordered 2-factorizations of an 
-vertex 
-regular graph satisfies
 |
where 
as 
,
uniformly over simple graphs 
. Every such factorization has 
factors, and the number of unordered
2-factorizations is 
.
Lee (2026) reports ChatGPT assistance with an auxiliary proof.
