Chetwynd–Hilton 1-factorization conjecture

Let $G$ be a regular simple graph of order $2n$, with degree at least $n$. A 1-factorization of $G$ is a decomposition of its edge set into perfect matchings.

Chetwynd–Hilton 1-factorization conjecture. Every regular simple graph of order $2n$ and degree at least $n$ is 1-factorizable.

This conjecture, formulated by Chetwynd and Hilton in 1985, is the classical 1-Factorization Conjecture. If true, it would imply that for every regular graph of even order, at least one of the graph and its complement is 1-factorizable.