Dirac's 1-Factorization Conjecture

Let $G$ be a graph of even order, and let $k$ be an integer. A graph is 1-factorable if its edges can be partitioned into 1-factors, equivalently if its chromatic index equals its maximum degree. 1-Factorization Conjecture. If $G$ is $k$-regular for some

$$k\geq 2\left\lceil\frac{|V(G)|}{4}\right\rceil-1,$$

then $G$ is 1-factorable; equivalently, $\chi'(G)=\Delta(G)$. The conjecture is a central dense-graph edge-coloring assertion and was verified for all sufficiently large graphs by Csaba, Kühn, Lo, Osthus, and Treglown in 2016; the supplied source does not state that the finite conjecture is completely resolved.