Proof of the 1-Factorization and Hamilton Decomposition Conjectures

In this paper the authors prove the following results for all sufficiently large $n$: [$1$-factorization conjecture] Suppose that $n$ is even and $D\geq 2\lceil n/4\rceil -1$; [Hamilton decomposition conjecture] Suppose that $D \ge \lfloor n/2 \rfloor $; [Optimal packings of Hamilton cycles] Suppose that $G$ is a graph on $n$ vertices with minimum degree $\delta\ge n/2$.