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In this paper the authors prove the following results for all sufficiently large $n$: [$1$-factorization conjecture] Suppose that $n$ is even and $Dgeq 2lceil n/4rceil -1$; [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 $deltage n/2$.