Resolution of the Oberwolfach problem

The Oberwolfach problem, posed by Ringel in 1967, asks for a decomposition of K₂ₙ₊₁ into edge-disjoint copies of a given 2-factor. We show that this can be achieved for all large n . We actually prove a significantly more general result, which allows for decompositions into more general types of factors. In particular, this also resolves the Hamilton–Waterloo problem for large n .