Resolution of the Oberwolfach problem

Abstract

The Oberwolfach problem, posed by Ringel in 1967, asks for a decomposition of $K_{2n+1}$ 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 $n$.