Resolution of the Oberwolfach problem

Stefan Glock, Felix Joos, Jaehoon Kim, Daniela Kühn, Deryk Osthus

Published 2018-06-12Version 1

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 $n$.