Solutions to the Oberwolfach Problem for Orders 18 to 40

Abstract

The Oberwolfach problem (OP) asks whether $K_n$ (for $n$ odd) or $K_n$ minus a $1$-factor (for $n$ even) admits a $2$-factorization where each $2$-factor is isomorphic to a given $2$-factor $F$. The order $n$ and the type of the $2$-factor $F$ are the parameters of the problem. For $n\le 17$, the existence of a solution has been resolved for all possible parameters. There are also many special types of $2$-factors for which solutions to OP are known. We provide solutions to OP for all orders $n$, $18\le n\le 40$. The computational results for higher orders were obtained using the SHARCNET high-performance computing cluster.