  For every $2$-regular graph $F$ of order $v$, the Oberwolfach problem $OP(F)$
asks whether there is a $2$-factorization of $K_v$ ($v$ odd) or $K_v$ minus a
$1$-factor ($v$ even) into copies of $F$. Posed by Ringel in 1967 and
extensively studied ever since, this problem is still open. In this paper we
construct solutions to $OP(F)$ whenever $F$ contains a cycle of length greater
than an explicit lower bound. Our constructions combine the
amalgamation-detachment technique with methods aimed at building
$2$-factorizations with an automorphism group having a nearly-regular action on
the vertex-set.
