A constructive solution to the Oberwolfach problem with a large cycle

For every 2 -regular graph F of order v , the Oberwolfach problem O P(F) asks whether there is a 2 -factorization of Kv (v odd) or Kv 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 O P(F) whenever F contains a cycle of length greater than an explicit lower bound. Our constructions combine the amalgamationdetachment technique with methods aimed at building 2 -factorizations with an automorphism group having a nearly -regular action on the vertex -set. (c) 2024 Elsevier B.V. All rights reserved.