Almost resolvable decompositions of 2Kn into cycles of odd length

The complete graph on n vertices is denoted by K, and the graph on n vertices in which each pair of vertices is joined by exactly 2 edges is denoted by 2K,. An m-cycle is a sequence of m distinct vertices (u1, u2, . . . . u,) such that ui is adjacent to ui+ 1 and U, is adjacent to u1 . A spanning subgraph H of G is a subgraph for which V(H) = V(G). An i-factor of a graph G is a spanning subgraph of G that is regular of degree i (so each component of a 2-factor is a cycle). An m-cycle decomposition of a graph G is defined to be an ordered pair (G, C(m)), where C(m) is a collection of edge-disjoint m-cycles which partition the edge set E(G) of G. An m-cycle decomposition is resolvable if the m-cycles in C(m) can be partitioned into 2-factors of G. The Oberwolfach problem was first formulated by Ringel and was first mentioned in [8]. The part of this problem which has attracted the most