Almost resolvable maximum packings of complete graphs with 5-cycles

Let X be the vertex set of Kn. A k-cycle packing of Kn is a triple (X, C, L), where C is a collection of edge disjoint k-cycles of Kn and L is the collection of edges of Kn not belonging to any of the k-cycles in C. A k-cycle packing (X, C, L) is called resolvable if C can be partitioned into almost parallel classes. A resolvable maximum k-cycle packing of Kn, denoted by k-RMCP(n), is a resolvable k-cycle packing of Kn, (X, C, L), in which the number of almost parallel classes is as large as possible. Let D(n, k) denote the number of almost parallel classes in a k-RMCP(n). D(n, k) for k = 3, 4 has been decided. When n ≡ k (mod 2k) and k ≡ 1 (mod 2) or n ≡ 1 (mod 2k) and k ∈ {6, 8, 10, 14} ∪ {m: 5 ⩽ m ⩽ 49, m ≡ 1 (mod 2)}, D(n, k) also has been decided with few possible exceptions. In this paper, we shall decide D(n, 5) for all values of n ⩾ 5.