Almost resolvable maximum packings of complete graphs with 5-cycles

Let X be the vertex set of K (n) . A k-cycle packing of K (n) is a triple (X, C, L), where C is a collection of edge disjoint k-cycles of K (n) and L is the collection of edges of K (n) 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 K (n) , denoted by k-RMCP(n), is a resolvable k-cycle packing of K (n) , (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 a parts per thousand k (mod 2k) and k a parts per thousand 1 (mod 2) or n a parts per thousand 1 (mod 2k) and k a {6, 8, 10, 14} a(a) {m: 5 a (c) 1/2 m a (c) 1/2 49, m a parts per thousand 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.