The Maximum Almost Decomposable 6-turn Fill Of The Complete Graph

Let X be the vertex of Kn, where Kn denote the complete graph with n ver-tices. A k-cycle packing of Kn, denoted by k-CP(n), 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. Suppose (X, C, L) is a k-CP(n). A collection of ?n/k? vertex disjoint k-cycles in C is called an almost parallel class. If n?0 (mod k), an almost parallel class is said to be a parallel class. If C can be partitioned into almost parallel classes, the k-cycle packing is called resolvable, denoted by k-ARCP(n). Furthermore, if the number of almost parallel classes is maximum, then (X, C, L) is maximum, denoted by k-MARCP(n).Let D(n, k) denote the number of almost parallel classes in a k-MARCP(n). When k= 3,4,5, D(n, k) has been decided completely. When n= 1 (mod 2k) and k?{6,8,10,14}?{m:5?m?49, m? 1 (mod 2)}, D(n,k) has been decided with few possible exceptions. In this thesis, we shall decide D(n,6) for all values of n.