More Results On Cycle Frames With Uniform Group Size

Suppose H is a complete m-partite graph Km(n1,n2,…,nm) with vertex set V and m independent sets Gi, G2,…,Gm of n1; n2,…,nm vertices respectively. Let g={G1,G2,…,Gm}. If the edges of λH can be partitioned into a set C of κ-cycles, then (v, g, C) is called a κ-cycle group divisible design with index A, denoted by{k,λ)-CGDD.A (κ,λ)-cycle frame of type gu, denoted by (k,λ)-CF(gu), is a (k,λ)-CGDD (V,g,C) in which|v|=gu,g={G1,G2,…,Gu) and|Gi|=g(1≤i≤u),and C can be partitioned into holey2-factors, each holey2-factor being a partition of the vertex set V\Gi for some Gi∈g.The existence of a (k,λ)-CF(gu) with3≤k≤6has been solved completely. In this paper, we show the existence of a (κ,λ)-CF(gu) with7≤k≤13.