On DRC - covering of ) ( nKt λ by cycles

This paper considers the cycle covering of complete multipartite graphs motivated by the design of survivable WDM networks, where the requests are routed on sub-networks which are protected independently from each other. The problem can be stated as follows: for a given graph G, find a cycle covering of the edge set of ) (n Kt λ , where V( Kt (n))=V(G), such that each cycle in the covering satisfies the disjoint routing constraint (DRC). Here we consider the case where G=Ctn, a ring of size tn and we want to minimize the number of cycles ) , ( λ ρ t n in the covering. For the problem, we give the lower bound of ) , ( λ ρ t n , and obtain the optimal solutions when n is even or n is odd and both λ and t are even.