On DRC-covering of K(n) t 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 λKt (n), 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 ρ(nt, λ) in the covering. For the problem, we give the lower bound of ρ(nt, λ), and obtain the optimal solutions when n is even or n is odd and both λ and t are even.