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 K (n) t ? , 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 ? (nt, ?) in the covering. For the problem, we give the lower bound of ? (nt, ?), and obtain the optimal solutions when n is even or n is odd and both ? and t are even.
On the choice number of complete multipartite graphs with part size four
