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On DRC-covering of K(n) t λ by cycles

Liang Zhihe (School of Mathematics and Information Science Hebei Normal University Shijiazhuang, P.R. China)

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 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 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.

Keywords: Kt(n), DRC-covering, cycle, WDM network