scholarly journals Resolvable Group Divisible Designs with Large Groups

10.37236/5435 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Peter J. Dukes ◽  
Esther R. Lamken ◽  
Alan C.H. Ling
Keyword(s):  
Fixed Number ◽  
Group Divisible Designs ◽  
Product Construction ◽  
Group Divisible ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Transversal Designs ◽  
Complete Multipartite ◽  
Large Groups ◽  
Resolvable Group

We prove that the necessary divisibility conditions are sufficient for the existence of resolvable group divisible designs with a fixed number of sufficiently large groups. Our method combines an application of the Rees product construction with a streamlined recursion based on incomplete transversal designs. With similar techniques, we also obtain new results on decompositions of complete multipartite graphs into a prescribed graph.

scholarly journals On DRC-covering of K(n) t λ by cycles

2009 ◽  
Vol 6 (2) ◽  
pp. 229-237 ◽  
Author(s):  
Zhihe Liang
Keyword(s):  
Lower Bound ◽  
Wdm Networks ◽  
Optimal Solutions ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Number Of Cycles ◽  
Complete Multipartite

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.

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