کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1149865 | 957900 | 2008 | 10 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: The metamorphosis of λλ-fold K4-eK4-e designs into maximum packings of λKnλKn with 4-cycles, λ⩾2λ⩾2 The metamorphosis of λλ-fold K4-eK4-e designs into maximum packings of λKnλKn with 4-cycles, λ⩾2λ⩾2](/preview/png/1149865.png)
Let K4-e=. If we remove the “diagonal” edge the result is a 4-cycle. Let (X,B)(X,B) be a λλ-fold K4-eK4-e design of order n ; i.e., a decomposition of λKnλKn into copies of K4-eK4-e. Let D(B)D(B) be the collection of “diagonals” removed from the graphs in B and C1(B)C1(B) the resulting collection of 4-cycles. If C2(B)C2(B) is a reassembly of these edges into 4-cycles and L is the collection of edges in D(B)D(B) not used in a 4-cycle of C2(B)C2(B), then (X,C1(B)∪C2(B),L)(X,C1(B)∪C2(B),L) is a packing of λKnλKn with 4-cycles and is called a metamorphosis of (X,B)(X,B). In Lindner and Tripodi [2005. The metamorphosis of K4-eK4-e designs into maximum packings of KnKn with 4-cycles. Ars Combin. 75, 333–349.] a complete solution is given for the existence problem of K4-eK4-e designs (λ=1λ=1) having a metamorphosis into a maximum packing of KnKn with all possible leaves. The purpose of this paper is the complete solution of the above problem for all values of λ>1λ>1.
Journal: Journal of Statistical Planning and Inference - Volume 138, Issue 11, 1 November 2008, Pages 3316–3325