The metamorphosis of λ-fold block designs with block size four into a maximum packing of λKn with 4-cycles
✍ Scribed by Selda Küçükçifçi; C.C Lindner; A Rosa
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 281 KB
- Volume
- 278
- Category
- Article
- ISSN
- 0012-365X
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✦ Synopsis
Let (X; B) be a -fold block design with block size four and deÿne sets B(C) and E(K4 \ C) as follows: for each block b ∈ B, partition b into a 4-cycle and a pair of disjoint edges and place the 4-cycle in B(C) and the 2 disjoint edges in E(K4 \ C). If we can reassemble the edges belonging to E(K4 \ C) into a collection of 4-cycles E(C) with leave L, then (X; B(C) ∪ E(C); L) is a packing of Kn with 4-cycles and is called a metamorphosis of the -fold block design (X; B). In this paper we give a complete solution of the metamorphosis problem for -fold block designs into maximum packings of Kn with 4-cycles for all (with the possible exception of = 1, n = 37, and leave 2 disjoint triangles). That is, for each we determine the set of all n such that there exists a -fold block design of order n having a metamorphosis into a maximum packing of Kn with 4-cycles.