Halving transversal designs
| dc.contributor.author | Fronček, Dalibor | |
| dc.contributor.author | Meszka, Mariusz | |
| dc.date.accessioned | 2006-11-10T05:42:52Z | |
| dc.date.available | 2006-11-10T05:42:52Z | |
| dc.date.issued | 2000 | |
| dc.identifier.citation | Journal of Combinatorial Designs. 2000, vol. 8, issue 2, p. 83-99. | en |
| dc.identifier.issn | 1063-8539 | |
| dc.identifier.uri | http://hdl.handle.net/10084/58024 | |
| dc.language.iso | en | en |
| dc.publisher | Wiley | en |
| dc.relation.ispartofseries | Journal of Combinatorial Designs | en |
| dc.relation.uri | https://doi.org/10.1002/(SICI)1520-6610(2000)8:2<83::AID-JCD2>3.0.CO;2-V | en |
| dc.subject | transversal designs | en |
| dc.subject | complete multipartite graphs | en |
| dc.subject | isomorphic factors | en |
| dc.subject | self complementary factors | en |
| dc.subject | diameter | en |
| dc.title | Halving transversal designs | en |
| dc.type | article | en |
| dc.identifier.location | Není ve fondu ÚK | en |
| dc.description.abstract-en | A factor H of a transversal design TD(k,n) = (V,, ), where V is the set of points, the set of groups of size n and the set of blocks of size k, is a triple (V,, ) such that is a subset of . A halving of a TD (k, n) is a pair of factors Hi = (V, , i), i = 1,2 such that 1 2 = , 1 2 = and H1 is isomorphic to H2. A path of length q is a sequence x0, x1,,xq of points such that for each i = 1, 2,, q the points xi-1 and xi belong to a block Bi and no point appears more than once. The distance between points x and y in a factor H is the length of the shortest path from x to y. The diameter of a connected factor H is the maximum of the set of distances among all pairs of points of H. We prove that a TD (3, n) is halvable into isomorphic factors of diameter d only if d = 2,3,4, or and we completely determine for which values of n there exists such a halvable TD (3, n). We also show that if any group divisible design with block size at least 3 is decomposed into two factors with the same finite diameter d, then d 4. | en |
| dc.identifier.doi | 10.1002/(SICI)1520-6610(2000)8:2<83::AID-JCD2>3.0.CO;2-V | |
| dc.identifier.wos | 000085540000002 |
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