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Minimum embedding of Steiner triple systems into -designs II
- Source :
-
Discrete Mathematics . Jan2009, Vol. 309 Issue 2, p400-411. 12p. - Publication Year :
- 2009
-
Abstract
- Abstract: A -design of order embeds a given Steiner triple system if there is a subset of points on which the graphs of the design induce the blocks of the original Steiner triple system. It has been established that , and that when equality is met, such a minimum embedding of an STS() exists, except when . Equality only holds when . One natural question is: What is the smallest order such that some STS can be embedded into a -design of order ? We solve the problem for 7 of the 10 congruence classes modulo 30. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 309
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 35621858
- Full Text :
- https://doi.org/10.1016/j.disc.2007.12.026