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Steiner triple systems satisfying the 4-vertex condition.
- Source :
- Designs, Codes & Cryptography; Mar2012, Vol. 62 Issue 3, p323-330, 8p
- Publication Year :
- 2012
-
Abstract
- Higman asked which block graphs of Steiner triple systems of order v satisfy the 4-vertex condition and left the cases v = 9, 13, 25 unsettled.We give a complete answer to this question by showing that the affine plane of order 3 and the binary projective spaces are the only such systems. The major part of the proof is to show that no block graph of a Steiner triple system of order 25 satisfies the 4-vertex condition. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09251022
- Volume :
- 62
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Designs, Codes & Cryptography
- Publication Type :
- Academic Journal
- Accession number :
- 71112339
- Full Text :
- https://doi.org/10.1007/s10623-011-9520-2