Abstract
Properties of the 11 084 874 829 Steiner triple systems of order 19 are examined. In particular, there is exactly one 5-sparse, but no 6-sparse, STS(19); there is exactly one uniform STS(19); there are exactly two STS(19) with no almost parallel classes; all STS(19) have chromatic number 3; all have chromatic index 10, except for 4 075 designs with chromatic index 11 and two with chromatic index 12; all are 3-resolvable; and there are exactly two 3-existentially closed STS(19).
Original language | English (US) |
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Pages (from-to) | 1-30 |
Number of pages | 30 |
Journal | Electronic Journal of Combinatorics |
Volume | 17 |
Issue number | 1 |
DOIs | |
State | Published - 2010 |
Keywords
- Automorphism
- Chromatic index
- Chromatic number
- Configuration
- Cycle structure
- Existential closure
- Independent set
- Partial parallel class
- Rank
- Steiner triple system of order 19
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics