### 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) |
---|---|

Pages (from-to) | 1-30 |

Number of pages | 30 |

Journal | Electronic Journal of Combinatorics |

Volume | 17 |

Issue number | 1 |

State | Published - 2010 |

### Fingerprint

### 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

- Geometry and Topology
- Theoretical Computer Science
- Computational Theory and Mathematics

### Cite this

*Electronic Journal of Combinatorics*,

*17*(1), 1-30.

**Properties of the steiner triple systems of order 19.** / Colbourn, Charles; Forbes, Anthony D.; Grannell, Mike J.; Griggs, Terry S.; Kaskit, Petteri; Östergård, Patric R J; Pike, David A.; Pottonen, Olli.

Research output: Contribution to journal › Article

*Electronic Journal of Combinatorics*, vol. 17, no. 1, pp. 1-30.

}

TY - JOUR

T1 - Properties of the steiner triple systems of order 19

AU - Colbourn, Charles

AU - Forbes, Anthony D.

AU - Grannell, Mike J.

AU - Griggs, Terry S.

AU - Kaskit, Petteri

AU - Östergård, Patric R J

AU - Pike, David A.

AU - Pottonen, Olli

PY - 2010

Y1 - 2010

N2 - 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).

AB - 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).

KW - Automorphism

KW - Chromatic index

KW - Chromatic number

KW - Configuration

KW - Cycle structure

KW - Existential closure

KW - Independent set

KW - Partial parallel class

KW - Rank

KW - Steiner triple system of order 19

UR - http://www.scopus.com/inward/record.url?scp=77955592425&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77955592425&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77955592425

VL - 17

SP - 1

EP - 30

JO - Electronic Journal of Combinatorics

JF - Electronic Journal of Combinatorics

SN - 1077-8926

IS - 1

ER -