Properties of the steiner triple systems of order 19

Charles Colbourn; Anthony D. Forbes; Mike J. Grannell; Terry S. Griggs; Petteri Kaskit; Patric R J Östergård; David A. Pike; Olli Pottonen

doi:10.37236/370

Properties of the steiner triple systems of order 19

Charles Colbourn, Anthony D. Forbes, Mike J. Grannell, Terry S. Griggs, Petteri Kaskit, Patric R J Östergård, David A. Pike, Olli Pottonen

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

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
DOIs	https://doi.org/10.37236/370
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

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Cite this

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title = "Properties of the steiner triple systems of order 19",

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).",

keywords = "Automorphism, Chromatic index, Chromatic number, Configuration, Cycle structure, Existential closure, Independent set, Partial parallel class, Rank, Steiner triple system of order 19",

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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

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Properties of the steiner triple systems of order 19

Abstract

Keywords

ASJC Scopus subject areas

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