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 journalArticle

12 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)1-30
Number of pages30
JournalElectronic Journal of Combinatorics
Volume17
Issue number1
StatePublished - 2010

Fingerprint

Chromatic Index
Steiner Triple System
Chromatic number
Closed

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

Colbourn, C., Forbes, A. D., Grannell, M. J., Griggs, T. S., Kaskit, P., Östergård, P. R. J., ... Pottonen, O. (2010). Properties of the steiner triple systems of order 19. 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.

In: Electronic Journal of Combinatorics, Vol. 17, No. 1, 2010, p. 1-30.

Research output: Contribution to journalArticle

Colbourn, C, Forbes, AD, Grannell, MJ, Griggs, TS, Kaskit, P, Östergård, PRJ, Pike, DA & Pottonen, O 2010, 'Properties of the steiner triple systems of order 19', Electronic Journal of Combinatorics, vol. 17, no. 1, pp. 1-30.
Colbourn C, Forbes AD, Grannell MJ, Griggs TS, Kaskit P, Östergård PRJ et al. Properties of the steiner triple systems of order 19. Electronic Journal of Combinatorics. 2010;17(1):1-30.
Colbourn, Charles ; Forbes, Anthony D. ; Grannell, Mike J. ; Griggs, Terry S. ; Kaskit, Petteri ; Östergård, Patric R J ; Pike, David A. ; Pottonen, Olli. / Properties of the steiner triple systems of order 19. In: Electronic Journal of Combinatorics. 2010 ; Vol. 17, No. 1. pp. 1-30.
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