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 journalArticlepeer-review

22 Scopus citations


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
Issue number1
StatePublished - 2010


  • 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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