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

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

Fingerprint Dive into the research topics of 'Properties of the steiner triple systems of order 19'. Together they form a unique fingerprint.

Cite this