Properties of the Steiner Triple Systems of Order 19

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


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).

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