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

doi:10.37236/370

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

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

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).