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

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).


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