Properties of the Steiner Triple Systems of Order 19

Colbourn, Charles J.; Forbes, Anthony D.; Grannell, Mike J.; Griggs, Terry S.; Kaski, Petteri; Östergard, Patric R. J.; Pike, David A. and Pottonen, Olli (2010). Properties of the Steiner Triple Systems of Order 19. Electronic Journal of Combinatorics, 17(1) article no. R98.

URL: http://www.combinatorics.org/

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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