Properties of the Steiner Triple Systems of Order 19

ELECTRONIC JOURNAL OF COMBINATORICS(2010)

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摘要
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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关键词
automorphism,chromatic index,chromatic number,configuration,cycle structure,existential closure,independent set,partial parallel class,rank,Steiner triple system of order 19
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