Properties of the Steiner Triple Systems of Order 19
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Date
Keywords
Automorphism; Chromatic index; Chromatic number; Configuration; Cycle structure; Existential closure; Independent set; Partial parallel class; Rank; Steiner triple system of order 19
Degree Level
Advisor
Degree Name
Volume
17
Issue
R98
Publisher
Electronic Journal of Combinatorics
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).