Properties of the Steiner Triple Systems of Order 19

Colbourn, Charles J., Forbes, Anthony D., Grannell, Mike J., Griggs, Terry S., Kaski, Petteri, Ostergard, 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: 1-30.

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Author Colbourn, Charles J.
Forbes, Anthony D.
Grannell, Mike J.
Griggs, Terry S.
Kaski, Petteri
Ostergard, Patric R. J.
Pike, David A.
Pottonen, Olli
Title Properties of the Steiner Triple Systems of Order 19
Journal name Electronic Journal of Combinatorics   Check publisher's open access policy
ISSN 1077-8926
Publication date 2010-07
Sub-type Article (original research)
Open Access Status File (Publisher version)
Volume 17
Issue 1
Start page 1
End page 30
Total pages 30
Place of publication Clemson, United States
Publisher Electronic Journal of Combinatorics
Language eng
Formatted 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).
Keyword Automorphism
Chromatic index
Chromatic number
Cycle structure
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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