Geodesic
Properties of the Steiner triple systems of order 19
The electronic journal of combinatorics, Tome 17 (2010)
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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).
DOI : 10.37236/370
Classification : 05B07
Mots-clés : automorphism, chromatic index, chromatic number, configuration, cycle structure, existential closure, independent set, partial parallel class, rank, Steiner triple system of order 19 
@article{10_37236_370,
     author = {Charles J. Colbourn and Anthony D. Forbes and Mike J. Grannell and Terry S. Griggs and Petteri Kaski and Patric R. J. \"Osterg\r{a}rd and David A. Pike and Olli Pottonen},
     title = {Properties of the {Steiner} triple systems of order 19},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/370},
     zbl = {1193.05039},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/370/}
}
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AU  - Petteri Kaski
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AU  - Olli Pottonen
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%A Charles J. Colbourn
%A Anthony D. Forbes
%A Mike J. Grannell
%A Terry S. Griggs
%A Petteri Kaski
%A Patric R. J. Östergård
%A David A. Pike
%A Olli Pottonen
%T Properties of the Steiner triple systems of order 19
%J The electronic journal of combinatorics
%D 2010
%V 17
%U http://geodesic.mathdoc.fr/articles/10.37236/370/
%R 10.37236/370
%F 10_37236_370
Charles J. Colbourn; Anthony D. Forbes; Mike J. Grannell; Terry S. Griggs; Petteri Kaski; Patric R. J. Östergård; David A. Pike; Olli Pottonen. Properties of the Steiner triple systems of order 19. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/370

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