scholarly journals On the chromatic number of Steiner triple systems of order 25

2005 ◽  
Vol 299 (1-3) ◽  
pp. 120-128 ◽  
Author(s):  
Peter Horak
Keyword(s):  
Chromatic Number ◽  
Steiner Triple Systems ◽  
Triple Systems

scholarly journals Properties of the Steiner Triple Systems of Order 19

10.37236/370 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Charles J. Colbourn ◽  
Anthony D. Forbes ◽  
Mike J. Grannell ◽  
Terry S. Griggs ◽  
Petteri Kaski ◽  
...  
Keyword(s):  
Chromatic Number ◽  
Steiner Triple Systems ◽  
Chromatic Index ◽  
Triple Systems ◽  
Existentially Closed

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).

scholarly journals Extending bicolorings for Steiner triple systems

2013 ◽  
Vol 7 (2) ◽  
pp. 225-234 ◽  
Author(s):  
M. Gionfriddo ◽  
E. Guardo ◽  
L. Milazzo
Keyword(s):  
Chromatic Number ◽  
Steiner Triple Systems ◽  
Triple Systems ◽  
Doubling Construction

We initiate the study of extended bicolorings of Steiner triple systems (STS) which start with a k-bicoloring of an STS(v) and end up with a k-bicoloring of an STS(2v + 1) obtained by a doubling construction, using only the original colors used in coloring the subsystem STS(v). By producing many such extended bicolorings, we obtain several infinite classes of orders for which there exist STSs with different lower and upper chromatic number.

scholarly journals On 6-sparse Steiner triple systems

2007 ◽  
Vol 114 (2) ◽  
pp. 235-252 ◽  
Author(s):  
A.D. Forbes ◽  
M.J. Grannell ◽  
T.S. Griggs
Keyword(s):  
Steiner Triple Systems ◽  
Triple Systems

scholarly journals Maximum genus embeddings of Steiner triple systems

2005 ◽  
Vol 26 (3-4) ◽  
pp. 401-416 ◽  
Author(s):  
Mike J. Grannell ◽  
Terry S. Griggs ◽  
Jozef Širáň
Keyword(s):  
Steiner Triple Systems ◽  
Maximum Genus ◽  
Triple Systems
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