scholarly journals Steiner Triple Systems with High Chromatic Index

2017 ◽  
Vol 31 (4) ◽  
pp. 2603-2611 ◽  
Author(s):  
Darryn Bryant ◽  
Charles J. Colbourn ◽  
Daniel Horsley ◽  
Ian M. Wanless
Keyword(s):  
Steiner Triple Systems ◽  
Chromatic Index ◽  
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 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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