ISSN:
1573-7586
Keywords:
caps
;
Steiner triple systems
;
colouring
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract Hill [6] showed that the largest cap in PG(5,3) has cardinality 56. Using this cap it is easy to construct a cap of cardinality 45 in AG(5,3). Here we show that the size of a cap in AG(5,3) is bounded above by 48. We also give an example of three disjoint 45-caps in AG(5,3). Using these two results we are able to prove that the Steiner triple system AG(5,3) is 6-chromatic, and so we exhibit the first specific example of a 6-chromatic Steiner triple system.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008293805734
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