Caps and Colouring Steiner Triple Systems |
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| Authors: | Aiden Bruen Lucien Haddad David Wehlau |
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| Affiliation: | (1) Department of Mathematics, University of Western Ontario, London, ON, N6A 5B7, Canada;(2) Department of Mathematics and CS, Royal Military College, P.O. Box 17000, STN Forces, Kingston, ON, K7K 7B4, Canada |
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| 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. |
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| Keywords: | caps Steiner triple systems colouring |
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