Holroyd, Fred and Skoviera, Martin
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|DOI (Digital Object Identifier) Link:||http://doi.org/10.1016/j.jctb.2003.10.003|
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Let S be a Steiner triple system and G a cubic graph. We say that G is S-colourable if its edges can be coloured so that at each vertex the incident colours form a triple of S. We show that if S is a projective system PG(n, 2), n >= 2, then G is S-colourable if and only if it is bridgeless, and that every bridgeless cubic graph has an S-colouring for every Steiner triple system of order greater than 3. We establish a condition on a cubic graph with a bridge which ensures that it fails to have an S-colouring if S is an affine system, and we conjecture that this is the only obstruction to colouring any cubic graph with any non-projective system of order greater than 3.
|Item Type:||Journal Article|
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|Keywords:||Graph colourings; cubic graphs; Steiner triple systems|
|Academic Unit/Department:||Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
|Depositing User:||Fred Holroyd|
|Date Deposited:||27 Jun 2006|
|Last Modified:||02 Aug 2016 13:38|
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