Holroyd, Fred and Skoviera, Martin
Colouring of cubic graphs by Steiner triple systems.
Journal of Combinatorial Theory, Series B, 91(1) pp. 57–66.
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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.
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||Graph colourings; cubic graphs; Steiner triple systems
||Mathematics, Computing and Technology > Mathematics and Statistics
||27 Jun 2006
||04 Dec 2010 13:51
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