Colouring of cubic graphs by Steiner triple systems

Holroyd, Fred and Skoviera, Martin (2004). Colouring of cubic graphs by Steiner triple systems. Journal of Combinatorial Theory, Series B, 91(1) pp. 57–66.

DOI: https://doi.org/10.1016/j.jctb.2003.10.003

URL: http://www.elsevier.com/wps/find/journaldescriptio...

Abstract

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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• Item ORO ID
• 3491
• Item Type
• Journal Item
• ISSN
• 0095-8956
• Extra Information
• Some of the symbols may not have transferred correctly into this bibliographic record and/or abstract.---
  The DOI leads direct to the article; the URL leads direct to the journal homepage.
• Keywords
• Graph colourings; cubic graphs; Steiner triple systems
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• Fred Holroyd