Abelian Colourings of Cubic Graphs

  • Máčajová E
  • Raspaud A
  • Škoviera M
  • 5


    Mendeley users who have this article in their library.
  • 1


    Citations of this article.


We prove that every bridgeless cubic graph G can have its edges properly coloured by non-zero elements of any given Abelian group A of order at least 12 in such a way that at each vertex of G the three colours sum to zero in A. The proof relies on the fact that such colourings depend on certain configurations in Steiner triple systems. In contrast, a similar statement for cyclic groups of order smaller than 10 is false, leaving the problem open only for Z4× Z2, Z3× Z3, Z10and Z11. All the extant cases are closely related to certain conjectures concerning cubic graphs, most notably to the celebrated Berge-Fulkerson Conjecture. © 2005 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Abelian group
  • Cubic graph
  • Fulkerson's Conjecture
  • Steiner triple system
  • edge-colouring

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free