Abelian Colourings of Cubic Graphs

Citations of this article
Mendeley users who have this article in their library.
Get full text


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.




Máčajová, E., Raspaud, A., & Škoviera, M. (2005). Abelian Colourings of Cubic Graphs. Electronic Notes in Discrete Mathematics, 22, 333–339. https://doi.org/10.1016/j.endm.2005.06.080

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free