Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9514578 | Electronic Notes in Discrete Mathematics | 2005 | 7 Pages |
Abstract
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 Z4ÃZ2, Z3ÃZ3, Z10 and Z11. All the extant cases are closely related to certain conjectures concerning cubic graphs, most notably to the celebrated Berge-Fulkerson Conjecture.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Edita MáÄajová, André Raspaud, Martin Å koviera,