Publication details for Professor Matthew JohnsonFeghali, C., Johnson, M. & Paulusma, D. (2017). Kempe equivalence of colourings of cubic graphs. European Journal of Combinatorics 59: 1-10.
- Publication type: Journal Article
- ISSN/ISBN: 0195-6698
- DOI: 10.1016/j.ejc.2016.06.008
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
Given a graph G=(V,E) and a proper vertex colouring of G, a Kempe chain is a subset of V that induces a maximal connected subgraph of G in which every vertex has one of two colours. To make a Kempe change is to obtain one colouring from another by exchanging the colours of vertices in a Kempe chain. Two colourings are Kempe equivalent if each can be obtained from the other by a series of Kempe changes. A conjecture of Mohar asserts that, for k≥3, all k-colourings of connected k-regular graphs that are not complete are Kempe equivalent. We address the case k=3 by showing that all 3-colourings of a connected cubic graph G are Kempe equivalent unless G is the complete graph K4 or the triangular prism.