Kempe equivalence of colourings of cubic graphs

Feghali, C.; Johnson, M.; Paulusma, D.

Abstract

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.

Citation

Feghali, C., Johnson, M., & Paulusma, D. (2017). Kempe equivalence of colourings of cubic graphs. European Journal of Combinatorics, 59, 1-10. https://doi.org/10.1016/j.ejc.2016.06.008

• Journal Article Type: Article
• Acceptance Date: Jun 29, 2016
• Online Publication Date: Jul 22, 2016
• Publication Date: Jan 1, 2017
• Deposit Date: Jun 29, 2016
• Publicly Available Date: Jul 22, 2017
• Journal: European Journal of Combinatorics
• Print ISSN: 0195-6698
• Electronic ISSN: 1095-9971
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 59
• Pages: 1-10
• DOI: https://doi.org/10.1016/j.ejc.2016.06.008
• Public URL: https://durham-repository.worktribe.com/output/1378561