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Kempe equivalence of colourings of cubic graphs

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

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C. Feghali


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.


Feghali, C., Johnson, M., & Paulusma, D. (2017). Kempe equivalence of colourings of cubic graphs. European Journal of Combinatorics, 59, 1-10.

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
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 59
Pages 1-10


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