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Kempe equivalence of colourings of cubic graphs.

Feghali, C. and Johnson, M. and Paulusma, D. (2017) 'Kempe equivalence of colourings of cubic graphs.', European journal of combinatorics., 59 . pp. 1-10.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:© 2016 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:29 June 2016
Date deposited:30 June 2016
Date of first online publication:22 July 2016
Date first made open access:22 January 2017

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