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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. (2015). Kempe equivalence of colourings of cubic graphs. .

Conference Name European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2015),
Conference Location Bergen, Norway
Publication Date Nov 12, 2015
Deposit Date Aug 12, 2015
Publicly Available Date Nov 12, 2016
Volume 49
Pages 243-249
Series Title Electronic Notes in Discrete Mathematics
Series ISSN 1571-0653
Keywords Kempe equivalence, Cubic graph, Graph colouring.


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