@article { ,
title = {On a conjecture of Mohar concerning Kempe equivalence of regular graphs},
abstract = {Let G be a graph with a vertex colouring α. Let a and b be two colours. Then a connected component of the subgraph induced by those vertices coloured either a or b is known as a Kempe chain. A colouring of G obtained from α by swapping the colours on the vertices of a Kempe chain is said to have been obtained by a Kempe change. Two colourings of G are Kempe equivalent if one can be obtained from the other by a sequence of Kempe changes. A conjecture of Mohar (2007) asserts that, for , all k-colourings of a k-regular graph that is not complete are Kempe equivalent. It was later shown that all 3-colourings of a cubic graph that is neither nor the triangular prism are Kempe equivalent. In this paper, we prove that the conjecture holds for each . We also report the implications of this result on the validity of the Wang–Swendsen–Kotecký algorithm for the antiferromagnetic Potts model at zero-temperature.},
doi = {10.1016/j.jctb.2018.08.002},
issn = {0095-8956},
journal = {Journal of Combinatorial Theory, Series B},
note = {EPrint Processing Status: Full text deposited in DRO},
pages = {179-199},
publicationstatus = {Published},
publisher = {Elsevier},
volume = {135},
keyword = {Algorithms and Complexity in Durham (ACiD)},
year = {2019},
author = {Bonamy, Marthe and Bousquet, Nicolas and Feghali, Carl and Johnson, Matthew}
}