Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Computer Science

Profile

Publication details for Professor Matthew Johnson

Bonamy, Marthe, Bousquet, Nicolas, Feghali, Carl & Johnson, Matthew (2019). On a conjecture of Mohar concerning Kempe equivalence of regular graphs. Journal of Combinatorial Theory, Series B 135: 179-199.

Author(s) from Durham

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.