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

Feghali, C., Johnson, M. & Paulusma, D. (2015), Kempe equivalence of colourings of cubic graphs, Electronic Notes in Discrete Mathematics 49: The Eight European Conference on Combinatorics, Graph Theory and Applications, EuroComb 2015. Bergen, Norway, Bergen, 243-249.

Author(s) from Durham

Abstract

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.