Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4651904 | Electronic Notes in Discrete Mathematics | 2015 | 7 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics