Publication details for Professor Matthew JohnsonCereceda, Luis, van den Heuvel, Jan & Johnson, Matthew (2009). Mixing 3-colourings in bipartite graphs. European Journal of Combinatorics 30(7): 1593-1606.
- Publication type: Journal Article
- ISSN/ISBN: 0195-6698
- DOI: 10.1016/j.ejc.2009.03.011
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
For a 3-colourable graph G, the 3-colour graph of G, denoted C_3(G), is the graph with node set the proper vertex 3-colourings of G, and two nodes adjacent whenever the corresponding colourings differ on precisely one vertex of G. We consider the following question: given G, how easily can one decide whether or not C_3(G) is connected? We show that the 3-colour graph of a 3-chromatic graph is never connected, and characterise the bipartite graphs for which View the MathML source is connected. We also show that the problem of deciding the connectedness of the 3-colour graph of a bipartite graph is coNP-complete, but that restricted to planar bipartite graphs, the question is answerable in polynomial time.