Mixing 3-colourings in bipartite graphs

Cereceda, Luis; van den Heuvel, Jan; Johnson, Matthew

Abstract

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.

Citation

Cereceda, L., van den Heuvel, J., & Johnson, M. (2009). Mixing 3-colourings in bipartite graphs. European Journal of Combinatorics, 30(7), 1593-1606. https://doi.org/10.1016/j.ejc.2009.03.011

• Journal Article Type: Article
• Publication Date: Oct 1, 2009
• Deposit Date: Sep 30, 2010
• Publicly Available Date: Oct 29, 2010
• Journal: European Journal of Combinatorics
• Print ISSN: 0195-6698
• Electronic ISSN: 1095-9971
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 30
• Issue: 7
• Pages: 1593-1606
• DOI: https://doi.org/10.1016/j.ejc.2009.03.011
• Public URL: https://durham-repository.worktribe.com/output/1516038