Location of Repository

Mixing 3-colourings in bipartite graphs.

By Luis Cereceda, Jan van den Heuvel and Matthew Johnson


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

Publisher: Elsevier
Year: 2009
DOI identifier: 10.1016/j.ejc.2009.03.011
OAI identifier: oai:dro.dur.ac.uk.OAI2:7398

Suggested articles



  1. (1995). A very simple algorithm for estimating the number of k-colourings of a low degree graph. doi
  2. (2004). Computational complexity of compaction to irre cycles. doi
  3. (2008). Connectedness of the graph of vertexcolourings.
  4. (2003). Counting, Sampling and Integrating : Algorithms and Complexity.
  5. (1982). Exactly Solved Models in Statistical Mechanics.
  6. (2007). Finding paths between 3-colourings.
  7. (2007). Finding paths between graph colourings: PSPACEcompleteness and superpolynomial distances.
  8. (2005). Frequency reassignment in cellular phone networks.
  9. (1979). Graph folding.
  10. (2005). Graph Theory, 3rd edition. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.