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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

Provided by:
Durham Research Online

Downloaded from
http://dro.dur.ac.uk/7398/1/7398.pdf

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