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Mixing 3-colourings in bipartite graphs

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

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Luis Cereceda

Jan van den Heuvel


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.


Cereceda, L., van den Heuvel, J., & Johnson, M. (2009). Mixing 3-colourings in bipartite graphs. European Journal of Combinatorics, 30(7), 1593-1606.

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
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 30
Issue 7
Pages 1593-1606


Accepted Journal Article (393 Kb)

Copyright Statement
NOTICE: this is the author's version of a work that was accepted for publication in European journal of combinatorics.

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