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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 C3(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 we decide whether or not C3(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 C3(G) 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. (2007). Mixing 3-colourings in bipartite graphs. Lecture Notes in Computer Science, 166-177.

Journal Article Type Article
Publication Date Dec 6, 2007
Deposit Date Oct 7, 2009
Publicly Available Date Oct 28, 2009
Journal Lecture Notes in Computer Science
Print ISSN 0302-9743
Electronic ISSN 1611-3349
Publisher Springer
Peer Reviewed Peer Reviewed
Issue 4769
Pages 166-177


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