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 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. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Cereceda, L., Van Den Heuvel, J., & Johnson, M. (2007). Mixing 3-colourings in bipartite graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4769 LNCS, pp. 166–177). Springer Verlag. https://doi.org/10.1007/978-3-540-74839-7_17
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