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Mixing 3-colourings in bipartite graphs

By L Cereceda, Jan van den Heuvel and M Johnson

Abstract

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

Topics: H Social Sciences (General)
Publisher: London school of economics and political science
Year: 2007
OAI identifier: oai:eprints.lse.ac.uk:6781
Provided by: LSE Research Online
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