Centre for Discrete and Applicable Mathematics |
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CDAM Research Report, LSE-CDAM-2007-06February 2007 |
Mixing 3-Colourings in Bipartite Graphs
Luis Cereceda, Jan van den Heuvel, and Matthew Johnson
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.A PDF file (258 kB) with the full contents of this report can be downloaded by clicking here.
(This paper supersedes the earlier paper Mixing 3-colourings in Bipartite Graphs, which is obsolete.)
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