Cereceda, Luis and van den Heuvel, Jan and Johnson, Matthew (2007) 'Mixing 3-colourings in bipartite graphs.', in Graph-theoretic concepts in computer science. Berlin: Springer, pp. 166-177. Lecture notes in computer science. (4769).
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.
|Item Type:||Book chapter|
|Additional Information:||Revised papers of the 33rd International Workshop, WG 2007, Dornburg, Germany, June 21-23, 2007.|
|Full text:||(AM) Accepted Manuscript|
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|Publisher Web site:||http://dx.doi.org/10.1007/978-3-540-74839-7_17|
|Publisher statement:||The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-540-74839-7_17|
|Date accepted:||No date available|
|Date deposited:||28 October 2009|
|Date of first online publication:||December 2007|
|Date first made open access:||No date available|
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