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# Mixing 3-colourings in bipartite graphs.

Cereceda, Luis. and van den Heuvel, Jan. and Johnson, Matthew. (2007) 'Mixing 3-colourings in bipartite graphs.', in Graph-theoretic concepts in computer science. Heidelberg: Springer, pp. 166-177. Lecture notes in computer science. (4769).

## Abstract

For a 3-colourable graph G, the 3-colour graph of G, denoted $\mathcal{C}_3(G)$ , 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 $\mathcal{C}_3(G)$ is connected? We show that the 3-colour graph of a 3-chromatic graph is never connected, and characterise the bipartite graphs for which $\mathcal{C}_3(G)$ 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 Revised papers of the 33rd International Workshop, WG 2007, Dornburg, Germany, June 21-23, 2007. PDF - Accepted Version (263Kb) Peer-reviewed http://dx.doi.org/10.1007/978-3-540-74839-7_17 The original publication is available at www.springerlink.com 07 Oct 2009 11:35 25 Nov 2011 09:51

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