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Mixing 3-colourings in bipartite graphs

Cereceda, Luis, van den Heuvel, Jan and Johnson, Matthew (2009) Mixing 3-colourings in bipartite graphs. European Journal of Combinatorics, 30 (7). pp. 1593-1606. ISSN 0195-6698

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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 one 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: Article
Official URL: http://www.elsevier.com/wps/find/journaldescriptio...
Additional Information: © 2009 Elsevier Ltd.
Library of Congress subject classification: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 30 Mar 2010 13:57
URL: http://eprints.lse.ac.uk/27630/

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