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Mixing 3-colourings in bipartite graphs

Cereceda, L, van den Heuvel, Jan and Johnson, M (2007) Mixing 3-colourings in bipartite graphs. LSE-CDAM-2007-06. London school of economics and political science, London, UK.

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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 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: Monograph (Report)
Official URL: http://www.cdam.lse.ac.uk/Reports/
Additional Information: © 2007 London school of economics and political science
Library of Congress subject classification: H Social Sciences > H Social Sciences (General)
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: LSE-CDAM-2007-06
Date Deposited: 10 Jul 2008 09:27
URL: http://eprints.lse.ac.uk/6781/

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