Cereceda, Luis, van den Heuvel, Jan ORCID: 0000-0003-0897-9148 and Johnson, Matthew
(2009)
*Mixing 3-colourings in bipartite graphs.*
European Journal of Combinatorics, 30 (7).
pp. 1593-1606.
ISSN 0195-6698

## 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 |
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Official URL: | http://www.elsevier.com/wps/find/journaldescriptio... |

Additional Information: | © 2009 Elsevier Ltd. |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics H Social Sciences > HA Statistics |

Date Deposited: | 30 Mar 2010 13:57 |

Last Modified: | 20 Oct 2021 01:47 |

URI: | http://eprints.lse.ac.uk/id/eprint/27630 |

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