Cereceda, L, van den Heuvel, Jan and Johnson, M
(2007)
*Finding paths between 3-colourings.*
LSE-CDAM-2007-31.
London school of economics and political science, London, UK.

## Abstract

Given a 3-colourable graph G and two proper vertex 3-colourings α and β of G, consider the following question: is it possible to transform α into β by recolouring vertices of G one at a time, making sure that all intermediate colourings are proper 3-colourings? We prove that this question is answerable in polynomial time. We do so by characterising the instances G,α,β where the transformation is possible; the proof of this characterisation is via an algorithm that either finds a sequence of recolourings between α and β, or exhibits a structure which proves that no such sequence exists. In the case that a sequence of recolourings does exist, the algorithm uses O(|V(G)|2) recolouring steps and in many cases returns a shortest sequence of recolourings. We also exhibit a class of instances G,α,β that require Ω(|V(G)|2) recolouring steps.

Item Type: | Monograph (Report) |
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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 |

Identification Number: | LSE-CDAM-2007-31 |

Date Deposited: | 10 Jul 2008 09:23 |

URL: | http://eprints.lse.ac.uk/6785/ |

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