Cereceda, Luis and van den Heuvel, Jan and Johnson, Matthew
(2011)
*Finding paths between 3-colorings.*
Journal of Graph Theory, 67 (1).
pp. 69-82.
ISSN 0364-9024

## Abstract

Given a 3-colorable graph G together with two proper vertex 3-colorings alpha and beta of G, consider the following question: is it possible to transform alpha into beta by recoloring vertices of G one at a time, making sure that all intermediate colorings are proper 3-colorings? We prove that this question is answerable in polynomial time. We do so by characterizing the instances G, alpha, beta where the transformation is possible; the proof of this characterization is via an algorithm that either finds a sequence of recolorings between alpha and beta, or exhibits a structure which proves that no such sequence exists. In the case that a sequence of recolorings does exist, the algorithm uses O(vertical bar V(G)vertical bar(2)) recoloring steps and in many cases returns a shortest sequence of recolorings. We also exhibit a class of instances G, alpha, beta that require Omega(vertical bar V(G)vertical bar(2)) recoloring steps.

Item Type: | Article |
---|---|

Official URL: | http://eu.wiley.com/WileyCDA/WileyTitle/productCd-... |

Additional Information: | © 2010 Wiley Periodicals, Inc. |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 19 May 2011 11:48 |

Last Modified: | 30 May 2014 13:58 |

URI: | http://eprints.lse.ac.uk/id/eprint/36005 |

### Actions (login required)

View Item |