Skip to main content
Article thumbnail
Location of Repository

Finding paths between 3-colourings

By L Cereceda, Jan van den Heuvel and M Johnson


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

Topics: H Social Sciences (General)
Publisher: London school of economics and political science
Year: 2007
OAI identifier:
Provided by: LSE Research Online
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • (external link)
  • (external link)
  • Suggested articles

    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.