Finding paths between 3-colourings

Cereceda, L, van den Heuvel, Jan ORCID: 0000-0003-0897-9148 and Johnson, M (2007) Finding paths between 3-colourings. . London School of Economics and Political Science, London, UK.

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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)
Official URL:	http://www.cdam.lse.ac.uk/Reports/
Additional Information:	© 2007 London school of economics and political science
Divisions:	Mathematics
Subjects:	H Social Sciences > H Social Sciences (General)
Date Deposited:	10 Jul 2008 09:23
Last Modified:	12 Dec 2024 05:45
URI:	http://eprints.lse.ac.uk/id/eprint/6785

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