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Finding paths between 3-colorings.

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.


Given a 3-colorable graph G together with two proper vertex 3-colorings α and β of G, consider the following question: is it possible to transform α into β 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, α, β where the transformation is possible; the proof of this characterization is via an algorithm that either finds a sequence of recolorings between α and β, 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(|V(G)|2) recoloring steps and in many cases returns a shortest sequence of recolorings. We also exhibit a class of instances G, α, β that require Ω(|V(G)|2) recoloring steps

Item Type:Article
Keywords:Graph coloring, Algorithms, Graph recoloring, Reconfigurations.
Full text:Full text not available from this repository.
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Date accepted:No date available
Date deposited:No date available
Date of first online publication:May 2011
Date first made open access:No date available

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