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Finding paths between 3-colorings

Cereceda, Luis, van den Heuvel, Jan ORCID: 0000-0003-0897-9148 and Johnson, Matthew (2011) Finding paths between 3-colorings. Journal of Graph Theory, 67 (1). pp. 69-82. ISSN 0364-9024

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Identification Number: 10.1002/jgt.20514


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:
Additional Information: © 2010 Wiley Periodicals, Inc.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 19 May 2011 11:48
Last Modified: 20 Oct 2021 03:14

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