Cereceda, Luis, 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
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.
|Additional Information:||© 2010 Wiley Periodicals, Inc.|
|Uncontrolled Keywords:||colorings, graph|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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