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On the diameter of reconfiguration graphs for vertex colourings.

Bonamy, M. and Johnson, M. and Lignos, I.M. and Patel, V. and Paulusma, Daniel (2011) 'On the diameter of reconfiguration graphs for vertex colourings.', Electronic notes in discrete mathematics., 38 (1). pp. 161-166.


The reconfiguration graph of the k-colourings of a graph G contains as its vertex set the proper vertex k-colourings of G, and two colourings are joined by an edge in the reconfiguration graph if they differ in colour on just one vertex of G. We prove that for a graph G on n vertices that is chordal or chordal bipartite, if G is k-colourable, then the reconfiguration graph of its ℓ-colourings, for ℓ⩾k+1, is connected and has diameter O(n2). We show that this bound is asymptotically tight up to a constant factor.

Item Type:Article
Keywords:Reconfiguration, Graph colouring, Graph diameter.
Full text:(AM) Accepted Manuscript
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Publisher statement:NOTICE: this is the author’s version of a work that was accepted for publication in Electronic notes in discrete mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Electronic notes in discrete mathematics, 38/1, 2011, 10.1016/j.endm.2011.09.028
Date accepted:No date available
Date deposited:09 January 2015
Date of first online publication:December 2011
Date first made open access:29 October 2021

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