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.
|Keywords:||Reconfiguration, Graph colouring, Graph diameter.|
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|Publisher Web site:||http://dx.doi.org/10.1016/j.endm.2011.09.028|
|Record Created:||07 Dec 2011 14:51|
|Last Modified:||03 Apr 2013 16:21|
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