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Conference Papers Year : 2011

On the diameter of reconfiguration graphs for vertex colourings

Abstract

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(n^2). We show that this bound is asymptotically tight up to a constant factor.
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Dates and versions

lirmm-00782875 , version 1 (30-01-2013)

Identifiers

  • HAL Id : lirmm-00782875 , version 1

Cite

Marthe Bonamy, Matthew Johnson, Ioannis Lignos, Viresh Patel, Daniël Paulusma. On the diameter of reconfiguration graphs for vertex colourings. EuroComb'11: European Conference on Combinatorics, Graph Theory and Applications, Aug 2011, Budapest, Hungary. pp.161-166. ⟨lirmm-00782875⟩
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