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Connectedness of the graph of vertex-colourings.

Cereceda, L. and van den Heuvel, J. and Johnson, M. (2008) 'Connectedness of the graph of vertex-colourings.', Discrete mathematics., 308 (5-6). pp. 913-919.


For a positive integer k and a graph G, the k-colour graph of G , Ck(G), is the graph that has the proper k-vertex-colourings of G as its vertex set, and two k -colourings are joined by an edge in Ck(G) if they differ in colour on just one vertex of G . In this note some results on the connectedness of Ck(G) are proved. In particular, it is shown that if G has chromatic number k∈{2,3}, then Ck(G) is not connected. On the other hand, for k⩾4 there are graphs with chromatic number k for which Ck(G) is not connected, and there are k -chromatic graphs for which Ck(G) is connected.

Item Type:Article
Keywords:Vertex colouring, k-colour graph, Glauber dynamics.
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:© 2007 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:No date available
Date deposited:11 December 2015
Date of first online publication:March 2008
Date first made open access:16 April 2021

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