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DM
2008

Connectedness of the graph of vertex-colourings

13 years 3 months ago
Connectedness of the graph of vertex-colourings
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 connectivity 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. Keywords : vertex-colouring, k-colour graph, Glauber dynamics.
Luis Cereceda, Jan van den Heuvel, Matthew Johnson
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where DM
Authors Luis Cereceda, Jan van den Heuvel, Matthew Johnson
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