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Durham University

Computer Science


Publication details for Professor Matthew Johnson

Cereceda, Luis, van den Heuvel, Jan & Johnson, Matthew (2008). Connectedness of the graph of vertex-colourings. Discrete Mathematics 308(5-6): 913-919.

Author(s) from Durham


For a positive integer k and a graph G, the k-colour graph of 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 the k-colour graph if they differ in colour on just one vertex of G. In this note some results on the connectivity of the k-colour graph are proved. In particular it is shown that if G has chromatic number k=2 or 3, then the k-colour graph is not connected. On the other hand, for k>3 there are graphs with chromatic number k for which the k-colour graph is not connected, and there are k-chromatic graphs for which the k-colour graph is connected.