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Removing Edges Can Increase the Average Number of Colours in the Colourings of a Graph

Published online by Cambridge University Press:  01 June 1998

Mathematical Institute, University of Oxford, and Wolfson College, Oxford, UK (e-mail:


It was conjectured by Bartels and Welsh [1] that removing an edge from an n-vertex graph G will not increase the average number of colours in the proper colourings of G if k=n colours are available. This paper shows that for all n>3, and for each k∈{3, 4, …, [lfloor ](3n−6)/2[rfloor ]}, there is a graph on n vertices with an edge whose removal increases the average number of colours in the k-colourings, thus disproving the conjecture.

Research Article
1998 Cambridge University Press

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