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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

MICHELE MOSCA
MICHELE MOSCA
Affiliation:
Mathematical Institute, University of Oxford, and Wolfson College, Oxford, UK (e-mail: mosca@maths.ox.ac.uk)
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Abstract

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.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 7 , Issue 2 , June 1998 , pp. 211 - 216
Copyright
1998 Cambridge University Press

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