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Title: Minimizing unsatisfaction in colourful neighbourhoods
Authors: Wong, Michael Kwok-Yee
Saad, David
Keywords: Colouring sparse graphs
Spin glass theory
Colour diversity
Issue Date: 30-Jul-2008
Citation: Journal of physics A: mathematical and theoretical, v. 41, no. 32, p. 324023, 2008
Abstract: Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods, given a predetermined number of colours. In the analytical framework of a tree approximation, carried out at both zero and finite temperatures, solutions obtained by population dynamics give rise to estimates of the threshold connectivity for the incomplete to complete transition, which are consistent with those of existing algorithms. The nature of the transition as well as the validity of the tree approximation are investigated.
Rights: Journal of of Physics A: Mathematical and Theoretical © copyright (2008) IOP Publishing Ltd. The Journal's web site is located at
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