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Minimizing unsatisfaction in colourful neighbourhoods

Authors Wong, K. Y. Michael View this author's profile
Saad, David
Issue Date 2008
Source Journal OF PHYSICS a-mathematical and THEORETICAL , v. 41, (32), 2008, AUG 15, article number 324023
Summary 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.
ISSN 1751-8113
Rights Journal of of Physics A: Mathematical and Theoretical © copyright (2008) IOP Publishing Ltd. The Journal's web site is located at
Language English
Format Article
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