Minimizing Unsatisfaction in Colourful Neighbourhoods

Details Minimizing Unsatisfaction in Colourful Neighbourhoods Minimizing Unsatisfaction in Colourful Neighbourhoods

2007-04-29

arxiv.org/abs/0704.3835v3

J. Phys. A: Math. Theor. 41, 324023 (2008).

Computer Science

Data Structures and Algorithms

28 pages, 12 figures, substantially revised with additional explanation

Scientific paper

10.1088/1751-8113/41/32/324023

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.

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