Minimizing Unsatisfaction in Colourful Neighbourhoods
نویسندگان
چکیده
Abstract. Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximising 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.
منابع مشابه
Minimizing Unsatisfaction in Colorful Neighborhoods
Abstract. Coloring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colors available at the nodes and their neighborhoods, given a predetermined number of colors. In the analytical framework of a tree approximation, solutions obtained by population dynamics show that existing ...
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