Minimizing unsatisfaction in colourful neighbourhoods

Wong, K.Y. Michael and Saad, David Minimizing unsatisfaction in colourful neighbourhoods. Journal of Physics A: Mathematical and General, 41 (32), p. 324023.

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.

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Additional Information: © 2008 IOP Publishing Ltd.
Uncontrolled Keywords: colouring sparse graphs under various restrictions,nodes,neighbourhoods,analytical framework,tree approximation,solutions,population dynamics,threshold connectivity,transition,Mathematical Physics,Modelling and Simulation,Statistics and Probability,Physics and Astronomy(all),Statistical and Nonlinear Physics

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