Parallelism in Binary Hopfield Networks

Some neural networks have been proposed as a model of computation for solving combinatorial optimization problems. The ability to solve interesting classic problems has motivated the use of neural networks as models for parallel computing. In this paper the degree of parallelism of a binary Hopfield network is studied using the chromatic number of the graph G associated to the network. We propose a rule to coloring the vertices of the neural network associated to the Traveling Salesman Problem such that the neurons with the same color can be simultaneously updated.