  We show how graph neural networks can be used to solve the canonical graph
coloring problem. We frame graph coloring as a multi-class node classification
problem and utilize an unsupervised training strategy based on the statistical
physics Potts model. Generalizations to other multi-class problems such as
community detection, data clustering, and the minimum clique cover problem are
straightforward. We provide numerical benchmark results and illustrate our
approach with an end-to-end application for a real-world scheduling use case
within a comprehensive encode-process-decode framework. Our optimization
approach performs on par or outperforms existing solvers, with the ability to
scale to problems with millions of variables.
