Textbook in PDF format This book explores the problem of minimal valid graph coloring, first in the form of games and then of resolution algorithms. Emphasis is placed on deterministic, guaranteed and non-guaranteed methods. Stochastic methods are then just mentioned because they are already widely described in previous publications. The study then details a general quantum algorithm of polynomial complexity. A final chapter provides elements of reflection on diplomatic algorithms that, for the problem of coloring under resource constraints, seek a compromise minimizing frustrations. The appendix includes some mathematical additions and the source codes of the main algorithms presented, in particular the one of the quantum method. Preface Games A Few Applications Encoding Deterministic Resolutions Stochastic Methods A Quantum Method Diplomatic Algorithms Appendix References Index