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Graph coloring: color sequences and algorithm for color sequence

There are basically three main graph coloring problems: vertex, edge, or face colorings of a given graph G. Graph colorings have applications in many optimization problems mainly in scheduling and assignment. In this study, we define color sequence, maximum color sequence, perfect color sequence, and almost perfect color sequence. Determining exact maximum color sequence of any given graph G is NP-hard problem. We developed a polynomial time greedy algorithm which computes color sequence of given graph G. This algorithm computes maximum color sequence for some graph families.