Graph coloring is a popular research topic in graph theory. In a proper coloring, vertices in a graph are colored such that no two adjacent vertices are assigned the same color. The chromatic number of a graph is the fewest number of colors that must be used in a proper coloring of the graph. We are looking at variations of the chromatic number problem: Grundy colorings, pseudo-Grundy colorings, paired colorings (where paired vertices must be colored the same color), achromatic colorings, iterated colorings, etc.