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In this video, I explain what a coloring of a graph is in graph theory. I also define the chromatic number of a graph and discuss a good procedure for coloring a graph. The procedure will consist of coloring vertices beginning with the vertex of highest degree such that no two vertices of the same color share an edge. This process is repeated with different colors until all vertices are colored. The next video will discuss how to apply this technique to the coloring of maps so that no two adjacent regions are the same color.