Find a proper vertex coloring using some number of colors. That is, color vertices using any number of colors but in such a way that no pair of adjacent vertices have the same color.
Find the fewest number of colors you need to properly coloring the vertices of the graph. This is called the chromatic number of the graph. Think about how you know your answer is correct.
Can you generalize? Can you conclude anything about the chromatic number for particular sorts of graphs?
