Chapter 6.3, Problem 24MS

Getting greedy. (H) Suppose you are asked to color the vertices of this graph in the following way: You must color the vertices one-by-one in numerical order and no two vertices joined by an edge can be the same color. You are given the list of colors red, yellow, blue, green, purple, and orange. The coloring rule is to look at this ordered list of colors, and select the first color on the list that satisfies the criteria above. So, for example, $vertex\#1$ would be colored red. Following the rules, how many colors did you use? (A method that uses the first available item on a list to complete a series of tasks in an example of a greedy algorithm.)