Question: In Example, we had a busy city street that intersected a one-way street. Suppose the traffic signal includes a protected left turn, and remodel the traffic pattern as a graph. How many vertex colors are needed for this graph? Is that more colors, fewer colors, or the same number of colors as was needed before? Now, look at your graph. Can you change the coloring (but still keep it proper) so that traffic flow will improve?
Example: Imagine, if you will, a road intersection with a traffic light. Every so often the traffic light changes, and after a while, the pattern of greens and reds and yellows on the traffic light repeats. This is a traffic-light cycle.