You will be representing a map by a graph and finding the coloring of the graph that uses the fewest number of colors. Complete the following tasks:

Part 1:

1. Find the county map of New Hampshire, and create a graph that represents it.Counties should be represented as the vertices and the edges should be drawn between them when two counties share a border.
2. Determine if your graph is 2-colorable, 3-colorable, or 4-colorable.
3. Discuss how you found your answer to part (b) and what real-world applications there might be for your findings.

Part 2:

1. Draw a map of a fictional state consisting of four counties that is 3-colorable.
2. Discuss your method for creating the map in part (a). Be sure to explain how you verified that your map is indeed 3-colorable.