Applications of Four Color Theorem
Explanation of the graph coloring problem stated above:

So each vertex represents a class. Each edge represents a timing conflict between two classes. Suppose there was a graph with 4 vertices and a single edge between two. This would require only 2 colors, which translates to two time slots. Draw this graph. Write out a few scenarios of class schedules and draw their corresponding graphs to get a better idea. Answer the question on whether or not these graphs are planar. If so, what does that mean w.r.t. the four color theorem?