We begin by making a graph using the data in the table. Draw the following graph on a piece of paper. In our graph, each vertex represents one of the classes. Two vertices are connected if there is a student taking both of those classes. Note that if a student is taking both of those classes, then those final exams cannot occur at the same time. D E C G F A Use the graph you drew to determine what is the minimum number of final exam times slots needed so that the people can take all of their final exams. (Hint: Would a vertex coloring or an edge coloring be more useful here?) In the following table, indicate in which final exam time slot each class could be placed (i.e. 1,2, etc). Religion French Astronomy Ethics History Underwater Basket Weaving Journalism Graph theory can be used to help solve many real world problems. For example, we can use graph colorings to help us solve situations like the one described below. There are 7 people enrolled in the Extended Learning classes as part of a summer study abroad program. They are taking the classes as shown in the table. Noel Hans Elsie Gene Mica Ethics, Journalism Journalism, Underwater Basket Weaving, Religion Astronomy, Religion, French, History Underwater Basket Weaving, Astronomy, French Ethics, Religion Ollie Ethics, Journalism, Underwater Basket Weaving, Astronomy Jamie French, Religion The host university needs to schedule final exams for these students and would like to use the minimum number of time slots required. We can use graph theory to help us analyze this situation. We begin by making a graph using the data in the table. Draw the following graph on a piece of paper. In our graph, each vertex represents one of the classes. Two vertices are connected if there is a student taking both of those classes. Note that if a student is taking both of those classes, then those final exams cannot occur at the same time. A E F G A Use the graph you drew to determine what is the minimum number of final exam times slots needed so that the people can take all of their final exams. (Hint: Would a vertex coloring or an edge coloring be more useful here?)