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 $9$ 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.

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.

of those classes, then those final exams cannot occur at the same time.

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$).$