sed 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 8 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 Mica Psychology Game Design Beatrix Psychology Literature Jamie Sociology Literature Psychology Game Design Hans Farah Callie Ignacio Landry Ethics Sociology Psychology Business Literature Journalism 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 D Business Psychology Game Design Sociology Literature Ethics 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 E C F B G 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 Psychology Sociology Ethics In the following table indicate in which final exam time slot each class could be placed i e 1 2 etc