Represent the map by a graph and then find a coloring of the graph that uses the least possible number of colors. (Green) Green Yellow Blue Blue Blue da da Red Red Red Red (Green) (Green) Blue Blue Red (Green) Yellow Yellow (Green) Red Blue (Green Yellow Blue Red (Green) Red Blue Blue Red Blue Green

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