This is a scheduling problem that involves graph coloring.

A small college has a summer school session that offers $12$ courses. An $"x"$ on the chart below

shows which courses have students in common. There are time slots available each day

$($Monday$,$ Tuesday, Wednesday, Thursday, Friday, and Saturday$)$ to schedule final exams. The

college wishes to schedule the $12$ final exams over as few days as possible without creating

conflicts for the students scheduled to take them. It is OK to have more than one exam

scheduled on the same day, as long as the courses do not have any students in common, e$.$g$.$

Algebra and Chemistry could both have their final exams on Monday since they do not have any

students in common.

The courses are coded as follows:

A is algebra, B is biology, C is chemistry, D is design, $E$ is economics, $F$ is French, $G$ is

government, $H$ is history, I is Italian, $J$ is journalism, $K$ is Korean, $L$ is literature

Read the instructions on the next page.

Draw a graph below that represents this situation to help you solve the problem.

Vertices represent the courses. Label the vertices with the letter of the courses.

Edges represent courses with students in common. Connect $2$ vertices if the courses they

represent have students in common.

Colors represent

Color the graph to help you determine when to schedule the final exams. Follow the rules for

graph coloring and use as few colors as possible. PLEASE USE COLORS and not the letters or

names of colors.

Draw your graph below and color it$.$ Make sure to label the vertices with the names of the

courses.

Write your final exam schedule $($which courses are taking the exam on which days$),$

according to your graph coloring.