Question 3.116

86. A small college has a mini-session in January (between its regular semesters) in which nine classes are offered: ; , ; ; , , , , . The accompanying table indicates those courses that have students in common.

X X X
X X X
X X X X
X X X
X X X
X X X X
X X X X
X X X X
X X X X
  1. Draw a graph model for the information in this table.
  2. What is the minimum number of time slots in which final examinations can be scheduled for these nine courses?
  3. Can this minimum be achieved if only three rooms are large enough to hold the finals?