The math department plans to offer 10 classes next semester. Some classes cannot run at the same time (perhaps they are taught by the same professor, or are required for seniors). Class:Conflicts with:
A D I
B D I J
C E F I
D A B F
E H I
F I
G J
H E I J
I A B C E F H
J B G H

How many different time slots are needed to teach these classes (and which should be taught at the same time)? More importantly, how could we use graph coloring to answer this question?