1. Solving a scheduling problem such as the one that follows can be accomplished by constructing a related graph and then coloring it in a way that adjacent vertices have different colors. Explore the problem of graph coloring in the Graph Coloring applet.

2. A mathematics department has seven faculty committees—$A$, $B$, $C$, $D$, $E$, $F$, and $G$, Because there is overlap in the composition of the committees, the chairman of the department is attempting to work out a schedule that will avoid conflicts among the committees. The accompanying chart indicates the overlapping committee structure. Help the chairman arrange a schedule without conflicts in the Scheduling applet.