2619	 Graph Coloring Conditions for the Existence of Solutions to the Timetable Problem	 A necessary and sufficient condition is presented for the existence of a solution to the Gotlieb class-teacher timetable problem. Several relationships are established between the class-teacher timetable problem and graphs with preconditions. These preconditions place additional restrictions on the coloration of a graph. The preconditions correspond to the unavailability constraints and preassigned meetings in the class-teacher timetable problem. Using some recent results that convert graphs with preconditions to graphs without them it is shown that the existence of a coloration of a graph is the required necessary and sufficient condition. graphs coloration preassignment prevention of assignment class-teacher timetables
