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.
CACM August, 1974
Neufeld, G. A.
Tartar, J.
