A mathematical model for a simplified version of a time schedule for classes was devised and studied. An explanation of the problem in terms of Boolean algebra is presented. The problem is restated in terms of graph theory, showing that the problem is the same as that of finding the chromatic number of a given graph. An attempt is made to gain insight into a solution of this problem by studying all graphs of order six and less, which are tabulated along with certain of their attributes. Random graphs of higher order are then studied. The digital computer is used to find the number of complete subgraphs of every order within each graph examined.