Graph coloring is an important aspect of graph theory with great application in University timetable scheduling. The examination timetable scheduling maximizes the time and minimizes resources (venue and invigilators) to give effective output of the event. The constraint based approach method is implemented in scheduling examination timetable for Faculty of Science, Federal University Lokoja. Then the results on thirteen (13) departments give a 3-timeslot within twelve (12) days examination period with no students having two (2) examinations per day. In all, there is no conflict of venues and courses thereby giving an efficient scheduling process for the entire examination.