Graph coloring conditions for the existence of solutions to the timetable problem

Authors:
G. A. Neufeld;J. Tartar
Affiliations:
Univ. of Alberta, Edmonton, Alta., Canada;Univ. of Alberta, Edmonton, Alta., Canada
Venue:
Communications of the ACM
Year:
1974

Citing 3
Cited 11

Some Results Concerning the Reduction of Binary Matrices

Journal of the ACM (JACM)
Matrix reduction using the Hungarian method for the generation of school timetables

Communications of the ACM
Algorithm 286: Examination scheduling

Communications of the ACM

ACM forum

Communications of the ACM
A Survey of Automated Timetabling

Artificial Intelligence Review
Current Approaches for Solving Over-Constrained Problems

Constraints
Current Approaches for Solving Over-Constrained Problems

Constraints
A Constructive Evolutionary Approach to School Timetabling

Proceedings of the EvoWorkshops on Applications of Evolutionary Computing
Graph Colouring by Maximal Evidence Edge Adding

PATAT '00 Selected papers from the Third International Conference on Practice and Theory of Automated Timetabling III
Solving a School Timetabling Problem Using a Bee Algorithm

MICAI '08 Proceedings of the 7th Mexican International Conference on Artificial Intelligence: Advances in Artificial Intelligence
School timetabling for quality student and teacher schedules

Journal of Scheduling
Very large-scale neighborhood search techniques in timetabling problems

PATAT'06 Proceedings of the 6th international conference on Practice and theory of automated timetabling VI
Tabu search techniques for large high-school timetabling problems

AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Three heuristics to solve Timetabling

ICCOM'06 Proceedings of the 10th WSEAS international conference on Communications

Quantified Score

Hi-index	48.23

Visualization

Abstract

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.