Computing the Ramsey number R(4,3,3) using abstraction and symmetry breaking

Codish, M., Frank, M., Itzhakov, A. and Miller, A. (2016) Computing the Ramsey number R(4,3,3) using abstraction and symmetry breaking. Constraints, 21(3), pp. 375-393. (doi: 10.1007/s10601-016-9240-3)

Abstract

The number R(4, 3, 3) is often presented as the unknown Ramsey number with the best chances of being found “soon”. Yet, its precise value has remained unknown for almost 50 years. This paper presents a methodology based on abstraction and symmetry breaking that applies to solve hard graph edge-coloring problems. The utility of this methodology is demonstrated by using it to compute the value R(4, 3, 3) = 30. Along the way it is required to first compute the previously unknown set R(3,3,3;13)R(3,3,3;13) consisting of 78,892 Ramsey colorings.

• Item Type: Articles
• Additional Information: Papers from The 13th International Conference on Integration of Artificial Intelligence and Operations Research Techniques in Constraint Programming, Banff, Canada, May 29–June 1, 2016.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Miller, Professor Alice
• Authors: Codish, M., Frank, M., Itzhakov, A., and Miller, A.
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Constraints
• Publisher: Springer US
• ISSN: 1383-7133
• ISSN (Online): 1572-9354
• Published Online: 10 March 2016
• Copyright Holders: Copyright © 2016 Springer
• First Published: First published in Constraints 21(3):375-393
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher