Solving graph coloring problems with abstraction and symmetry

Codish, M., Miller, A. , Frank, M. and Itzhakov, A. (2015) Solving graph coloring problems with abstraction and symmetry. In: Fifth International Workshop on the Cross-Fertilization Between CSP and SAT, Cork, Ireland, 31 Aug 2015,

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Abstract

This paper introduces a general methodology, based on abstraction and symmetry, that applies to solve hard graph edge-coloring problems and demonstrates its use to provide further evidence that the Ramsey number R(4; 3; 3) = 30. 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 more than 50 years. We illustrate our approach by showing that: (1) there are precisely 78,892 (3; 3; 3; 13) Ramsey colorings; and (2) if there exists a (4; 3; 3; 30) Ramsey coloring then it is (13,8,8) regular. Specifically each node has 13 edges in the first color, 8 in the second, and 8 in the third. We conjecture that these two results will help provide a proof that no (4; 3; 3; 30) Ramsey coloring exists implying that R(4; 3; 3) = 30.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Miller, Dr Alice
Authors: Codish, M., Miller, A., Frank, M., and Itzhakov, A.
College/School:College of Science and Engineering > School of Computing Science
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