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

Michael Codish, Michael Frank, Avraham Itzhakov and Alice Miller   

Constraints; 21 (3): 375--393, 2016


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 of (3,3,3;13) colorings consisting of 78,892 Ramsey colorings.

Available:    bibtex entry

Related sites:   from the arXiv   from Springer

Michael Codish
The Department of Computer Science
Ben-Gurion University of the Negev
PoB 653, Beer-Sheva, 84105, Israel

© copyright notice