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

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) consisting of 78,892 Ramsey colorings.