An Upper Bound of $62$ on the Classical Ramsey Number $R(3,3,3,3)$

Abstract

We show that the classical Ramsey number $R(3,3,3,3)$ is no greater than $62$. That is, any edge coloring with four colors of a complete graph on $62$ vertices must contain a monochromatic triangle. Basic notions and a historical overview are given along with the theoretical framework underlying the main result. The algorithms for the computational verification of the result are presented along with a brief discussion of the software tools that were utilized.