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.