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.
Department, Program, or Center
Center for Advancing the Study of CyberInfrastructure
Ars Combinatoria LXXII (2004) 41-63
RIT – Main Campus