\(30 \leq R(3,3,4) \leq 31\)

Konrad Piwakowski1, Stanistaw P. Radziszowski2
1 Department of Foundations of Informatics Technical University of Gdatisk 80-952 Gdatisk, Poland
2 Department of Computer Science Rochester Institute of Technology Rochester, NY 14623, USA

Abstract

With the help of computer algorithms, we improve the upper bound on the classical three-color Ramsey number \(R(3,3,4)\), and thus we show that the exact value of this number
is \(30\) or \(31\).

We also present computer enumeration of all \(3\)-colorings of edges on at least \(14\) vertices without monochromatic triangles.