An improved upper bound for Ramsey number \(R(3,3,3,3;2)\) (Q1893181)

The author shows that any 4-colouring of the edges of \(K_{65}\) must contain a monochromatic triangle. Thus \(R(3,3,3,3; 2)\leq 64\). (The previous upper bound was 65.) It is known that \(R(3,3,3,3; 2)\geq 51\); that is, \(K_{50}\) can be 4-coloured with no monochromatic triangle.