Constructive Lower Bounds on Classical Multicolor Ramsey Numbers

Abstract

This paper studies lower bounds for classical multicolor Ramsey numbers, first by giving a short overview of past results, and then by presenting several general constructions establishing new lower bounds for many diagonal and off-diagonal multicolor Ramsey numbers. In particular, we improve several lower bounds for $R_k(4)$ and $R_k(5)$ for some small $k$, including $415 \le R_3(5)$, $634 \le R_4(4)$, $2721 \le R_4(5)$, $3416 \le R_5(4)$ and $26082 \le R_5(5)$. Most of the new lower bounds are consequences of general constructions.