Constructive Lower Bounds on Classical Multicolor Ramsey Numbers

Xu Xiaodong, Xie Zheng, Geoffrey Exoo, Stanisław P. Radziszowski

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.


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