New upper bound for multicolor Ramsey number of odd cycles

Qizhong Lin, Weiji Chen

Let $r_k(C_{2m+1})$ be the $k$-color Ramsey number of an odd cycle $C_{2m+1}$ of length $2m+1$. It is shown that for each fixed $m\ge 2$, \[r_k(C_{2m+1})<c^{k}\sqrt{k!}\] for all su…