Given two graphs $G$ and $H$ and a positive integer $k$, the $k$-color Gallai-Ramsey number, denoted by $gr_{ k}(G : H)$, is the minimum integer $N$ such that for all $n \geq N$, every $k$-coloring of the edges of $K_{ n}$ contains either a rainbow copy of $G$ or a monochromatic copy of $H$. We prove that $gr_{ k} (K_{ 3} : C_{ 2\ell + 1}) = \ell \cdot 2^{ k} + 1$ for all $k \geq 1$ and $\ell \geq 3$.
Categories: math.CO