Three-color online Ramsey numbers $\tilde{r}(P_3,P_3,P_{\ell })$ and $\tilde{r}(P_3,P_3,C_{\ell })$

Hexuan Zhi, Yanbo Zhang

For given graphs $G_1,\dots ,G_k$, let $\tilde{r}(G_1,\dots ,G_k)$ denote their online Ramsey number. In an influential paper on the online Ramsey numbers for paths and cycles,…