Arsenii Sagdeev

Vertex-Ramsey theorems for Cartesian powers of graphs

For graphs $G,H$ and positive integers $r$ and $n$ we write $G^{\square n} \xrightarrow{r} H$ if every $r$-vertex-coloring of the Cartesian power $G^{\square n}$ of $G$ contains a monochromatic copy of $H$. Since chromatic number $\chi$ of $G^{\square n}$ is the same as $\chi(G)$, there is an $r$-vertex coloring of $G^...