All Questions

Every finite directed graph has a majority coloring with $4$ colors. (The notion of majority coloring is defined below.) Question. Can every infinite directed graph be majority-colored with $4$ ...

For any set $X$ set $[X]^2 = \{\{x,y\}: x,y\in X, x\neq y\}$. If $n\geq 2$ is an integer, we endow $\mathbb{Z}$ with a graph structure in the following way. If $x,y\in \mathbb{Z}^n$ we say $x,y$ are ...