2 problems

Improper coloring conjecture for toroidal graphs. Every toroidal graph is $(0,0,0,3)$-colorable.

Let $G$ be a graph and let $d$ be a nonnegative integer. Let $\chi^d(G)$ and $\chi_l^d(G)$ denote respectively the $d$-improper chromatic number and the $d$-improper list chromatic…