4 problems

Let $\mathcal F$ be a family of graphs and let $k$ be a positive integer. Say that $\mathcal F$ has exponentially many $\mathbb Z_k$-colorings if there is a constant $c>1$ such tha…

Edge group choosability conjecture. Every graph with maximum degree $\Delta$ is $(\Delta+1)$-edge group choosable.

Weak total group coloring conjecture. For every graph $G$,

Total group choice equality conjecture. For every graph $G$,