3 problems

Jaeger–Linial–Payan–Tarsi's $\mathbb Z_3$-Group Connectivity Conjecture. Every $5$-edge-connected graph is $\mathbb Z_3$-connected.

Group-flow conjecture. Every flow-admissible signed graph has a nowhere-zero $A$-flow for every abelian group $A$ with $|A|\geq 6$.

Let $G$ be a graph. Write … The graph $G$ is $\mathbb Z_{3}$-connected if, for every $b\in Z(G,\mathbb Z_{3})$, there is an orientation $D$ such that … for every vertex $v\in V(G)$…