4 problems

Wong and Zhu's conjecture. For any graph $G$,

Wong and Zhu's conjecture. Every graph with no isolated edges is $(1,3)$-choosable.

The 1-2-Conjecture. For every graph $G$, there is a weighting $\omega:E(G)\cup V(G)\to\{1,2\}$ such that the induced total vertex weights properly color $V(G)$.

The 1-2-3-Conjecture. For every graph $G$ without isolated edges, there is a weighting $\omega:E(G)\to\{1,2,3\}$ such that the induced vertex weights properly color $V(G)$.