6 problems

Lai et al.'s conjecture.

Let $G$ be a graph. The $2$-dynamic choosability of $G$, denoted by $\operatorname{ch}_2(G)$, is the least positive integer $k$ such that a $2$-dynamic coloring can be chosen from…

Dynamic coloring conjecture.

Let $G$ be a graph, with maximum and minimum degrees denoted by $\Delta(G)$ and $\delta(G)$, respectively. Let $\chi(G)$ be its chromatic number and $\chi_2(G)$ its dynamic chromat…

Let $G$ be a regular graph with chromatic number $\chi(G)\geq 4$. Its dynamic chromatic number is denoted by $\chi_2(G)$. Ahadi et al.'s conjecture. The chromatic number and dynami…

Let $G$ be a nontrivial connected graph. Write $\Delta(G)$ and $\delta(G)$ for its maximum and minimum degrees, respectively, and let $\chi(G)$ and $\chi_2(G)$ denote its chromatic…