4 problems

Let $G$ be a regular graph. Its chromatic number is denoted by $\chi(G)$, and its dynamic chromatic number, the smallest number of colors in a dynamic proper vertex coloring, is de…

Lai et al.'s conjecture.

Dynamic coloring conjecture.

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…