Planar graphs having no cycle of length $4$, $6$ or $8$ are DP-3-colorable (2412.19059v1)

Abstract: The concept of DP-coloring of graphs was introduced by Dvo\v{r}\'{a}k and Postle, and was used to prove that planar graphs without cycles of length from $4$ to $8$ are $3$-choosable. In the same paper, they proposed a more natural and stronger claim that such graphs are DP-$3$-colorable. This paper confirms that claim by proving a stronger result that planar graphs having no cycle of length $4$, $6$ or $8$ are DP-3-colorable.