DP-coloring for planar graphs of diameter two

TL;DR

This paper proves that planar graphs with diameter at most two are DP-4-colorable, extending previous results on their 4-choosability, and broadening understanding of coloring properties in such graphs.

Contribution

It establishes that planar graphs with diameter two are DP-4-colorable, generalizing known 4-choosability results to the DP-coloring framework.

Findings

Planar graphs with diameter at most two are DP-4-colorable.

Extension of previous 4-choosability results to DP-coloring.

Provides new insights into coloring properties of diameter-restricted planar graphs.

Abstract

DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced by Dvo\u{r}\'{a}k and Postle (2017). Recently, Huang et al. [https://doi.org/10.1016/j.amc.2019.124562] showed that planar graphs with diameter at most two are $4$-choosable. In this paper, we will prove that planar graphs with diameter at most two are DP-$4$-colorable, which is an extension of the above result.