A sufficient condition for planar graphs to be DP-4-colorable

Abstract

In 2017, Dvořák and Postle introduced DP-coloring (known as correspondence coloring) as a generalization of list coloring. Recently, a lot of attention has been put on sufficient conditions for planar graphs to be DP-4-colorable. Liu et al. [17] proved that every planar graph without triangles adjacent to cycles of length five is DP-4-colorable. Let  be the family of planar graphs without 3-cycles adjacent to two cycles of length five. In this paper, we prove that every member in  is DP-4-colorable, which generalizes a result of [17]. As a consequence, every graph in  is 4-choosable.