DP-4-colorability of planar graphs without chorded 6-cycles

Prove that every planar graph without chorded 6-cycles is DP-4-colorable, thereby extending the paper’s result from planar graphs avoiding the three forbidden subgraphs in Fig. 4 to the full class of planar graphs without chorded 6-cycles.

Background

The paper establishes DP-4-colorability for planar graphs without any subgraph isomorphic to the three configurations depicted in Fig. 4. These restrictions define a subclass of planar graphs without chorded 6-cycles. The authors explicitly note that their methods do not prove the corresponding statement for all planar graphs without chorded 6-cycles, although earlier work had obtained the result for another restricted subclass.

The unresolved question is whether the restriction to the configurations in Fig. 4 can be removed entirely. A positive answer would show that excluding chorded 6-cycles alone suffices for DP-4-colorability and would complete the broader coloring result suggested by the paper.