DP-4-colorability conjecture for planar graphs without chorded 6-cycles

Let GG be a planar graph, and suppose that GG contains no chorded 66-cycle, meaning no cycle of length six with an edge joining two nonconsecutive vertices on the cycle. A graph is DP-44-colorable if every cover of GG admits a DP-coloring with four colors.

DP-4-colorability conjecture. Every planar graph without chorded 66-cycles is DP-44-colorable.

The preceding results establish DP-44-colorability for a narrower class of planar graphs excluding specified configurations, but the paper does not prove the conjecture for all planar graphs without chorded 66-cycles.

Sources & referencesView supporting material

Primary source

Huihui Fang, Danjun Huang, Tao Wang and Weifan Wang, “Variable degeneracy of planar graphs without chorded 6-cycles”, arXiv:2502.18089 (2025).

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