DP-4-colorability conjecture for planar graphs without chorded 6-cycles
DP-4-colorability conjecture for planar graphs without chorded 6-cycles
Let be a planar graph, and suppose that contains no chorded -cycle, meaning no cycle of length six with an edge joining two nonconsecutive vertices on the cycle. A graph is DP--colorable if every cover of admits a DP-coloring with four colors.
DP-4-colorability conjecture. Every planar graph without chorded -cycles is DP--colorable.
The preceding results establish DP--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 -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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