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DP-4-coloring of planar graphs with some restrictions on cycles

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arxiv 1909.08511 v2 pith:AEKSUGHG submitted 2019-09-17 math.CO cs.DM

Rui Li , Tao Wang This is my paper · ORCID
classification math.COcs.DM
keywords planarcyclesgraphactuallyborodinchoosablecolorcoloring
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DP-coloring was introduced by Dvo\v{r}\'{a}k and Postle as a generalization of list coloring. It was originally used to solve a longstanding conjecture by Borodin, stating that every planar graph without cycles of lengths 4 to 8 is 3-choosable. In this paper, we give three sufficient conditions for a planar graph to be DP-4-colorable. Actually all the results (Theorem 1.3, 1.4 and 1.7) are stated in the ``color extendability'' form, and uniformly proved by vertex identification and discharging method.

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  1. Planar graphs without normally adjacent short cycles

    math.CO 2019-08 conditional novelty 6.0 of 10

    Every planar graph with no triangles normally adjacent to 8−-cycles, no 4-cycles normally adjacent to 6−-cycles, and no normally adjacent 5-cycles is 3-choosable.

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