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# 3-choosable planar graphs with some precolored vertices and no $$5^{-}$$-cycles normally adjacent to $$8^{-}$$-cycles

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### Abstract

DP-coloring was introduced by Dvo\v{r}\'{a}k and Postle [J. Combin. Theory Ser. B 129 (2018) 38--54] as a generalization of list coloring. They used a "weak" version of DP-coloring to solve a longstanding conjecture by Borodin, stating that every planar graph without cycles of length $$4$$ to $$8$$ is $$3$$-choosable. Liu and Li improved the result by showing that every planar graph without adjacent cycles of length at most $$8$$ is $$3$$-choosable. In this paper, it is showed that every planar graph without $$5^{-}$$-cycles normally adjacent to $$8^{-}$$-cycles is $$3$$-choosable. Actually, all these three papers give more stronger results by stating them in the form of "weakly" DP-$$3$$-coloring and color extension.

### Most cited references8

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### Every Planar Graph Is 5-Choosable

(1994)
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### 3-List-Coloring Planar Graphs of Girth 5

(1995)
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• Record: found

### Colorings of plane graphs: A survey

(2013)
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### Author and article information

###### Journal
13 August 2019
###### Article
1908.04902