Flexibility of planar graphs of girth at least six

@article{Dvok2020FlexibilityOP,
  title={Flexibility of planar graphs of girth at least six},
  author={Z. Dvoř{\'a}k and Tom{\'a}{\vs} Masař{\'i}k and Jan Mus{\'i}lek and Ondrej Pangr{\'a}c},
  journal={ArXiv},
  year={2020},
  volume={abs/1902.04069}
}
Let G be a planar graph with a list assignment L. Suppose a preferred color is given for some of the vertices. We prove that if G has girth at least six and all lists have size at least three, then there exists an L-coloring respecting at least a constant fraction of the preferences. 
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