Flexibility of planar graphs of girth at least six

Zdeněk Dvořák, Tomáš Masařík, Jan Musílek, Ondřej Pangrác

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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