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Flexibility of planar graphs of girth at least six (1902.04069v1)
Published 11 Feb 2019 in math.CO and cs.DM
Abstract: 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.