Flexibility of planar graphs of girth at least six

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.

Keywords

• Flexibility
• planar
• graphs
• girth
• least
• six