On sufficient conditions for planar graphs to be 5-flexible
Abstract
In this paper, we study the flexibility of two planar graph classes H1, H2, where H1, H2 denote the set of all hopper-free planar graphs and house-free planar graphs, respectively. 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∈ H1 or G∈ H2 such that all lists have size at least 5, then there exists an L-coloring respecting at least a constant fraction of the preferences.
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