Weakly and Strongly Fan-Planar Graphs

08/17/2023

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by   Otfried Cheong, et al.

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We study two notions of fan-planarity introduced by (Cheong et al., GD22), called weak and strong fan-planarity, which separate two non-equivalent definitions of fan-planarity in the literature. We prove that not every weakly fan-planar graph is strongly fan-planar, while the upper bound on the edge density is the same for both families.