Weakly and Strongly Fan-Planar Graphs

Abstract

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.

Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023)