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.

翻译：我们研究了(Cheong 等, GD22)提出的两种扇平面性概念，分别称为弱扇平面性和强扇平面性，它们分离了文献中两种不等价的扇平面性定义。我们证明并非每个弱扇平面图都是强扇平面图，而这两个图族在边密度上的上界相同。