Algorithms and Characterizations for 2-Layer Fan-planarity: From Caterpillar to Stegosaurus - Binucci, Carla; Chimani, Markus; Didimo, Walter; Gronemann, Martin; Klein, Karsten; Kratochvíl, Jan; Montecchiani, Fabrizio; Tollis, Ioannis (Journal of Graph Algorithms and Applications, 2017)
In a fan-planar drawing of a graph there is no edge that crosses two other independent edges. We study 2-layer fan-planar drawings, i.e., fan-planar drawings such that the vertices are restricted to two distinct horizontal layers and edges are straight-line segments that connect vertices of different layers. We characterize 2-layer fan-planar drawable graphs and describe a linear-time testing and embedding algorithm for biconnected graphs. We also study the relationship between 2-layer fan-planar graphs and 2-layer right-angle crossing graphs.