Algorithms and Characterizations for 2-Layer Fan-planarity: From Caterpillar to Stegosaurus
Journal of Graph Algorithms and Applications, Special Issue on Selected papers from the Twenty-third International Symposium on Graph Drawing and Network Visualization, GD 2015 , Tome 21 (2017) no. 1, pp. 81-102.

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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.
DOI : 10.7155/jgaa.00398
Keywords: graph drawings, layered drawings, 2-layer drawings, fan planarity
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Carla Binucci; Markus Chimani; Walter Didimo; Martin Gronemann; Karsten Klein; Jan Kratochvíl; Fabrizio Montecchiani; Ioannis Tollis. Algorithms and Characterizations for 2-Layer Fan-planarity: From Caterpillar to Stegosaurus. Journal of Graph Algorithms and Applications, 
							Special Issue on Selected papers from the Twenty-third International Symposium on Graph Drawing and Network Visualization, GD 2015
					, Tome 21 (2017) no. 1, pp. 81-102. doi : 10.7155/jgaa.00398. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00398/

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