Geodesic
Planar L-Drawings of Bimodal Graphs
Journal of Graph Algorithms and Applications, Special issue on Selected papers from the Twenty-eighth International Symposium on Graph Drawing and Network Visualization, GD 2020 , Tome 26 (2022) no. 3, pp. 307-334.

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In a planar L-drawing of a directed graph (digraph) each edge $e$ is represented as a polyline composed of a vertical segment starting at the tail of $e$ and a horizontal segment ending at the head of $e$. Distinct edges may overlap, but not cross. Our main focus is on bimodal graphs, i.e., digraphs admitting a planar embedding in which the incoming and outgoing edges around each vertex are contiguous. We show that every plane bimodal graph without 2-cycles admits a planar L-drawing. This includes the class of upward-plane graphs. Bimodal graphs with 2-cycles admit a planar L-drawing if the underlying undirected graph with merged 2-cycles is a planar 3-tree. Finally, outerplanar digraphs admit a planar L-drawing - although they do not always have a bimodal embedding - but not necessarily with an outerplanar embedding.
DOI : 10.7155/jgaa.00596
Keywords: Planar L-Drawings, Directed Graphs, Bimodality 
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Patrizio Angelini; Steven Chaplick; Sabine Cornelsen; Giordano Da Lozzo. Planar L-Drawings of Bimodal Graphs. Journal of Graph Algorithms and Applications, 
							Special issue on Selected papers from the Twenty-eighth International Symposium on Graph Drawing and Network Visualization, GD 2020
					, Tome 26 (2022) no. 3, pp. 307-334. doi : 10.7155/jgaa.00596. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00596/

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