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Special issue on Selected papers from the Twenty-eighth International Symposium on Graph Drawing and Network Visualization, GD 2020
DOI: 10.7155/jgaa.00596
Planar L-Drawings of Bimodal Graphs
Vol. 26, no. 3, pp. 307-334, 2022. Regular paper.
Abstract 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.
This work is licensed under the terms of the CC-BY license.
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Submitted: October 2020.
Reviewed: May 2022.
Revised: May 2022.
Accepted: May 2022.
Final: June 2022.
Published: June 2022.
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