Planar L-Drawings of Bimodal Graphs

Patrizio Angelini; Steven Chaplick; Sabine Cornelsen; Giordano Da Lozzo

doi:10.7155/JGAA.00596

Planar L-Drawings of Bimodal Graphs

Patrizio Angelini^*, Steven Chaplick, Sabine Cornelsen, Giordano Da Lozzo

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	307-334
Journal	Journal of Graph Algorithms and Applications
Volume	26
Issue number	3
DOIs	https://doi.org/10.7155/JGAA.00596
Publication status	Published - 2022

Access to Document

10.7155/JGAA.00596Licence: CC BY

https://dblp.org/rec/journals/jgaa/AngeliniCCL22

1 Conference article in proceeding
1 Preprint

Planar L-Drawings of Bimodal Graphs
Angelini, P., Chaplick, S., Cornelsen, S. & Lozzo, G. D., 2021, Graph Drawing and Network Visualization. GD 2020. Auber, D. & Valtr, P. (eds.). Springer, Cham, Vol. 12590. p. 205-219 (Lecture Notes in Computer Science, Vol. 12590).
Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Open Access
Planar L-Drawings of Bimodal Graphs
Angelini, P., Chaplick, S., Cornelsen, S. & Lozzo, G. D., 2020, 28 p.
Research output: Working paper / Preprint › Preprint

Cite this

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title = "Planar L-Drawings of Bimodal Graphs",

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.",

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