Axis-Parallel Right Angle Crossing Graphs Article Swipe
Patrizio Angelini
,
Michael A. Bekos
,
Julia Katheder
,
Michael Kaufmann
,
Maximilian Pfister
,
Torsten Ueckerdt
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.4230/lipics.esa.2023.9
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.4230/lipics.esa.2023.9
A RAC graph is one admitting a RAC drawing, that is, a polyline drawing in which each crossing occurs at a right angle. Originally motivated by psychological studies on readability of graph layouts, RAC graphs form one of the most prominent graph classes in beyond planarity. In this work, we study a subclass of RAC graphs, called axis-parallel RAC (or apRAC, for short), that restricts the crossings to pairs of axis-parallel edge-segments. apRAC drawings combine the readability of planar drawings with the clarity of (non-planar) orthogonal drawings. We consider these graphs both with and without bends. Our contribution is as follows: (i) We study inclusion relationships between apRAC and traditional RAC graphs. (ii) We establish bounds on the edge density of apRAC graphs. (iii) We show that every graph with maximum degree 8 is 2-bend apRAC and give a linear time drawing algorithm. Some of our results on apRAC graphs also improve the state of the art for general RAC graphs. We conclude our work with a list of open questions and a discussion of a natural generalization of the apRAC model.
Related Topics
Concepts
Combinatorics
Book embedding
Planar graph
Outerplanar graph
Readability
1-planar graph
Generalization
Mathematics
Planarity testing
Graph
Pathwidth
Graph drawing
Discrete mathematics
Computer science
Line graph
Mathematical analysis
Programming language
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.9
- OA Status
- green
- Cited By
- 3
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4382766530
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4382766530Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.4230/lipics.esa.2023.9Digital Object Identifier
- Title
-
Axis-Parallel Right Angle Crossing GraphsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-01-01Full publication date if available
- Authors
-
Patrizio Angelini, Michael A. Bekos, Julia Katheder, Michael Kaufmann, Maximilian Pfister, Torsten UeckerdtList of authors in order
- Landing page
-
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.9Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.9Direct OA link when available
- Concepts
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Combinatorics, Book embedding, Planar graph, Outerplanar graph, Readability, 1-planar graph, Generalization, Mathematics, Planarity testing, Graph, Pathwidth, Graph drawing, Discrete mathematics, Computer science, Line graph, Mathematical analysis, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
3Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1, 2024: 1, 2023: 1Per-year citation counts (last 5 years)
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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