LIPIcs.MFCS.2020.14.pdf
- Filesize: 0.72 MB
- 13 pages
Document
Layered Fan-Planar Graph Drawings
Authors
Therese Biedl 
,
Steven Chaplick ,
Michael Kaufmann ,
Fabrizio Montecchiani ,
Martin Nöllenburg ,
Chrysanthi Raftopoulou
-
Part of:
Volume:
45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Mathematical Foundations of Computer Science (MFCS) - License:
Creative Commons Attribution 3.0 Unported license
- Publication date: 2020-08-18
File
Document Identifiers
Author Details
Acknowledgements
Research initiated while Fabrizio Montecchiani was visiting the University of Waterloo and continued at the Bertinoro Workshop on Graph Drawing 2018.
Cite AsGet BibTex
Therese Biedl, Steven Chaplick, Michael Kaufmann, Fabrizio Montecchiani, Martin Nöllenburg, and Chrysanthi Raftopoulou. Layered Fan-Planar Graph Drawings. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 14:1-14:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.MFCS.2020.14
https://doi.org/10.4230/LIPIcs.MFCS.2020.14
Abstract
In a fan-planar drawing of a graph an edge can cross only edges with a common end-vertex. In this paper, we study fan-planar drawings that use h (horizontal) layers and are proper, i.e., edges connect adjacent layers. We show that if the embedding of the graph is fixed, then testing the existence of such drawings is fixed-parameter tractable in h, via a reduction to a similar result for planar graphs by Dujmović et al. If the embedding is not fixed, then we give partial results for h = 2: It was already known how to test the existence of fan-planar proper 2-layer drawings for 2-connected graphs, and we show here how to test this for trees. Along the way, we exhibit other interesting results for graphs with a fan-planar proper h-layer drawing; in particular we bound their pathwidth and show that they have a bar-1-visibility representation.
Subject Classification
ACM Subject Classification
- Theory of computation → Computational geometry
- Mathematics of computing → Graph algorithms
Keywords
- Graph Drawing
- Parameterized Complexity
- Beyond Planar Graphs
Metrics
- Access Statistics
-
Total Accesses (updated on a weekly basis)
0PDF Downloads
References
- T. Biedl. Height-preserving transformations of planar graph drawings. In C. Duncan and A. Symvonis, editors, Graph Drawing (GD'14), volume 8871 of LNCS, pages 380-391. Springer, 2014. URL: https://doi.org/10.1007/978-3-662-45803-7_32.
- Carla Binucci, Markus Chimani, Walter Didimo, Martin Gronemann, Karsten Klein, Jan Kratochvíl, Fabrizio Montecchiani, and Ioannis G. Tollis. Algorithms and characterizations for 2-layer fan-planarity: From caterpillar to stegosaurus. J. Graph Algorithms Appl., 21(1):81-102, 2017. URL: https://doi.org/10.7155/jgaa.00398.
- Walter Didimo, Giuseppe Liotta, and Fabrizio Montecchiani. A survey on graph drawing beyond planarity. ACM Comput. Surv., 52(1):4:1-4:37, 2019. URL: https://doi.org/10.1145/3301281.
- V. Dujmović, M. Fellows, M. Kitching, G. Liotta, C. McCartin, N. Nishimura, P. Ragde, F. Rosamond, S. Whitesides, and D. Wood. On the parameterized complexity of layered graph drawing. Algorithmica, 52:267-292, 2008. URL: https://doi.org/10.1007/s00453-007-9151-1.
- S. Felsner, G. Liotta, and S. Wismath. Straight-line drawings on restricted integer grids in two and three dimensions. J. Graph Algorithms Appl., 7(4):335-362, 2003. URL: https://doi.org/10.7155/jgaa.00075.
- L.S. Heath and A.L. Rosenberg. Laying out graphs using queues. SIAM Journal on Computing, 21(5):927-958, 1992. URL: https://doi.org/10.1137/0221055.
- Michael Kaufmann and Torsten Ueckerdt. The density of fan-planar graphs. CoRR, abs/1403.6184, 2014. URL: http://arxiv.org/abs/1403.6184.
- Stephen G. Kobourov, Giuseppe Liotta, and Fabrizio Montecchiani. An annotated bibliography on 1-planarity. Computer Science Review, 25:49-67, 2017. URL: https://doi.org/10.1016/j.cosrev.2017.06.002.
-
M. Schaefer. Crossing Numbers of Graphs. CRC Press, 2018.
- M. Suderman. Pathwidth and layered drawings of trees. Intl. J. Comp. Geom. Appl., 14(3):203-225, 2004. URL: https://doi.org/10.1142/S0218195904001433.