LIPIcs.MFCS.2020.14.pdf
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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
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Acknowledgements
Research initiated while Fabrizio Montecchiani was visiting the University of Waterloo and continued at the Bertinoro Workshop on Graph Drawing 2018.
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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
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References
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