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DOI: 10.4230/LIPIcs.MFCS.2020.14
URN: urn:nbn:de:0030-drops-126835
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12683/
Biedl, Therese ; Chaplick, Steven ; Kaufmann, Michael ; Montecchiani, Fabrizio ; Nöllenburg, Martin ; Raftopoulou, Chrysanthi
Layered Fan-Planar Graph Drawings
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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.
BibTeX - Entry
@InProceedings{biedl_et_al:LIPIcs:2020:12683,
author = {Therese Biedl and Steven Chaplick and Michael Kaufmann and Fabrizio Montecchiani and Martin N{\"o}llenburg and Chrysanthi Raftopoulou},
title = {{Layered Fan-Planar Graph Drawings}},
booktitle = {45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
pages = {14:1--14:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-159-7},
ISSN = {1868-8969},
year = {2020},
volume = {170},
editor = {Javier Esparza and Daniel Kr{\'a}ľ},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12683},
URN = {urn:nbn:de:0030-drops-126835},
doi = {10.4230/LIPIcs.MFCS.2020.14},
annote = {Keywords: Graph Drawing, Parameterized Complexity, Beyond Planar Graphs}
}
| Keywords: | Graph Drawing, Parameterized Complexity, Beyond Planar Graphs | |
| Seminar: | 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 18.08.2020 |
