License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2020.14
URN: urn:nbn:de:0030-drops-126835
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12683/
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Biedl, Therese ; Chaplick, Steven ; Kaufmann, Michael ; Montecchiani, Fabrizio ; Nöllenburg, Martin ; Raftopoulou, Chrysanthi

Layered Fan-Planar Graph Drawings

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LIPIcs-MFCS-2020-14.pdf (0.7 MB)

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
Collection: 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
Issue Date: 2020
Date of publication: 18.08.2020

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