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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.SoCG.2016.37
URN: urn:nbn:de:0030-drops-59292
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/5929/
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Felsner, Stefan ; Igamberdiev, Alexander ; Kindermann, Philipp ; Klemz, Boris ; Mchedlidze, Tamara ; Scheucher, Manfred

Strongly Monotone Drawings of Planar Graphs

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LIPIcs-SoCG-2016-37.pdf (0.6 MB)

Abstract

A straight-line drawing of a graph is a monotone drawing if for each pair of vertices there is a path which is monotonically increasing in some direction, and it is called a strongly monotone drawing if the direction of monotonicity is given by the direction of the line segment connecting the two vertices.

We present algorithms to compute crossing-free strongly monotone drawings for some classes of planar graphs; namely, 3-connected planar graphs, outerplanar graphs, and 2-trees. The drawings of 3-connected planar graphs are based on primal-dual circle packings. Our drawings of outerplanar graphs depend on a new algorithm that constructs strongly monotone drawings of trees which are also convex. For irreducible trees, these drawings are strictly convex.

BibTeX - Entry

@InProceedings{felsner_et_al:LIPIcs:2016:5929,
  author =	{Stefan Felsner and Alexander Igamberdiev and Philipp Kindermann and Boris Klemz and Tamara Mchedlidze and Manfred Scheucher},
  title =	{{Strongly Monotone Drawings of Planar Graphs}},
  booktitle =	{32nd International Symposium on Computational Geometry (SoCG 2016)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-009-5},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{51},
  editor =	{S{\'a}ndor Fekete and Anna Lubiw},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5929},
  URN =		{urn:nbn:de:0030-drops-59292},
  doi =		{10.4230/LIPIcs.SoCG.2016.37},
  annote =	{Keywords: graph drawing, planar graphs, strongly monotone, strictly convex, primal-dual circle packing}
}

Keywords: graph drawing, planar graphs, strongly monotone, strictly convex, primal-dual circle packing
Collection: 32nd International Symposium on Computational Geometry (SoCG 2016)
Issue Date: 2016
Date of publication: 10.06.2016

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