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DOI: 10.4230/LIPIcs.SoCG.2016.37

Strongly Monotone Drawings of Planar Graphs

Authors: Stefan Felsner, Alexander Igamberdiev, Philipp Kindermann, Boris Klemz, Tamara Mchedlidze, and Manfred Scheucher

Published in: LIPIcs, Volume 51, 32nd International Symposium on Computational Geometry (SoCG 2016)

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.

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Stefan Felsner, Alexander Igamberdiev, Philipp Kindermann, Boris Klemz, Tamara Mchedlidze, and Manfred Scheucher. Strongly Monotone Drawings of Planar Graphs. In 32nd International Symposium on Computational Geometry (SoCG 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 51, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{felsner_et_al:LIPIcs.SoCG.2016.37,
  author =	{Felsner, Stefan and Igamberdiev, Alexander and Kindermann, Philipp and Klemz, Boris and Mchedlidze, Tamara and Scheucher, Manfred},
  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 =	{Fekete, S\'{a}ndor and Lubiw, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2016.37},
  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}
}

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Strongly Monotone Drawings of Planar Graphs

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