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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2017.34
URN: urn:nbn:de:0030-drops-82234
URL: http://drops.dagstuhl.de/opus/volltexte/2017/8223/
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Fulek, Radoslav

Embedding Graphs into Embedded Graphs

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LIPIcs-ISAAC-2017-34.pdf (0.6 MB)


Abstract

A (possibly degenerate) drawing of a graph G in the plane is approximable by an embedding if it can be turned into an embedding by an arbitrarily small perturbation. We show that testing, whether a drawing of a planar graph G in the plane is approximable by an embedding, can be carried out in polynomial time, if a desired embedding of G belongs to a fixed isotopy class, i.e., the rotation system (or equivalently the faces) of the embedding of G and the choice of outer face are fixed. In other words, we show that c-planarity with embedded pipes is tractable for graphs with fixed embeddings. To the best of our knowledge an analogous result was previously known essentially only when G is a cycle.

BibTeX - Entry

@InProceedings{fulek:LIPIcs:2017:8223,
  author =	{Radoslav Fulek},
  title =	{{Embedding Graphs into Embedded Graphs}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{34:1--34:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Yoshio Okamoto and Takeshi Tokuyama},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8223},
  URN =		{urn:nbn:de:0030-drops-82234},
  doi =		{10.4230/LIPIcs.ISAAC.2017.34},
  annote =	{Keywords: Graph embedding, C-planarity, Weakly simple polygons}
}

Keywords: Graph embedding, C-planarity, Weakly simple polygons
Seminar: 28th International Symposium on Algorithms and Computation (ISAAC 2017)
Issue Date: 2017
Date of publication: 04.12.2017


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