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.ISAAC.2017.34
URN: urn:nbn:de:0030-drops-82234
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8223/
Fulek, Radoslav
Embedding Graphs into Embedded Graphs
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}
}
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Keywords: |
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Graph embedding, C-planarity, Weakly simple polygons |
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Collection: |
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28th International Symposium on Algorithms and Computation (ISAAC 2017) |
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Issue Date: |
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2017 |
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Date of publication: |
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07.12.2017 |
