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.2017.24
URN: urn:nbn:de:0030-drops-82675
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8267/
Da Lozzo, Giordano ;
Devanny, William E. ;
Eppstein, David ;
Johnson, Timothy
Square-Contact Representations of Partial 2-Trees and Triconnected Simply-Nested Graphs
Abstract
A square-contact representation of a planar graph G = (V,E) maps vertices in V to interior-disjoint axis-aligned squares in the plane and edges in E to adjacencies between the sides of the corresponding squares. In this paper, we study proper square-contact representations of planar graphs, in which any two squares are either disjoint or share infinitely many points.
We characterize the partial 2-trees and the triconnected cycle-trees allowing for such representations. For partial 2-trees our characterization uses a simple forbidden subgraph whose structure forces a separating triangle in any embedding. For the triconnected cycle-trees, a subclass of the triconnected simply-nested graphs, we use a new structural decomposition for the graphs in this family, which may be of independent interest. Finally, we study square-contact representations of general triconnected simply-nested graphs with respect to their outerplanarity index.
BibTeX - Entry
@InProceedings{dalozzo_et_al:LIPIcs:2017:8267,
author = {Giordano Da Lozzo and William E. Devanny and David Eppstein and Timothy Johnson},
title = {{Square-Contact Representations of Partial 2-Trees and Triconnected Simply-Nested Graphs}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {24:1--24:14},
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/2017/8267},
URN = {urn:nbn:de:0030-drops-82675},
doi = {10.4230/LIPIcs.ISAAC.2017.24},
annote = {Keywords: Square-Contact Representations, Partial 2-Trees, Simply-Nested Graphs}
}
Keywords: |
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Square-Contact Representations, Partial 2-Trees, Simply-Nested Graphs |
Collection: |
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28th International Symposium on Algorithms and Computation (ISAAC 2017) |
Issue Date: |
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2017 |
Date of publication: |
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07.12.2017 |