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/
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Da Lozzo, Giordano ; Devanny, William E. ; Eppstein, David ; Johnson, Timothy

Square-Contact Representations of Partial 2-Trees and Triconnected Simply-Nested Graphs

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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: Square-Contact Representations, Partial 2-Trees, Simply-Nested Graphs
Collection: 28th International Symposium on Algorithms and Computation (ISAAC 2017)
Issue Date: 2017
Date of publication: 07.12.2017

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