Touching triangle representations for 3-connected planar graphs

Stephen G Kobourov, Debajyoti Mondal, Rahnuma Islam Nishat

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Citations (Scopus)

Abstract

A touching triangle graph (TTG) representation of a planar graph is a planar drawing Γ of the graph, where each vertex is represented as a triangle and each edge e is represented as a side contact of the triangles that correspond to the end vertices of e. We call Γ a proper TTG representation if Γ determines a tiling of a triangle, where each tile corresponds to a distinct vertex of the input graph. In this paper we prove that every 3-connected cubic planar graph admits a proper TTG representation. We also construct proper TTG representations for parabolic grid graphs and the graphs determined by rectangular grid drawings (e.g., square grid graphs). Finally, we describe a fixed-parameter tractable decision algorithm for testing whether a 3-connected planar graph admits a proper TTG representation.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages199-210
Number of pages12
Volume7704 LNCS
DOIs
StatePublished - 2013
Event20th International Symposium on Graph Drawing, GD 2012 - Redmond, WA, United States
Duration: Sep 19 2012Sep 21 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7704 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other20th International Symposium on Graph Drawing, GD 2012
CountryUnited States
CityRedmond, WA
Period9/19/129/21/12

Fingerprint

Tile
Planar graph
Connected graph
Triangle
Graph Representation
Testing
Grid Graph
Graph in graph theory
Cubic Graph
Vertex of a graph
Tiling
Contact
Grid
Distinct

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Kobourov, S. G., Mondal, D., & Nishat, R. I. (2013). Touching triangle representations for 3-connected planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7704 LNCS, pp. 199-210). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7704 LNCS). https://doi.org/10.1007/978-3-642-36763-2_18

Touching triangle representations for 3-connected planar graphs. / Kobourov, Stephen G; Mondal, Debajyoti; Nishat, Rahnuma Islam.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7704 LNCS 2013. p. 199-210 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7704 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kobourov, SG, Mondal, D & Nishat, RI 2013, Touching triangle representations for 3-connected planar graphs. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 7704 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7704 LNCS, pp. 199-210, 20th International Symposium on Graph Drawing, GD 2012, Redmond, WA, United States, 9/19/12. https://doi.org/10.1007/978-3-642-36763-2_18
Kobourov SG, Mondal D, Nishat RI. Touching triangle representations for 3-connected planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7704 LNCS. 2013. p. 199-210. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-36763-2_18
Kobourov, Stephen G ; Mondal, Debajyoti ; Nishat, Rahnuma Islam. / Touching triangle representations for 3-connected planar graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7704 LNCS 2013. pp. 199-210 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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