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

8 Scopus citations

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 publicationGraph Drawing - 20th International Symposium, GD 2012, Revised Selected Papers
Pages199-210
Number of pages12
DOIs
StatePublished - Feb 26 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)0302-9743
ISSN (Electronic)1611-3349

Other

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Kobourov, S. G., Mondal, D., & Nishat, R. I. (2013). Touching triangle representations for 3-connected planar graphs. In Graph Drawing - 20th International Symposium, GD 2012, Revised Selected Papers (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