Touching Triangle Representations for 3-Connected Planar Graphs

  • Stephen G. Kobourov
  • Debajyoti Mondal
  • Rahnuma Islam Nishat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7704)


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.


Planar Graph Input Graph Grid Graph Path Covering Planar Embedding 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Stephen G. Kobourov
    • 1
  • Debajyoti Mondal
    • 2
  • Rahnuma Islam Nishat
    • 3
  1. 1.Department of Computer ScienceUniversity of ArizonaUSA
  2. 2.Department of Computer ScienceUniversity of ManitobaCanada
  3. 3.Department of Computer ScienceUniversity of VictoriaCanada

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