Strongly-Connected Outerplanar Graphs with Proper Touching Triangle Representations

  • J. Joseph Fowler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8242)


A proper touching triangle representation \(\mathcal{R}\) of an n-vertex planar graph consists of a triangle divided into n non-overlapping triangles. A pair of triangles are considered to be adjacent if they share a partial side of positive length. Each triangle in \(\mathcal{R}\) represents a vertex, while each pair of adjacent triangles represents an edge in the planar graph. We consider the problem of determining when a proper touching triangle representation exists for a strongly-connected outerplanar graph, which is biconnected and after the removal of all degree-2 vertices and outeredges, the resulting connected subgraph only has chord edges (w.r.t. the original graph). We show that such a graph has a proper representation if and only if the graph has at most two internal faces (i.e., faces with no outeredges).


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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • J. Joseph Fowler
    • 1
  1. 1.Department of Computer ScienceUniversity of ArizonaTucsonUSA

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