Open Rectangle-of-Influence Drawings of Inner Triangulated Plane Graphs

  • Kazuyuki Miura
  • Tetsuya Matsuno
  • Takao Nishizeki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4372)


A straight-line drawing of a plane graph is called an open rectangle-of-influence drawing if there is no vertex in the proper inside of the axis-parallel rectangle defined by the two ends of every edge. In an inner triangulated plane graph, every inner face is a triangle although the outer face is not always a triangle. In this paper, we first obtain a sufficient condition for an inner triangulated plane graph G to have an open rectangle-of-influence drawing; the condition is expressed in terms of a labeling of angles of a subgraph of G. We then present an O(n 1.5/logn)-time algorithm to examine whether G satisfies the condition and, if so, construct an open rectangle-of-influence drawing of G on an (n − 1) ×(n − 1) integer grid, where n is the number of vertices in G.


Plane Graph Outer Face Good Label Outer Vertex Facial Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Kazuyuki Miura
    • 1
  • Tetsuya Matsuno
    • 2
  • Takao Nishizeki
    • 2
  1. 1.Faculty of Symbiotic Systems Science, Fukushima University, Fukushima 960-1296Japan
  2. 2.Graduate School of Information Sciences, Tohoku University, Sendai 980-8579Japan

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