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)

Abstract

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.

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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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