Discrete & Computational Geometry

, Volume 1, Issue 4, pp 321–341 | Cite as

A unified approach to visibility representations of planar graphs

  • Roberto Tamassia
  • Ioannis G. Tollis
Article

Abstract

We studyvisibility representations of graphs, which are constructed by mapping vertices to horizontal segments, and edges to vertical segments that intersect only adjacent vertex-segments. Every graph that admits this representation must be planar. We consider three types of visibility representations, and we give complete characterizations of the classes of graphs that admit them. Furthermore, we present linear time algorithms for testing the existence of and constructing visibility representations of planar graphs. Many applications of our results can be found in VLSI layout.

Keywords

Planar Graph Visibility Representation Hamiltonian Path Vertical Segment Linear Time Algorithm 
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-Verlag New York Inc. 1986

Authors and Affiliations

  • Roberto Tamassia
    • 1
  • Ioannis G. Tollis
    • 2
  1. 1.Coordinated Science Laboratory and Department of Electrical and Computer EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Coordinated Science Laboratory and Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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