On the number of directions in visibility representations of graphs (extended abstract)

  • Evangelos Kranakis
  • Danny Krizanc
  • Jorge Urrutia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 894)


We consider visibility representations of graphs in which the vertices are represented by a collection O of non-overlapping convex regions on the plane. Two points x and y are visible if the straight-line segment xy is not obstructed by any object. Two objects A, BO are called visible if there exist points xA, yB such that x is visible from y. We consider visibility only for a finite set of directions. In such a representation, the given graph is decomposed into a union of unidirectional visibility graphs, for the chosen set of directions. This raises the problem of studying the number of directions needed to represent a given graph. We study this number of directions as a graph parameter and obtain sharp upper and lower bounds for the represent ability of arbitrary graphs.

1980 Mathematics Subject Classification: 68R10, 68U05 CR Categories: F.2.2

Key words and phrases

Graph Number of directions Polygon Visibility 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Evangelos Kranakis
    • 1
  • Danny Krizanc
    • 1
  • Jorge Urrutia
    • 2
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada
  2. 2.Department of Computer ScienceUniversity of OttawaOttawaCanada

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