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Reports Year : 1995

Universal 3-Dimensional Visibility Representations for Graphs

Michael Godau
  • Function : Author
Sue Whitesides
  • Function : Author


This paper studies 3-dimensional visibility representations of graphs in which objects in 3-d correspond to vertices and vertical visibilities between these objects correspond to edges. We ask which classes of simple objects are {\em universal}, i.e. powerful enough to represent all graphs. In particular, we show that there is no constant $k$ for which the class of all polygons having $k$ or fewer sides is universal. However, we show by construction that every graph on $n$ vertices can be represented by polygons each having at most $2n$ sides. The construction can be carried out by an $O(n^2)$ algorithm. We also study the universality of classes of simple objects (translates of a single, not necessarily polygonal object) relative to cliques $K_n$ and similarly relative to complete bipartite graphs $K_{n,m}$.


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Dates and versions

inria-00074064 , version 1 (24-05-2006)


  • HAL Id : inria-00074064 , version 1


Helmut Alt, Michael Godau, Sue Whitesides. Universal 3-Dimensional Visibility Representations for Graphs. RR-2622, INRIA. 1995. ⟨inria-00074064⟩
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