inria-00074064, version 1
Universal 3-Dimensional Visibility Representations for Graphs
Helmut Alt 1Michael GodauSue Whitesides
N° RR-2622 (1995)
Résumé : 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 $K_{n,m}$.
- 1 : PRISME (INRIA Sophia Antipolis)
- INRIA
- Domaine : Informatique/Autre
- Mots-clés : COMPUTATIONAL GEOMETRY / VISIBILITY / GRAPHS
- Référence interne : RR-2622
- inria-00074064, version 1
- http://hal.inria.fr/inria-00074064
- oai:hal.inria.fr:inria-00074064
- Contributeur : Rapport De Recherche Inria
- Soumis le : Mercredi 24 Mai 2006, 14:24:53
- Dernière modification le : Mercredi 31 Mai 2006, 14:24:28






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