On a Visibility Representation of Graphs

@inproceedings{Cobos1995OnAV,
  title={On a Visibility Representation of Graphs},
  author={Francisco Javier Cobos and Juan Carlos Dana and Ferran Hurtado and A. M{\'a}rquez and F. Mateos},
  booktitle={Graph Drawing},
  year={1995}
}
We give a visibility representation of graphs which extends some very well-known representations considered extensively in the literature. Concretely, the vertices are represented by a collection of parallel hyper-rectangles in Rn and the visibility is orthogonal to those hyper-rectangles. With this generalization, we can prove that each graph admits a visibility representation. But, it arises the problem of determining the minimum Euclidean space where such representation is possible. We… 
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22 Citations
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11
Methods Citations
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22 Citations

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A Visibility Representation for Graphs in Three Dimensions
TLDR
An extension of the Erd} os-Szekeres Theorem in a geometric setting is applied to obtain an upper bound of n = 56 for the largest representable complete graph Kn, and it is shown by construction that n 22 are the best existing bounds.
3D Visibility Representations of 1-planar Graphs
We prove that every 1-planar graph G has a z-parallel visibility representation, i.e., a 3D visibility representation in which the vertices are isothetic disjoint rectangles parallel to the xy-plane,…
Thickness of Bar 1-Visibility Graphs
TLDR
For a special case of bar 1-visibility graphs, an algorithm partitioning the edges into two plane graphs is presented, showing that for this class the thickness is indeed bounded by 2.
Unit Hypercube Visibility Numbers of Trees
A visibility representation of a graph G is an assignment of the vertices of G to geometric objects such that vertices are adjacent if and only if their corresponding objects are “visible” each…
Bar 1-visibility representation of optimal 1-planar graph
In a visibility representation of a graph, the vertices map to objects in Euclidean space and the edges are determined by certain visibility relations. A bar visibility representation of a planar…
Simultaneous Visibility Representations of Undirected Pairs of Graphs
Colored anchored visibility representations in 2D and 3D space
Parameters of Bar k-Visibility Graphs
TLDR
An algorithm partitioning the edges of a semi bar 1-visibility graph into two plane graphs is presented, showing that for this subclass the (geometric) thickness is indeed bounded by 2.
On Aligned Bar 1-Visibility Graphs
TLDR
A new operation, called path-addition, is introduced that admits the addition of vertex-disjoint paths to a given graph and it is shown that AB1V graphs are closed under path- addition.
Rectangle and Box Visibility Graphs in 3D
TLDR
Lower and upper bounds for the size of the largest complete graph that can be represented in rectangle and box visibility representations of graphs in 3-dimensional space are examined.
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References

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TLDR
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