On a Visibility Representation of Graphs
Cobos, F. J. and Dana, J. C. and Hurtado, F. and Márquez, Alberto and Mateos, F. (1996) On a Visibility Representation of Graphs. In: Symposium on Graph Drawing, GD 1995, September 20-22, 1995, Passau, Germany , pp. 152-161 (Official URL: http://dx.doi.org/10.1007/BFb0021799).
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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 R^n 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 consider this problem for concrete well-known families of graphs such as planar graphs, complete graphs and complete bipartite graphs.
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