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Abstract: We discuss rectangle and box visibility representations of graphs in 3-dimensional space. In these representations, vertices are represented by axis-aligned disjoint rectangles or boxes. Two vertices are adjacent if and only if their corresponding boxes see each other along a small axis-parallel cylinder. We concentrate on lower and upper bounds for the size of the largest complete graph that can be represented. In particular, we examine these bounds under certain restrictions: What can be ... (Update)
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Three-Dimensional Orthogonal Graph Drawing - Wood (2000) (Correct)
Three-Dimensional Orthogonal Graph Drawing with Optimal Volume - Biedl, Thiele, Wood (2004) (Correct)
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0.4: On a Visibility Representation for Graphs in Three.. - Bose, Everett.. (1995) (Correct)
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16: Graph Drawing: 7th International Symp (context) - Kratochvil, Proc - 1999
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BibTeX entry: (Update)
S. P. Fekete and H. Meijer. Rectangle and box visibility graphs in 3D. To appear in Intern. J. Comp.Geom. Appl. http://citeseer.ist.psu.edu/fekete96rectangle.html More
@article{ fekete99rectangle,
author = "S. P. Fekete and H. Meijer",
title = "Rectangle and Box Visibility Graphs in 3{D}",
journal = "International Journal of Computational Geometry and Applications",
volume = "9",
number = "1",
pages = "1--27",
year = "1999",
url = "citeseer.ist.psu.edu/fekete96rectangle.html" }
Citations (may not include all citations):79 Cone trees: animated 3d visualizations of hierarchical infor.. (context) - Mackinley, Robertson et al. - 1991
62 A unified approach to visibility representations of planar g.. (context) - Tamassia, Tollis - 1986
40 On representatives of subsets (context) - Hall - 1935
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29 a visibility representation for graphs in three dimensions - Bose, Everett et al. - 1993
29 a visibility representation for graphs in three dimensions - Bose, Everett et al.
18 An application of three-dimensional visualization to object-.. (context) - Koike - 1992
16 On representations of some thickness-two graphs (context) - Hutchinson, Shermer et al. - 1996
10 Personal communication (context) - Rote, Zelle - 1996
8 Struktur und algorithmische Behandlung von praxisorientierte.. (context) - Wottawa - 1996
7 a visibility representation of graphs - Cobos, Dana et al. - 1996
2 New results on a visibility representation of graphs in 3D (context) - Fekete, Houle et al. - 1996
2 Universal 3-dimensional visibility representations for graph.. (context) - Alt, Godau et al. - 1996
1 K42 is a box visibility graph (context) - Bose, Josefczyk et al. - 1994
1 A practical insertion heuristic for 3dimensional packing pro.. (context) - Fekete, Schepers et al.
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