#### DMCA

## Bar k-Visibility Graphs

### Cached

### Download Links

- [www.math.gatech.edu]
- [www.cs.ubc.ca]
- [www.cs.ubc.ca]
- [www.emis.de]
- [www.math.gatech.edu]
- [www.emis.math.ca]
- [www.cs.brown.edu]
- [jgaa.info]
- [www.maths.tcd.ie]
- [emis.mi.ras.ru]
- [emis.maths.adelaide.edu.au]
- [emis.library.cornell.edu]
- [emis.u-strasbg.fr]
- [www.emis.ams.org]
- [www.math.ethz.ch]
- [emis.maths.tcd.ie]
- [www.univie.ac.at]
- [www.maths.soton.ac.uk]
- DBLP

### Other Repositories/Bibliography

### Citations

628 | Threedimensional graph drawing.
- Cohen, Eades, et al.
- 1996
(Show Context)
Citation Context ...is paper, we define a new generalization of bar visibility graphs, called bar k-visibility graphs, and discuss their properties. In what follows, we use the standard graph theory terminology found in =-=[8, 18]-=-. Let G be a bar visibility graph, and let S be a bar visibility layout of G. If each line of sight is required to be a rectangle of positive width, then S is an ε-visibility representation of G, and ... |

103 |
A unified approach to visibility representations of planar graphs.
- Tamassia, Tollis
- 1986
(Show Context)
Citation Context ... sight is required to be a rectangle of positive width, then S is an ε-visibility representation of G, and when each line of sight is a line segment, then S is a strong visibility representation of G =-=[15]-=-. In general, these definitions are not equivalent; K2,3 admits an ε-visibility representation but not a strong visibility representation, as shown in Figure 1. G H Figure 1: The bar visibility repres... |

83 |
Rectilinear planar layouts and bipolar orientations of planar graphs.
- Rosenstiehl, Tarjan
- 1986
(Show Context)
Citation Context ...uced in the 1980s [9, 13] as a modeling tool for VLSI layout problems. These graphs have been fully characterized as those planar graphs having a plane embedding with all cut points on the outer face =-=[12, 16, 19]-=-. Recent attention has been drawn to a variety of generalizations and restrictions of bar visibility graphs, including unit bar visibility graphs, arc visibility graphs, rectangle visibility graphs, a... |

55 |
An application of graph coloring to printed circuit testing.
- Garey, Johnson, et al.
- 1976
(Show Context)
Citation Context ...graph, and thus there are non-planar bar 1-visibility graphs. Motivated by the fact that all bar 0-visibility graphs ✷sA. Dean et al., Bar k-Visibility Graphs, JGAA, vol. 0, no. 0, 0000 15 are planar =-=[9]-=-, we are interested in measuring the closeness to planarity of bar 1-visibility graphs. The thickness Θ(G) of a graph G is the minimum number of planar graphs whose union is G. K8 has thickness 2 [11]... |

38 |
Characterizing bar line-of-sight graphs
- Wismath
- 1985
(Show Context)
Citation Context ...spondence between vertices of G and bars in S, such that there is an edge between two vertices in G if and only if there exists an unobstructed vertical line of sight between their corresponding bars =-=[1, 11, 12, 17]-=-. If each line of sight is required to be a rectangle of positive width, then S is an ε-visibility representation of G, and when each line of sight is a line segment, then S is a strong visibility rep... |

30 |
On representations of some thickness-two graphs
- Hutchinson, Shermer, et al.
- 1999
(Show Context)
Citation Context ...ttention has been drawn to a variety of generalizations and restrictions of bar visibility graphs, including unit bar visibility graphs, arc visibility graphs, rectangle visibility graphs, and others =-=[2, 3, 5, 4, 6, 7, 10, 11, 14, 15]-=-. In this paper, we define a new generalization of bar visibility graphs, called bar k-visibility graphs, and discuss their properties. In what follows, we use the standard graph theory terminology fo... |

22 | Rectangle-visibility representations of bipartite graphs
- Dean, Hutchinson
- 1997
(Show Context)
Citation Context ...ttention has been drawn to a variety of generalizations and restrictions of bar visibility graphs, including unit bar visibility graphs, arc visibility graphs, rectangle visibility graphs, and others =-=[2, 3, 5, 4, 6, 7, 10, 11, 14, 15]-=-. In this paper, we define a new generalization of bar visibility graphs, called bar k-visibility graphs, and discuss their properties. In what follows, we use the standard graph theory terminology fo... |

20 | On rectangle visibility graphs
- Bose, Dean, et al.
(Show Context)
Citation Context ...ttention has been drawn to a variety of generalizations and restrictions of bar visibility graphs, including unit bar visibility graphs, arc visibility graphs, rectangle visibility graphs, and others =-=[2, 3, 5, 4, 6, 7, 10, 11, 14, 15]-=-. In this paper, we define a new generalization of bar visibility graphs, called bar k-visibility graphs, and discuss their properties. In what follows, we use the standard graph theory terminology fo... |

12 |
On rectangle visibility graphs III. External visibility and complexity
- Shermer
- 1996
(Show Context)
Citation Context |

11 |
Representing a planar graph by vertical lines joining different levels
- Duchet, Hamidoune, et al.
- 1983
(Show Context)
Citation Context ...that there is an edge between two vertices in G if and only if there exists an unobstructed vertical line of sight between their corresponding bars. Bar visibility graphs were introduced in the 1980s =-=[9, 13]-=- as a modeling tool for VLSI layout problems. These graphs have been fully characterized as those planar graphs having a plane embedding with all cut points on the outer face [12, 16, 19]. Recent atte... |

11 |
Some results on visibility graphs
- Andreae
(Show Context)
Citation Context ...spondence between vertices of G and bars in S, such that there is an edge between two vertices in G if and only if there exists an unobstructed vertical line of sight between their corresponding bars =-=[1, 11, 12, 17]-=-. If each line of sight is required to be a rectangle of positive width, then S is an ε-visibility representation of G, and when each line of sight is a line segment, then S is a strong visibility rep... |

10 |
Every planar graph with nine points has a nonplanar complement
- BATTLE, HARARY, et al.
- 1962
(Show Context)
Citation Context ...lanar, we are interested in measuring the closeness to planarity of bar 1visibility graphs. The thickness Θ(G) of a graph G is the minimum number of planar graphs whose union is G. K8 has thickness 2 =-=[1, 17]-=-, so there exist bar 1-visibility graphs with thickness 2. Theorem 12 There are thickness-2 graphs with n vertices that are not bar 1visibility graphs for all n ≥ 15. Proof: Consider the graph G15, wh... |

10 |
A visibility problem in VLSI layout compaction
- Schlag, Luccio, et al.
- 1985
(Show Context)
Citation Context ...that there is an edge between two vertices in G if and only if there exists an unobstructed vertical line of sight between their corresponding bars. Bar visibility graphs were introduced in the 1980s =-=[9, 13]-=- as a modeling tool for VLSI layout problems. These graphs have been fully characterized as those planar graphs having a plane embedding with all cut points on the outer face [12, 16, 19]. Recent atte... |

8 |
Rectangle visibility graphs: characterization, construction, and compaction
- Streinu, Whitesides
- 2003
(Show Context)
Citation Context |

8 |
The non-biplanar character of the complete 9-graph
- Tutte
- 1963
(Show Context)
Citation Context ...anar, we are interested in measuring the closeness to planarity of bar 1-visibility graphs. The thickness Θ(G) of a graph G is the minimum number of planar graphs whose union is G. K8 has thickness 2 =-=[1, 17]-=-, so there exist bar 1-visibility graphs with thickness 2. Theorem 12 There are thickness-2 graphs with n vertices that are not bar 1-visibility graphs for all n ≥ 15. Proof: Consider the graph G15, w... |

7 | Unit bar-visibility layouts of triangulated polygons: Extended abstract
- Dean, Gethner, et al.
(Show Context)
Citation Context |

7 | Rectangle-visibility layouts of unions and products of trees
- Dean, Hutchinson
- 1998
(Show Context)
Citation Context |

4 |
Introduction to Graph Theory, 2E
- West
- 2001
(Show Context)
Citation Context ...his paper, we define a new generalization of bar visibility graphs called bar k-visibility graphs, and discuss their properties. In what follows, we use the standard graph theory terminology found in =-=[8, 16]-=-. Let S be a set of disjoint horizontal line segments, or bars, in the plane. We say that a graph G is a bar visibility graph, and S a bar visibility representation of G, if there exists a one-to-one ... |

3 |
A characterization of triangulated polygons that are unit bar-visibility graphs
- Dean, Gethner, et al.
- 2005
(Show Context)
Citation Context |

2 | Characterizations of 1, k-bar visibility trees
- Chen, Hutchinson, et al.
- 2005
(Show Context)
Citation Context |

2 | Arc- and circle-visibility graphs
- Hutchinson
- 2002
(Show Context)
Citation Context |