Drawings of planar graphs with few slopes and segments

Authors:
Vida Dujmović;David Eppstein;Matthew Suderman;David R. Wood
Affiliations:
Department of Mathematics and Statistics, McGill University, Montréal, Canada;Department of Computer Science, University of California, Irvine, California, USA;McGill Centre for Bioinformatics, School of Computer Science, McGill University, Montréal, Canada;Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Barcelona, Spain
Venue:
Computational Geometry: Theory and Applications
Year:
2007

Citing 11
Cited 13

On grid intersection graphs

Discrete Mathematics
A simple proof of the representation of bipartite planar graphs as the contact graphs of orthogonal straight line segments

Information Processing Letters
Rectangular grid drawings of plane graphs

Computational Geometry: Theory and Applications
Box-rectangular drawings of plane graphs

Journal of Algorithms
Rectangular drawings of plane graphs without designated corners

Computational Geometry: Theory and Applications
On the Computational Complexity of Upward and Rectilinear Planarity Testing

SIAM Journal on Computing
Hexagonal Grid Drawings

WG '92 Proceedings of the 18th International Workshop on Graph-Theoretic Concepts in Computer Science
Rectangular drawings of planar graphs

Journal of Algorithms
Graph drawings with few slopes

Computational Geometry: Theory and Applications
Graph treewidth and geometric thickness parameters

GD'05 Proceedings of the 13th international conference on Graph Drawing
Contact and intersection representations

GD'04 Proceedings of the 12th international conference on Graph Drawing

Happy endings for flip graphs

SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Graph drawings with few slopes

Computational Geometry: Theory and Applications
Drawing cubic graphs with at most five slopes

Computational Geometry: Theory and Applications
Minimum Segment Drawings of Series-Parallel Graphs with the Maximum Degree Three

Graph Drawing
Geometric representation of cubic graphs with four directions

Computational Geometry: Theory and Applications
Steinitz theorems for orthogonal polyhedra

Proceedings of the twenty-sixth annual symposium on Computational geometry
Drawing planar graphs of bounded degree with few slopes

GD'10 Proceedings of the 18th international conference on Graph drawing
Orthogonal cartograms with few corners per face

WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
The planar slope number of planar partial 3-trees of bounded degree

GD'09 Proceedings of the 17th international conference on Graph Drawing
Drawing cubic graphs with the four basic slopes

GD'11 Proceedings of the 19th international conference on Graph Drawing
On planar point sets with the pentagon property

Proceedings of the twenty-ninth annual symposium on Computational geometry
Orthogonal cartograms with at most 12 corners per face

Computational Geometry: Theory and Applications
Outerplanar graph drawings with few slopes

Computational Geometry: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study straight-line drawings of planar graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most segments and at most 2n slopes. We prove that every cubic 3-connected plane graph has a plane drawing with three slopes (and three bends on the outerface). In a companion paper, drawings of non-planar graphs with few slopes are also considered.