Abstract. Every planar graph has a concentric representation based on a breadth first search, see [24]. The vertices are placed on concentric circles and the edges are routed as curves without crossings. Here we take the opposite view. A graph with a given partitioning of its vertices onto k concentric circles is k-radial planar, if the edges can be routed monotonic between the circles without crossings. Radial planarity is a generalisation of level planarity, where the vertices are placed on k horizontal lines. We extend the technique for level planarity testing of [13, 14, 16–18, 20] and show that radial planarity is decidable in linear time, and that a radial planar embedding can be computed in linear time. 1
|
368
|
Testing for the consecutive ones property, interval graphs, and planarity using PQ-tree algorithms
– Booth, Lueker
- 1976
|
|
239
|
Methods for Visual Understanding of Hierarchical Systems
– Sugiyama, Tagawa, et al.
- 1981
|
|
204
|
Graph Drawing: algorithms for the visualization of graphs
– Battista, Eades, et al.
- 1999
|
|
102
|
A linear algorithm for embedding planar graphs using PQ-trees
– Chiba, Nishizeki, et al.
- 1985
|
|
97
|
An algorithm for planarity testing of graphs
– Lempel, Even, et al.
- 1967
|
|
91
|
How to draw a planar graph on a grid
– Fraysseix, Pach, et al.
- 1990
|
|
82
|
On-line planarity testing
– Battista, Tamassia
- 1989
|
|
59
|
Which aesthetic has the greatest effect on human understanding?, in proc Graph Drawing Symposium
– Purchase
- 1997
|
|
57
|
How to draw a planar graph on a grid. Combinatorica
– FRAYSSEIX, PACH, et al.
- 1990
|
|
56
|
a platform for combinatorial and geometric computing
– LEDA
- 1999
|
|
41
|
Small sets supporting Fary embeddings of planar graphs
– Fraysseix, Pach, et al.
- 1988
|
|
37
|
Laying out graphs using queues
– Heath, Rosenberg
- 1992
|
|
27
|
Depth-First Search and Kuratowski Subgraphs
– Williamson
- 1984
|
|
24
|
Drawing Free Trees. Bulletin of the Institute for Combinatorics and its Application
– Eades
- 1992
|
|
24
|
Drawing Free Trees
– Eades
- 1992
|
|
21
|
Hierarchies and planarity theory
– Battista, Nardelli
- 1989
|
|
19
|
Stack and queue layouts of directed acyclic graphs
– Heath, Pemmaraju
- 1999
|
|
17
|
Level planarity testing in linear time
– Jünger, Leipert, et al.
- 1998
|
|
14
|
Communicating Centrality in Policy Network Drawings
– Brandes, Kenis, et al.
- 1999
|
|
13
|
Recognizing leveled-planar dags in linear time
– Heath, Pemmaraju
- 1996
|
|
13
|
Level planar embedding in linear time
– Jünger, Leipert
|
|
12
|
On the parameterized complexity of layered graph drawing
– DUJMOVI'C, FELLOWS, et al.
- 2001
|
|
5
|
Upward numbering testing for triconnected graphs
– Chandramouli, Diwan
- 1996
|
|
5
|
The vertex-exchange graph: A new concept for multi-level crossing minimisation
– Healy, Kuusik
- 1999
|
|
5
|
Characterisation of level non-planar graphs by minimal patterns
– Healy, Kuusik
- 1998
|
|
5
|
Radial coordinate assignment for level graphs
– Bachmaier, Fischer, et al.
- 2005
|
|
4
|
Planarity Testing and Embedding in Linear Time. Dissertation, Mathematisch-Naturwissenschaftliche Fakultät der Universität zu
– Level
- 1998
|
|
3
|
Graph Template Library. http://www.infosun.fmi.uni-passau.de/GTL
– GTL
|
|
3
|
Track planarity testing and embedding
– Bachmaier, Brandenburg, et al.
- 2004
|
|
2
|
Algorithms, chapter 7
– Even
- 1979
|
|
2
|
Improved symmetric lists
– Bachmaier, Raitner
- 2003
|
|
1
|
Improved symmetric lists (preprint). http: //www.infosun.fmi.uni-passau.de/~chris/down/SymlistsPP.pdf
– Bachmaier, Raitner
- 2004
|
|
1
|
Classification and detection of obstructions to planarity
– Karaberg
- 1990
|
|
1
|
A satisfiability formulation of problems on level graphs. Rutcor Research Report RRR
– Randerath, Speckenmeyer, et al.
- 2001
|
|
1
|
Computational Aspects of VLSI, chapter 3.5
– Ullman
- 1984
|
|
1
|
et al. On the paramterized complexity of layered graph drawing
– Dujmovic
- 2001
|
|
1
|
Classi and detection of obstructions to planarity. Linear and Multilinear Algebra
– Karaberg
- 1990
|
|
1
|
Circle Planarity of Level Graphs
– Bachmaier
- 2004
|
|
1
|
Characterization of level non-planar graphs by minimal patterns
– Healy, Kuusik, et al.
- 2000
|
|
1
|
ArchE: A graph drawing system for archeology
– Hundack, Mutzel, et al.
- 1998
|
