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GD
2007
Springer
14 years 3 months ago
Efficient Extraction of Multiple Kuratowski Subdivisions
Abstract. A graph is planar if and only if it does not contain a Kuratowski subdivision. Hence such a subdivision can be used as a witness for non-planarity. Modern planarity testi...
Markus Chimani, Petra Mutzel, Jens M. Schmidt
GD
2007
Springer
14 years 3 months ago
Cover Contact Graphs
Nieves Atienza, Natalia de Castro, Carmen Cort&eac...
GD
2007
Springer
14 years 5 months ago
Drawing Graphs with GLEE
This paper describes novel methods we developed to lay out graphs using Sugiyama’s scheme [16] in a tool named GLEE. The main contributions are: a heuristic for creating a graph ...
Lev Nachmanson, George G. Robertson, Bongshin Lee
GD
2007
Springer
14 years 5 months ago
Crossing Numbers and Parameterized Complexity
The odd crossing number of G is the smallest number of pairs of edges that cross an odd number of times in any drawing of G. We show that there always is a drawing realizing the o...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...
GD
2007
Springer
14 years 5 months ago
Crossing Number of Graphs with Rotation Systems
We show that computing the crossing number of a graph with a given rotation system is NP-complete. This result leads to a new and much simpler proof of Hlinˇen´y’s result, tha...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...
GD
2007
Springer
14 years 5 months ago
Minimizing the Area for Planar Straight-Line Grid Drawings
Straight-line grid drawings of bounded size is a classical topic in graph drawing. The Graph Drawing Challenge 2006 dealt with minimizing the area of planar straight-line grid draw...
Marcus Krug, Dorothea Wagner
GD
2007
Springer
14 years 5 months ago
Moving Vertices to Make Drawings Plane
In John Tantalo’s on-line game Planarity the player is given a non-plane straight-line drawing of a planar graph. The aim is to make the drawing plane as quickly as possible by m...
Xavier Goaoc, Jan Kratochvíl, Yoshio Okamot...
GD
2007
Springer
14 years 5 months ago
Matched Drawings of Planar Graphs
Emilio Di Giacomo, Walter Didimo, Marc J. van Krev...
GD
2007
Springer
14 years 5 months ago
Constrained Simultaneous and Near-Simultaneous Embeddings
A geometric simultaneous embedding of two graphs G1 = (V1, E1) and G2 = (V2, E2) with a bijective mapping of their vertex sets γ : V1 → V2 is a pair of planar straightline drawi...
Fabrizio Frati, Michael Kaufmann, Stephen G. Kobou...
GD
2007
Springer
14 years 5 months ago
A Bipartite Strengthening of the Crossing Lemma
Let G = (V, E) be a graph with n vertices and m ≥ 4n edges drawn in the plane. The celebrated Crossing Lemma states that G has at least Ω(m3 /n2 ) pairs of crossing edges; or ...
Jacob Fox, János Pach, Csaba D. Tóth