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GD
2007
Springer
15 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
COCOON
2006
Springer
15 years 3 months ago
Fixed Linear Crossing Minimization by Reduction to the Maximum Cut Problem
Many real-life scheduling, routing and location problems can be formulated as combinatorial optimization problems whose goal is to find a linear layout of an input graph in such a ...
Christoph Buchheim, Lanbo Zheng
COMPGEOM
2000
ACM
15 years 3 months ago
When crossings count - approximating the minimum spanning tree
We present an (1+ε)-approximation algorithm for computing the minimum-spanning tree of points in a planar arrangement of lines, where the metric is the number of crossings betwee...
Sariel Har-Peled, Piotr Indyk
APVIS
2004
15 years 20 days ago
Optimal Leaf Ordering for Two and a Half Dimensional Phylogenetic Tree Visualisation
Two and a half dimensional graph visualisation is the stacking of a set of related graphs into the third dimension to support visual comparison. A new aesthetic criterion is intro...
Tim Dwyer, Falk Schreiber
ENDM
2007
106views more  ENDM 2007»
14 years 11 months ago
Removing Even Crossings on Surfaces
In this paper we investigate how certain results related to the HananiTutte theorem can be extended from the plane to surfaces. We give a simple topological proof that the weak Ha...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...