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» On the Decay of Crossing Numbers
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ISAAC
2007
Springer
124views Algorithms» more  ISAAC 2007»
14 years 1 months ago
Approximating the Crossing Number of Toroidal Graphs
Abstract. CrossingNumber is one of the most challenging algorithmic problems in topological graph theory, with applications to graph drawing and VLSI layout. No polynomial time con...
Petr Hlinený, Gelasio Salazar
ISAAC
2007
Springer
141views Algorithms» more  ISAAC 2007»
14 years 1 months ago
Algorithms for the Hypergraph and the Minor Crossing Number Problems
Abstract. We consider the problems of hypergraph and minor crossing minimization, and point out a relation between these two problems which has not been exploited before. We presen...
Markus Chimani, Carsten Gutwenger
COMPGEOM
2010
ACM
14 years 3 days ago
Adding one edge to planar graphs makes crossing number hard
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show that it is NP-hard to compute the crossing number of near-planar graphs. The main idea ...
Sergio Cabello, Bojan Mohar
COMPGEOM
2005
ACM
13 years 9 months ago
Abstract order type extension and new results on the rectilinear crossing number
Order Type Extension and New Results ectilinear Crossing Number - Extended Abstract Oswin Aichholzer∗ Hannes Krasser† We provide a complete data base of all realizable order t...
Oswin Aichholzer, Hannes Krasser
COMGEO
2011
ACM
13 years 2 months ago
On crossing numbers of geometric proximity graphs
Let P be a set of n points in the plane. A geometric proximity graph on P is a graph where two points are connected by a straight-line segment if they satisfy some prescribed prox...
Bernardo M. Ábrego, Ruy Fabila Monroy, Silv...