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COMPGEOM
2010
ACM
13 years 11 months 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
SIAMCOMP
2000
118views more  SIAMCOMP 2000»
13 years 6 months ago
On Bipartite Drawings and the Linear Arrangement Problem
The bipartite crossing number problem is studied, and a connection between this problem and the linear arrangement problem is established. It is shown that when the arboricity is ...
Farhad Shahrokhi, Ondrej Sýkora, Lás...
SOFSEM
2005
Springer
14 years 5 days ago
Outerplanar Crossing Numbers of 3-Row Meshes, Halin Graphs and Complete p-Partite Graphs
An outerplanar (also called circular, convex, one-page) drawing of an n-vertex graph G is a drawing in which the vertices are placed on a circle and each edge is drawn using one s...
Radoslav Fulek, Hongmei He, Ondrej Sýkora, ...
WEA
2007
Springer
112views Algorithms» more  WEA 2007»
14 years 24 days ago
Crossing Minimization in Weighted Bipartite Graphs
Given a bipartite graph G = (L0, L1, E) and a fixed ordering of the nodes in L0, the problem of finding an ordering of the nodes in L1 that minimizes the number of crossings has ...
Olca A. Çakiroglu, Cesim Erten, Ömer K...
SODA
2003
ACM
103views Algorithms» more  SODA 2003»
13 years 8 months ago
On the rectilinear crossing number of complete graphs
We prove a lower bound of 0.3288   n 4¡ for the rectilinear crossing number cr(Kn) of a complete graph on n vertices, or in other words, for the minimum number of convex quadril...
Uli Wagner