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» Adding one edge to planar graphs makes crossing number hard
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COMPGEOM
2010
ACM
13 years 8 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
ALGORITHMICA
2011
12 years 10 months ago
Crossing Number and Weighted Crossing Number of Near-Planar Graphs
A nonplanar graph G is near-planar if it contains an edge e such that G−e is planar. The problem of determining the crossing number of a near-planar graph is exhibited from diffe...
Sergio Cabello, Bojan Mohar
GD
2008
Springer
13 years 4 months ago
Crossing and Weighted Crossing Number of Near-Planar Graphs
A nonplanar graph G is near-planar if it contains an edge e such that G − e is planar. The problem of determining the crossing number of a near-planar graph is exhibited from di...
Sergio Cabello, Bojan Mohar
ENDM
2008
142views more  ENDM 2008»
13 years 3 months ago
Augmenting the Connectivity of Planar and Geometric Graphs
In this paper we study some connectivity augmentation problems. Given a connected graph G with some desirable property, we want to make G 2-vertex connected (or 2-edge connected) ...
Ignaz Rutter, Alexander Wolff
DIALM
2003
ACM
175views Algorithms» more  DIALM 2003»
13 years 8 months ago
Localized construction of bounded degree and planar spanner for wireless ad hoc networks
We propose a novel localized algorithm that constructs a bounded degree and planar spanner for wireless ad hoc networks modeled by unit disk graph (UDG). Every node only has to kn...
Yu Wang 0003, Xiang-Yang Li