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Crossing number (graph theory)

Known as: Crossing number 
In graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a… 
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Related topics

Related topics

44 relations
1-planar graphAlbertson conjectureAngular resolution (graph drawing)Approximation algorithm

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2014
2014
Life-time monitoring of in service switches and crossings through field experimentation
2007
2007
Crossings and Nestings of Two Edges in Set Partitions
Let $\pi$ and $\lambda$ be two set partitions with the same number of blocks. Assume $\pi$ is a partition of $[n]$. For any… 
2006
2006
Dynamics of group motions controlled by signal processing: A cellular-automaton model and its applications
2005
2005
The ATLAS Level-1 central trigger processor
ATLAS is a multi-purpose particle physics detector at CERN's Large Hadron Collider where two pulsed beams of protons are brought… 
Highly Cited
2001
Highly Cited
2001
Quantitative description of vessel features in hypertensive retinopathy fundus images
Methods. High resolution digital images of fundus are directly acquired from fundus cameras or scanned from slides. At first the… 
2001
2001
On graphs whose line graphs have crossing number one *
Necessary and sufficient conditions are given for a nonplanar graph to have a line graph with crossing number one. This corrects… 
Highly Cited
2000
Highly Cited
2000
Optical interconnection using VCSELs and polymeric waveguide circuits
We investigated the waveguide loss and transmission characteristics for optical interconnection using vertical-cavity surface… 
2000
2000
ON EGGLETON AND GUY'S CONJECTURED UPPER BOUND FOR THE CROSSING NUMBER OF THE n-CUBE
The crossing number v(G) of a graph G is the smallest integer such that there is a drawing for G with v(G) crossings of edges… 
2000
2000
Fabrication of Topologically Complex Three-Dimensional Microstructures: Metallic Microknots
This paper describes a method for fabricating three-dimensional (3D) microstructures with complex topologiestrefoil, figure eight… 
1991
1991
The crossing distribution problem
The authors study the problem of 'properly' distributing the set of crossings (i.e., intersection of nets) of a given global… 
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