Graphs drawn with few crossings per edge

@article{Pach1997GraphsDW,
  title={Graphs drawn with few crossings per edge},
  author={J{\'a}nos Pach and G{\'e}za T{\'o}th},
  journal={Combinatorica},
  year={1997},
  volume={17},
  pages={427-439}
}
We show that if a graph ofv vertices can be drawn in the plane so that every edge crosses at mostk>0 others, then its number of edges cannot exceed 4.108√kv. Fork≤4, we establish a better bound, (k+3)(v−2), which is tight fork=1 and 2. We apply these estimates to improve a result of Ajtai et al. and Leighton, providing a general lower bound for the crossing number of a graph in terms of its number of vertices and edges. 
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