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.
251 Citations
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