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Published in:
1997 | ReviewPaper | Chapter
Graphs drawn with few crossings per edge
Authors : János Pach, Géza Tóth
Published in: Graph Drawing
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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We show that if a graph of v vertices can be drawn in the plane so that every edge crosses at most k> 0 others, then its number of edges cannot exceed 4.108√kv. For k≤ 4, we establish a better bound, (k + 3)(u− 2), which is tight for k=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.