Graphs Drawn with Few Crossings per EdgePach, János and Tóth, Géza (1997) Graphs Drawn with Few Crossings per Edge. In: Symposium on Graph Drawing, GD '96, September 1820, 1996 , pp. 345354(Official URL: http://dx.doi.org/10.1007/3540624953_59). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/3540624953_59
AbstractWe 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 \sqrt{kv}. For k<=4, we establish a better bound, (k+3)(v2), 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 naumber of a graph in terms of its number of vertices and edges.
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