Publication

Degenerate crossing numbers

János Pach
2009
Journal Articles

Abstract

Let G be a graph with n vertices and ea parts per thousand yen4n edges, drawn in the plane in such a way that if two or more edges (arcs) share an interior point p, then they properly cross one another at p. It is shown that the number of crossing points, counted without multiplicity, is at least constant times e and that the order of magnitude of this bound cannot be improved. If, in addition, two edges are allowed to cross only at most once, then the number of crossing points must exceed constant times (e/n)(4).

Official source

https://infoscience.epfl.ch/entities/publication/0c5c9605-796e-4416-a65b-2003bba91827

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Degenerate crossing numbers

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