Upper bound constructions for untangling planar geometric graphs

Authors:
Javier Cano;Csaba D. Tó/th;Jorge Urrutia
Affiliations:
Posgrado en Ciencia e Ingenierí/a de la Computació/n, Universidad Nacional Autó/noma de Mé/xico, D.F., Mé/xico;Department of Math., University of Calgary, Canada;Instituto de Matem$#225/ticas, Universidad Nacional Autó/noma de Mé/xico, D.F., Mé/xico
Venue:
GD'11 Proceedings of the 19th international conference on Graph Drawing
Year:
2011

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Abstract

For every n∈ℕ, there is a straight-line drawing Dn of a planar graph on n vertices such that in any crossing-free straight-line drawing of the graph, at most O(n.4982) vertices lie at the same position as in Dn . This improves on an earlier bound of $O(\sqrt{n})$ by Goaoc et al. [6].