Upper Bound Constructions for Untangling Planar Geometric Graphs [chapter]

Javier Cano, Csaba D. Tóth, Jorge Urrutia
2012 Lecture Notes in Computer Science  
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( √ n) by Goaoc et al. [6].
doi:10.1007/978-3-642-25878-7_28 fatcat:l3tn3jiufvfxndwtcxlrhkocj4