We prove that the crossing number of a graph decays in a “continuous fashion” in the following sense. For any ε > 0 there is a δ > 0 such that for n sufficiently large...
Abstract. CrossingNumber is one of the most challenging algorithmic problems in topological graph theory, with applications to graph drawing and VLSI layout. No polynomial time con...
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show that it is NP-hard to compute the crossing number of near-planar graphs. The main idea ...
Order Type Extension and New Results ectilinear Crossing Number - Extended Abstract Oswin Aichholzer∗ Hannes Krasser† We provide a complete data base of all realizable order t...
The crossing number cr(G) of a graph G is the minimum number of crossings over all drawings of G in the plane. In 1993, Richter and Thomassen [RT93] conjectured that there is a co...