Let P be a set of n points in the plane. A geometric proximity graph on P is a graph where two points are connected by a straight-line segment if they satisfy some prescribed prox...
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 ...
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 topological graph is called k-quasi-planar, if it does not contain k pairwise crossing edges. It is conjectured that for every fixed k, the maximum number of edges in a kquasi-...
We show that computing the crossing number and the odd crossing number of a graph with a given rotation system is NP-complete. As a consequence we can show that many of the well-k...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...