It was proved by [Garey and Johnson, 1983] that computing the crossing number of a graph is an NP-hard problem. Their reduction, however, used parallel edges and vertices of very h...
A nonplanar graph G is near-planar if it contains an edge e such that G − e is planar. The problem of determining the crossing number of a near-planar graph is exhibited from di...
The crossing number of a graph is the least number of pairwise edge crossings in a drawing of the graph in the plane. We provide an O(n log n) time constant factor approximation al...
Given an n-vertex graph G, a drawing of G in the plane is a mapping of its vertices into points of the plane, and its edges into continuous curves, connecting the images of their ...
Julia Chuzhoy, Yury Makarychev, Anastasios Sidirop...
For n 27 we present exact values for the maximum number h(n) of halving lines and h(n) of halving pseudolines, determined by n points in the plane. For this range of values of n ...