We show that for every fixed ? there is a quadratic time algorithm that decides whether a given graph has crossing number at most and, if this is the case, computes a drawing of t...
Given any knot diagram E, we present a sequence of knot diagrams of the same knot type, for which the minimum number of Reidemeister moves required to pass to E is quadratic with ...
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...