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...
Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrar...
The Two-Sided Crossing Minimization (TSCM) problem calls for minimizing the number of edge crossings of a bipartite graph where the two sets of vertices are drawn on two parallel l...
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...
The crossing number problem is to find the smallest number of edge crossings necessary when drawing a graph into the plane. Eventhough the problem is NP-hard, we are interested in ...