We show that recognizing intersection graphs of convex sets has the same complexity as deciding truth in the existential theory of the reals. Comparing this to similar results on t...
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 ...
The nth crossing number of a graph G, denoted crn(G), is the minimum number of crossings in a drawing of G on an orientable surface of genus n. We prove that for every a > b &g...
Two sets are non-crossing if they are disjoint or one contains the other. The noncrossing graph NCn is the graph whose vertex set is the set of nonempty subsets of [n] = {1, . . ....
Abstract. Directed graphs are commonly drawn by the Sugiyama algorithm, where crossing reduction is a crucial phase. It is done by repeated one-sided 2-level crossing minimizations...
Christian Bachmaier, Franz-Josef Brandenburg, Wolf...