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, . . ....
Reachability and distance computation are known to be NL-complete in general graphs, but within UL co-UL if the graphs are planar. However, finding longest paths is known to be N...
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...