Let G = (V, E) be a graph with n vertices and m ≥ 4n edges drawn in the plane. The celebrated Crossing Lemma states that G has at least Ω(m3 /n2 ) pairs of crossing edges; or ...
Many real-life scheduling, routing and location problems can be formulated as combinatorial optimization problems whose goal is to find a linear layout of an input graph in such a ...
We present an (1+ε)-approximation algorithm for computing the minimum-spanning tree of points in a planar arrangement of lines, where the metric is the number of crossings betwee...
Two and a half dimensional graph visualisation is the stacking of a set of related graphs into the third dimension to support visual comparison. A new aesthetic criterion is intro...
In this paper we investigate how certain results related to the HananiTutte theorem can be extended from the plane to surfaces. We give a simple topological proof that the weak Ha...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...