Abstract. CrossingNumber is one of the most challenging algorithmic problems in topological graph theory, with applications to graph drawing and VLSI layout. No polynomial time con...
In an orthogonal drawing of a planar graph G, each vertex is drawn as a point, each edge is drawn as a sequence of alternate horizontal and vertical line segments, and any two edge...
A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V in the Euclidean plane without crossings between edges of the same graph. Fixed ...
This paper shows that any planar graph with n vertices can be point-set embedded with at most one bend per edge on a universal set of n points in the plane. An implication of this...
Hazel Everett, Sylvain Lazard, Giuseppe Liotta, St...
A topological graph is quasi-planar, if it does not contain three pairwise crossing edges. Agarwal et al. [2] proved that these graphs have a linear number of edges. We give a sim...