A string graph is the intersection graph of a set of curves in the plane. Each curve is represented by a vertex, and an edge between two vertices means that the corresponding curv...
Marcus Schaefer, Eric Sedgwick, Daniel Stefankovic
We extend (and somewhat simplify) the algebraic proof technique of Guth and Katz [7], to obtain several sharp bounds on the number of incidences between lines and points in three ...
We consider two classes of higher order proximity graphs defined on a set of points in the plane, namely, the k-Delaunay graph and the k-Gabriel graph. We give bounds on the follo...
We show that in the worst case, (ndd=2e;1 +n logn) sidedness queries are required to determine whether the convex hull of n points in IRd is simplicial, or to determine the number ...
According to a classical result of Gr¨unbaum, the transversal number τ(F) of any family F of pairwise-intersecting translates or homothets of a convex body C in Rd is bounded by...