We consider a variant of a question of Erdos on the number of empty k-gons (k-holes) in a set of n points in the plane, where we allow the k-gons to be non-convex. We show bounds and structural results on maximizing and ...

Two non-crossing geometric graphs on the same set of points are compatible if their union is also non-crossing. In this paper, we prove that every graph G that has an outerplanar embedding admits a non-crossing perfect ...

Let S be a k-colored (finite) set of n points in , da parts per thousand yen3, in general position, that is, no (d+1) points of S lie in a common (d-1)-dimensional hyperplane. We count the number of empty monochromatic ...

The geodesic between two points a and b in the interior of a simple polygon P is the shortest polygonal path inside P that connects a to b. It is thus the natural generalization of straight line segments on unconstrained ...

Let S be a set of n points in the plane in general position, that is, no three points of S are on a line. We consider an Erdos-type question on the least number h(k)(n) of convex k-holes in S, and give improved lower bounds ...

We study a generalization of the classical problem of illumination of polygons. Instead of modeling a light source we model a wireless device whose radio signal can penetrate a given number k of walls. We call these ...

We consider sets L = {l1,...., ln} of n labeled lines in general position in R3, and study the order types of point sets fp1; : : : ; png that stem from the intersections of the lines in L with (directed) planes II, not ...

We introduce a notion of k-convexity and explore some properties of polygons that have this property. In particular, 2-convex polygons can be recognized in O(n log n) time, and k-convex polygons can be triangulated in O(kn) time.