Deciding 3-colorability for general plane graphs is known to be an NP-complete problem. However, for certain families of graphs, like triangulations, polynomial time algorithms exist. We consider the family of pseudo-tri ...

We show that in every arrangement of n red and blue lines | in general position and not all of the same color | there is a path through a linear number of cells where red and blue lines are crossed alternatingly (and no ...

A geometric graph is a graph G = (V;E) drawn in the plane, such that V is a point set in general position and E is a set of straight-line segments whose endpoints belong to V . We study the following extremal problem for ...

A good drawing of a simple graph is a drawing on the sphere or, equivalently, in the plane in which vertices are drawn as distinct points, edges are drawn as Jordan arcs connecting their end vertices, and any pair of edges ...

The total angular resolution of a straight-line drawing is the minimum angle between two edges of the drawing. It combines two properties contributing to the readability of a drawing: the angular resolution, which is the ...

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.