We exhibit a family of graphs which can be realized as pseudo-visibility graphs of pseudo-polygons, but not of straight-line polygons. The example is based on the characterization of vertex-edge pseudo-visibility graphs of O’Rourke and Streinu [Proc. ACM Symp. Comput. Geometry, Nice, France, 1997, pp. 119–128] and extends a recent result of the author [Proc. ACM Symp. Comput. Geometry, Miami Be...

We present a model for controlling swarms of mobile agents via broadcast control, assumed to be detected by a random set of agents in the swarm. The agents that detect the control signal become ad-hoc leaders of the swarm. The agents are assumed to be velocity controlled, identical, anonymous, memoryless units with limited capabilities of sensing their neighborhood. Each agent is programmed to ...

We prove that a graph is 4-colorable if and only if it can be drawn with vertices in the integer lattice, using as edges only line segments not containing a third point of the lattice.

We consider visibility representations of graphs in which the vertices are represented by a collection O of non-overlapping convex regions on the plane. Two points x and y are visible if the straight-line segment xy is not obstructed by any object. Two objects A; B 2 O are called visible if there exist points x 2 A; y 2 B such that x is visible from y. We consider visibility only for a nite set...