## Gábor Lugosi

Connectivity and giant component in Bluetooth networks

### Abstract:

Consider a graph whose vertices represent n uniform random points in
the unit square.
One may form a random geometric graph by connecting two points by an
edge if the distance of the points is at most r. Let c be a positive
integer. We form a subgraph of the random geometric graph by
selecting, at random, c vertices among the neighbors of any given
vertex, and keeping only the edges joining the vertex to the selected
neighbors.
We present various results about connectivity properties of such
graphs.

Joint work with Nicolas Broutin and Luc Devroye.