Percolation, Connectivity, Coverage and Colouring of Random Geometric Graphs

Abstract

In this review paper, we shall discuss some recent results concerning severalmodels of random geometric graphs, including the Gilbert disc model Gr, thek-nearest neighbour model Gnn and the Voronoi model GP . Many of the results kconcern finite versions of these models. In passing, we shall mention some of the applications to engineering and biology.