#
On *k*-Connectivity for a Geometric Random Graph

##
By Mathew D. Penrose.

For *n* points uniformly randomly distributed on the unit cube in
*d*
dimensions, with *d* > 1, let *r*_{n},
(respectively *s*_{n}) denote
the minimum *r* at which the graph, obtained by adding an edge between
each pair of points distant at most *r* apart, is *k*-connected
(respectively, has minimum degree *k*). Then
*r*_{n} = s_{n}
with probability approaching 1 as *n* tends to infinity.
Random Structures and Algorithms 15, 145-164 (1999).