We show that there is a constant > 0 such that, for any set P of n 5 points in general position in the plane, a crossing-free geometric graph on P that is chosen uniformly at...
A random geometric graph Gn is constructed by taking vertices X1, . . . , Xn Rd at random (i.i.d. according to some probability distribution with a bounded density function) and...
We introduce a new realistic input model for geometric graphs and nonconvex polyhedra. A geometric graph G is local if (1) the longest edge at every vertex v is only a constant fa...
Consider a drawing of a graph G in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of G, is the classical graph...
The unit ball random geometric graph G = Gd p(λ, n) has as its vertices n points distributed independently and uniformly in the unit ball in Rd, with two vertices adjacent if and ...
Robert B. Ellis, Jeremy L. Martin, Catherine H. Ya...