Add to ORKGGiven any two vertices u, v of a random geometric graph G(n, r), denote by dE(u, v) their Euclidean distance and by dE(u, v) their graph distance. The problem of finding upper bounds on dG(u, v) conditional on dE(u, v) that hold asymptotically almost surely has received quite a bit of attention in the literature. In this paper we improve the known upper bounds for values of r=¿(vlogn) (that is, for r above the connectivity threshold). Our result also improves the best known estimates on the diameter of random geometric graphs. We also provide a lower bound on dE(u, v) conditional on dE(u, v).Peer Reviewe
In this paper, we study the acquaintance time AC(G) defined for a connected graph G. We focus on G(n...
The metric dimension of a graph G is the minimum number of vertices in a subset S of the vertex set ...
We give asymptotically exact values for the treewidth tw(G) of a random geometric graph G ∈ G(n, r) ...
Given any two vertices u, v of a random geometric graph G(n, r), denote by dE(u, v) their Euclidean ...
Abstract. Given any two vertices u, v of a random geometric graph, denote by dE(u, v) their Eu-clide...
We give asymptotically exact values for the treewidth tw(G) of a random geometric graph G ¿ G(n, r) ...
We give asymptotic upper and lower bounds for the diameter of almost every r-regular graph on n vert...
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the under...
Given independent random points X1,...,Xn∈ℝd with common probability distribution ν, and a positive ...
Random geometric graphs result from taking n uniformly distributed points in the unit cube, [0, 1] d...
Random geometric graphs result from taking n uniformly distributed points in the unit cube, [0, 1] ...
Abstract. We consider graphs obtained by placing n points at random on a unit sphere in Rd, and conn...
Abstract. In this paper, we study the acquaintance time AC(G) defined for a connected graph G. We fo...
Let n be a positive integer, λ> 0 a real number, and 1≤ p≤ ∞. We study the unit disk random geometri...
Let n be a positive integer and λ> 0 a real number. Let Vn be a set of n points in the unit disk ...
In this paper, we study the acquaintance time AC(G) defined for a connected graph G. We focus on G(n...
The metric dimension of a graph G is the minimum number of vertices in a subset S of the vertex set ...
We give asymptotically exact values for the treewidth tw(G) of a random geometric graph G ∈ G(n, r) ...
Given any two vertices u, v of a random geometric graph G(n, r), denote by dE(u, v) their Euclidean ...
Abstract. Given any two vertices u, v of a random geometric graph, denote by dE(u, v) their Eu-clide...
We give asymptotically exact values for the treewidth tw(G) of a random geometric graph G ¿ G(n, r) ...
We give asymptotic upper and lower bounds for the diameter of almost every r-regular graph on n vert...
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the under...
Given independent random points X1,...,Xn∈ℝd with common probability distribution ν, and a positive ...
Random geometric graphs result from taking n uniformly distributed points in the unit cube, [0, 1] d...
Random geometric graphs result from taking n uniformly distributed points in the unit cube, [0, 1] ...
Abstract. We consider graphs obtained by placing n points at random on a unit sphere in Rd, and conn...
Abstract. In this paper, we study the acquaintance time AC(G) defined for a connected graph G. We fo...
Let n be a positive integer, λ> 0 a real number, and 1≤ p≤ ∞. We study the unit disk random geometri...
Let n be a positive integer and λ> 0 a real number. Let Vn be a set of n points in the unit disk ...
In this paper, we study the acquaintance time AC(G) defined for a connected graph G. We focus on G(n...
The metric dimension of a graph G is the minimum number of vertices in a subset S of the vertex set ...
We give asymptotically exact values for the treewidth tw(G) of a random geometric graph G ∈ G(n, r) ...