The geographical threshold graph model is a random graph model with nodes distributed in a Euclidean space and edges assigned through a function of distance and node weights. We st...
We analyze the structure of random graphs generated by the geographical threshold model. The model is a generalization of random geometric graphs. Nodes are distributed in space, a...
We consider random walks on two classes of random graphs and explore the likely structure of the vacant set viz. the set of unvisited vertices. Let (t) be the subgraph induced by ...
We propose a random graph model which is a special case of sparse random graphs with given degree sequences. This model involves only a small number of parameters, called logsize ...
: The classical result in the theory of random graphs, proved by Erd˝os and Rényi in 1960, concerns the threshold for the appearance of the giant component in the random graph pr...
Tom Bohman, Alan M. Frieze, Michael Krivelevich, P...