We study the cover time of a random walk on the largest component of the random graph Gn,p. We determine its value up to a factor 1 + o(1) whenever np = c > 1, c = O(ln n). In ...
Consider a game in which edges of a graph are provided a pair at a time, and the player selects one edge from each pair, attempting to construct a graph with a component as large ...
Abraham Flaxman, David Gamarnik, Gregory B. Sorkin
The standard Erd˝os-Renyi model of random graphs begins with n isolated vertices, and at each round a random edge is added. Parametrizing n 2 rounds as one time unit, a phase tra...
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...
Given a sequence of non-negative real numbers 0 1 ::: which sum to 1, we consider a random graph having approximately in vertices of degree i. In 12] the authors essentially show ...