In order to perform an average-case analysis for specific input distributions one needs to derive and understand properties of a 'typical' input instance. In the case of...
In 2007 we introduced a general model of sparse random graphs with independence between the edges. The aim of this paper is to present an extension of this model in which the edge...
We give a new derivation of the threshold of appearance of the k-core of a random graph. Our method uses a hybrid model obtained from a simple model of random graphs based on rand...
Two classic “phase transitions” in discrete mathematics are the emergence of a giant component in a random graph as the density of edges increases, and the transition of a rand...
We give a polynomial-time algorithm for the following problem: Given a degree sequence in which each degree is bounded from above by a constant, select, uniformly at random, an un...