554 citations · 1.7k across the 51 of their papers we have counts for
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The k-core and branching processes
Oliver Riordan
The k-core of a graph G is the maximal subgraph of G having minimum degree at least k. In 1996, Pittel, Spencer and Wormald found the threshold for the emergence of a non-tri…
A note on the Harris-Kesten Theorem
Bela Bollobas, Oliver Riordan
Recently, a short proof of the Harris-Kesten result that the critical probability for bond percolation in the planar square lattice is 1/2 was given, using a sharp threshold result…
Spread-out percolation in R^d
Bela Bollobas, Svante Janson, Oliver Riordan
Let be either or the points of a Poisson process in of intensity 1. Given parameters and , join each pair of points of within distance independently…
The phase transition in inhomogeneous random graphs
Bela Bollobas, Svante Janson, Oliver Riordan
We introduce a very general model of an inhomogenous random graph with independence between the edges, which scales so that the number of edges is linear in the number of vertices.…