EDGE PERCOLATION ON A RANDOM REGULAR GRAPH OF LOW DEGREE 3 What about the window width ?

@inproceedings{Pittel2008EDGEPO,
  title={EDGE PERCOLATION ON A RANDOM REGULAR GRAPH OF LOW DEGREE 3 What about the window width ?},
  author={Boris Pittel},
  year={2008}
}
Consider a uniformly random regular graph of a fixed degree d ≥ 3, with n vertices. Suppose that each edge is open (closed), with probability p(q = 1 − p), respectively. In 2004 Alon, Benjamini and Stacey proved that p = (d − 1) is the threshold probability for emergence of a giant component in the subgraph formed by the open edges. In this paper we show that the transition window around p has width roughly of order n. More precisely, suppose that p = p(n) is such that ω := n|p− p| →∞. If p < p… CONTINUE READING

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