Name
Abstract | ||
|---|---|---|
In this paper we give a simple new proof of a result of Pittel and Wormald concerning the asymptotic value and (suitably rescaled) limiting distribution of the number of vertices in the giant component of G(n,p) above the scaling window of the phase transition. Nachmias and Peres used martingale arguments to study Karp@?s exploration process, obtaining a simple proof of a weak form of this result. We use slightly different martingale arguments to obtain a much sharper result with little extra work. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.jctb.2011.04.003 | Journal of Combinatorial Theory |
Keywords | Field | DocType |
simple proof,giant component,asymptotic value,random graphs,martingale argument,random walk,normal approximation,different martingale argument,asymptotic normality,simple new proof,extra work,phase transition,sharper result,exploration process | Martingale (probability theory),Combinatorics,Random graph,Vertex (geometry),Phase transition,Random walk,Giant component,Scaling,Mathematics,Asymptotic distribution | Journal |
Volume | Issue | ISSN |
102 | 1 | J. Combinatorial Theory B 102 (2012), 53--61 |
Citations | PageRank | References |
6 | 0.55 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Béla Bollobás | 1 | 2696 | 474.16 |
| Oliver Riordan | 2 | 285 | 38.31 |