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On the strength of connectedness of a random graph. (English) Zbl 0103.16302
Using the notation of the paper reviewed above the following theorem is proved: If $N(n) ={1 \over 2} n \log n + {1 \over 2} r n \log \log n + \alpha n + o(n)$, where $\alpha$ is a real constant and $r$ a non-negative integer, then $$\lim_{n \to +\infty} \text{Pr}(c_i(\Gamma_{n,N(n)}) = r) = 1-\exp(-e^{-2\alpha}/r!),$$ where $i=1,2,3$ and $c_1(G)$ denotes the minimal number of all edges starting from a single point in a given graph $G$, $c_2(G)$ or $c_3 (G)$ denotes the least number $k$ such that by deleting $k$ appropriately chosen points or edges the resulting graph is disconected (if $G$ is complete with $n$ points one puts $c_2(G) = n-1$).
Reviewer: K.Čulik

MSC:
05C40Connectivity
05C80Random graphs
Keywords:
topology
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