Geodesic
Asymptotic formulas for the probability of $k$-connectedness of random graphs
Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 2, pp. 253-265

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For graphs with vertices of sufficiently large, in a certain sense, degrees, asymptotical formulas are derived for the probability of $k$-connectedness of vertex subsets provided the edges of graphs are removed independently with given probabilities. 
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     author = {A. K. Kel'mans},
     title = {Asymptotic formulas for the probability of $k$-connectedness of random graphs},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {253--265},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1972_17_2_a3/}
}
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A. K. Kel'mans. Asymptotic formulas for the probability of $k$-connectedness of random graphs. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 2, pp. 253-265. http://geodesic.mathdoc.fr/item/TVP_1972_17_2_a3/