Geodesic
On the connectivity of configuration graphs
Diskretnaya Matematika, Tome 31 (2019) no. 2, pp. 114-122.

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We consider configuration graphs with vertex degrees being independent identically distributed random variables. The distribution of these variables satisfies only relatively weak constraints on the probabilities of large values of degrees. For the case when the number of vertices tends to infinity, the conditions are found under which the graph is asymptotically almost surely connected. We also give estimates of the rate of convergence to zero of the probability that the graph is not connected.
Keywords: configuration graph, random vertex degrees, graph connectivity. 
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Yu. L. Pavlov. On the connectivity of configuration graphs. Diskretnaya Matematika, Tome 31 (2019) no. 2, pp. 114-122. http://geodesic.mathdoc.fr/item/DM_2019_31_2_a8/

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