Abstract
Let G( n, p) be a graph with n labelled vertices in which each edge is present independently with probability p = p( n) and let C( k; n, p) be the maximal subgraph of G( n, p) with the minimal degree at least k = k( n). In this paper we estimate the size of C( k; n, p) and consider the probability that C( k; n, p) is k-connected when n→∞.
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