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k-connectivity threshold for superpositions of Bernoulli random graphs

2025/03/21 by Ardickas, Daumilas, Bloznelis, Mindaugas, Vaicekauskas, Rimantas
#05C40 #05C80 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2503.16925

Abstract

Let G1,…, Gm be independent identically distributed Bernoulli random subgraphs of the complete graph \cal Kn having vertex sets of random sizes X1,…, Xm∈ \0,1,2,…\ and random edge densities Q1,…, Qm∈ [0,1]. Assuming that each Gi has a vertex of degree 1 with positive probability, we establish the k-connectivity threshold as n,m→+∞ for the union ∪i=1mGi defined on the vertex set of \cal Kn.

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