k-connectivity threshold for superpositions of Bernoulli random graphs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909547309826048 |
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| author | Ardickas, Daumilas Bloznelis, Mindaugas Vaicekauskas, Rimantas |
| author_facet | Ardickas, Daumilas Bloznelis, Mindaugas Vaicekauskas, Rimantas |
| contents | Let $G_1,\dots, G_m$ be independent identically distributed Bernoulli random subgraphs of the complete graph ${\cal K}_n$ having vertex sets of random sizes $X_1,\dots, X_m\in \{0,1,2,\dots\}$ and random edge densities $Q_1,\dots, Q_m\in [0,1]$. Assuming that each $G_i$ has a vertex of degree $1$ with positive probability, we establish the $k$-connectivity threshold as $n,m\to+\infty$ for the union $\cup_{i=1}^mG_i$ defined on the vertex set of ${\cal K}_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16925 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | k-connectivity threshold for superpositions of Bernoulli random graphs Ardickas, Daumilas Bloznelis, Mindaugas Vaicekauskas, Rimantas Probability 05C80, 05C40 Let $G_1,\dots, G_m$ be independent identically distributed Bernoulli random subgraphs of the complete graph ${\cal K}_n$ having vertex sets of random sizes $X_1,\dots, X_m\in \{0,1,2,\dots\}$ and random edge densities $Q_1,\dots, Q_m\in [0,1]$. Assuming that each $G_i$ has a vertex of degree $1$ with positive probability, we establish the $k$-connectivity threshold as $n,m\to+\infty$ for the union $\cup_{i=1}^mG_i$ defined on the vertex set of ${\cal K}_n$. |
| title | k-connectivity threshold for superpositions of Bernoulli random graphs |
| topic | Probability 05C80, 05C40 |
| url | https://arxiv.org/abs/2503.16925 |