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The Asymptotic Number of Connected d-Uniform Hypergraphs
| Content Provider | Scilit |
|---|---|
| Author | Behrisch, Michael Coja-Oghlan, Amin Kang, Mihyun |
| Copyright Year | 2014 |
| Description | For d ≥ 2, let $H_{d}$(n,p) denote a random d-uniform hypergraph with n vertices in which each of the $\binom{n}{d}$ possible edges is present with probability p=p(n) independently, and let $H_{d}$(n,m) denote a uniformly distributed d-uniform hypergraph with n vertices and m edges. Let either $H=H_{d}$(n,m) or $H=H_{d}$(n,p), where m/n and $\binom{n-1}{d-1}p$ need to be bounded away from $(d−1)^{−1}$ and 0 respectively. We determine the asymptotic probability that H is connected. This yields the asymptotic number of connected d-uniform hypergraphs with given numbers of vertices and edges. We also derive a local limit theorem for the number of edges in $H_{d}$(n,p), conditioned on $H_{d}$(n,p) being connected. |
| Related Links | http://pdfs.semanticscholar.org/a15f/fa4e461f06eab3e4851d6f10216358e8affb.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/C73A1ECE380ADF627DCC3C3954C6E525/S0963548314000029a.pdf/div-class-title-the-asymptotic-number-of-connected-span-class-italic-d-span-uniform-hypergraphs-a-href-fn1a-ref-type-fn-span-class-sup-span-a-div.pdf |
| Ending Page | 385 |
| Page Count | 19 |
| Starting Page | 367 |
| ISSN | 09635483 |
| e-ISSN | 14692163 |
| DOI | 10.1017/s0963548314000029 |
| Journal | Combinatorics, Probability and Computing |
| Issue Number | 3 |
| Volume Number | 23 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2014-05-01 |
| Access Restriction | Open |
| Subject Keyword | Combinatorics, Probability and Computing Mathematical Physics Primary 05c80 Secondary 05c65 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics |
