Name
Abstract | ||
|---|---|---|
For d >= 2, let H-d(n, p) denote a random d-uniform hypergraph with n vertices in which each of the ((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 ((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. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1017/S0963548314000029 | COMBINATORICS PROBABILITY & COMPUTING |
DocType | Volume | Issue |
Journal | 23 | 3 |
ISSN | Citations | PageRank |
0963-5483 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael Behrisch | 1 | 49 | 8.77 |
| Amin Coja-Oghlan | 2 | 543 | 47.25 |
| Mihyun Kang | 3 | 163 | 29.18 |