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- W3044650568 abstract "Let $r$ and $ell$ be given integers such that $2leqellleq r-1$. An $r$-uniform hypergraph $H$ is said to be $(n,r,ell)$ if every subset of size $ell$ is contained in at most one edge. In particular, $(n,r,2)$-hypergraphs are linear. The random $(n,r,ell)$-hypergraph process ${mathbb{L}_r^ell(n,m)}_m$ begins with no edges at time $0$, adds one edge at a time such that each new edge is selected uniformly among all edges not already present and not violating $(n,r,ell)$-property. The number of $(n,r,ell)$-hypergraphs on $nrightarrowinfty$ vertices is determined asymptotically as $3leqellleq r-1$ and the number of edges $m(n)=o(n^{ frac{ell+1}{2}})$, which generalizes the corresponding result as $ell=2$. The probability of $(n,r,ell)$-property for the independent-edge random $r$-uniform hypergraph and the probability that a random $(n,r,ell)$-hypergraph with a given number of edges contains a given subhypergraph are also extended. As one application, we consider the hitting time of connectivity for random $(n,r,ell)$-hypergraph process ${mathbb{L}_r^ell(n,m)}_m$ by the way different with the random hypergraph process ${mathbb{H}_r(n,m)}_m$. The asymptotically precise estimate of the number of linear $k$-partite $r$-uniform hypergraph is also shown as a function of the number of edges as $3leq rleq kleq n$." @default.
- W3044650568 created "2020-07-29" @default.
- W3044650568 creator A5077565006 @default.
- W3044650568 date "2020-07-23" @default.
- W3044650568 modified "2023-09-27" @default.
- W3044650568 title "Hitting time of connectivity for random $(n,r,ell)$-hypergraph process" @default.
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