论文标题
HyperGraph Bootstrap Percolation的最大运行时间
The maximal running time of hypergraph bootstrap percolation
论文作者
论文摘要
我们表明，对于每$ r \ ge 3 $，$ k^{r} _ {r+1} $的最大运行时间 - 在$ n $ n $ vertices $ k_n^r $ IS $ the us is $ thytices上的完整$ r $ rub-rystrap Hypercolation中的bootstrap Percolation $ us-r均匀的hypergraph。这回答了Noel和Ranganathan的最新问题，并反驳了他们的猜想。此外，我们证明了预制器的形式为$ r^{ - r} \ mathrm {e}^{o（r）} $作为$ r \ to \ infty $。
We show that for every $r\ge 3$, the maximal running time of the $K^{r}_{r+1}$-bootstrap percolation in the complete $r$-uniform hypergraph on $n$ vertices $K_n^r$ is $Θ(n^r)$. This answers a recent question of Noel and Ranganathan in the affirmative, and disproves a conjecture of theirs. Moreover, we show that the prefactor is of the form $r^{-r} \mathrm{e}^{O(r)}$ as $r\to\infty$.
