论文标题
在部分Steiner $（n，r，\ ell）$ - 系统过程中
On partial Steiner $(n,r,\ell)$-system process
论文作者
论文摘要
对于给定的整数$ r $和$ \ ell $，以便$ 2 \ leqslant \ ell \ leqslant r-1 $，如果每个子集的大小$ \ el eell $都在$ h $ h $ h $ h $ h $ h $的每个子集中，则称为部分steiner $（n，r，\ ell）$ - 系统$（n，r，\ el）$ - 系统。特别是，部分施泰纳$（n，r，2）$ - 系统也称为线性超图。 The partial Steiner $(n,r,\ell)$-system process starts with an empty hypergraph on vertex set $[n]$ at time $0$, the $ \binom{n}{r}$ edges arrive one by one according to a uniformly chosen permutation, and each edge is added if and only if it does not overlap any of the previously-added edges in $\ell$ or more vertices.在本文中，我们显示出很高的可能性，独立于$ \ ell $，算法中连接的尖锐阈值为$ \ frac {n} {r} {r} \ log n $，而将最后一个隔离的顶点与另一个顶点链接到另一个隔离顶点的边缘使部分steiner $（N，r，r，r，\ ell，\ ell，\ ell，\ ell，\ ell）$ - 系统连接。
For given integers $r$ and $\ell$ such that $2\leqslant\ell\leqslant r-1$, an $r$-uniform hypergraph $H$ is called a partial Steiner $(n,r,\ell)$-system, if every subset of size $\ell$ lies in at most one edge of $H$. In particular, partial Steiner $(n,r,2)$-systems are also called linear hypergraphs. The partial Steiner $(n,r,\ell)$-system process starts with an empty hypergraph on vertex set $[n]$ at time $0$, the $ \binom{n}{r}$ edges arrive one by one according to a uniformly chosen permutation, and each edge is added if and only if it does not overlap any of the previously-added edges in $\ell$ or more vertices. In this paper, we show with high probability, independent of $\ell$, the sharp threshold of connectivity in the algorithm is $ \frac{n}{r}\log n$ and the very edge which links the last isolated vertex with another vertex makes the partial Steiner $(n,r,\ell)$-system connected.
