论文标题
在随机扰动超图中紧密的汉密尔顿周期的力量上
On powers of tight Hamilton cycles in randomly perturbed hypergraphs
论文作者
论文摘要
对于整数$ k \ geq 3 $和$ r \ geq 2 $，我们证明，对于每$α> 0 $，存在$ \ varepsilon> 0 $，使得$ k $ rostraph in $ n $ n $ bypraph in $ n $ nophypertices的结合至少$ n $ codegree，至少$αn$和binomial $ a $ k $ k $ k $ k $ k $ k $ - $ p \ geq n^{ - {\ binom {k+r-2} {k-1}}}^{ - 1} - \ \ varepsilon} $上的同一顶点集合包含$ r^{th {th} $ thth} $ thth hamilton周期的功率，具有很高的可能性。此外，建筑表明，一个人不能服用$ \ varepsilon>cα$，其中$ c = c（k，r）$是一个常数。因此，$ p $上的绑定最佳达到了$ \ varepsilon $的价值，这回答了贝登克尼奇，汉，kohayakawa和mota的问题。
For integers $k \geq 3$ and $r\geq 2$, we show that for every $α> 0$, there exists $\varepsilon > 0$ such that the union of $k$-uniform hypergraph on $n$ vertices with minimum codegree at least $αn$ and a binomial random $k$-uniform hypergraph $G^{(k)}(n,p)$ with $p\geq n^{-{\binom{k+r-2}{k-1}}^{-1}-\varepsilon}$ on the same vertex set contains the $r^{th}$ power of a tight Hamilton cycle with high probability. Moreover, a construction shows that one cannot take $\varepsilon > Cα$, where $C=C(k,r)$ is a constant. Thus the bound on $p$ is optimal up to the value of $\varepsilon$ and this answers a question of Bedenknecht, Han, Kohayakawa, and Mota.
