论文标题
随机扰动超图中的因素
Factors in randomly perturbed hypergraphs
论文作者
论文摘要
我们确定需要添加到$ k $ -graph $ h $中的最佳随机边数，并具有最低顶点$ω（n^{k-1}）$，以确保具有较高概率的$ f $ f $ f $，对于任何属于某个类别$ \ nthercal的$ f $的$ f $ $ k $ -partite $ k $ -graphs，$ k_4^{（3） - } $和fano plane。特别是，将$ f $作为单一优势，这解决了Krivelevich，Kwan和Sudakov [Combin。概率。计算。 25（2016），909--927]。我们还解决了主机图$ h $并不致密的情况，这表明从某些$ h $开始与从空图开始（即纯粹随机模型）基本相同。
We determine, up to a multiplicative constant, the optimal number of random edges that need to be added to a $k$-graph $H$ with minimum vertex degree $Ω(n^{k-1})$ to ensure an $F$-factor with high probability, for any $F$ that belongs to a certain class $\mathcal{F}$ of $k$-graphs, which includes, e.g., all $k$-partite $k$-graphs, $K_4^{(3)-}$ and the Fano plane. In particular, taking $F$ to be a single edge, this settles a problem of Krivelevich, Kwan and Sudakov [Combin. Probab. Comput. 25 (2016), 909--927]. We also address the case in which the host graph $H$ is not dense, indicating that starting from certain such $H$ is essentially the same as starting from an empty graph (namely, the purely random model).
