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  to ensure an F-factor with high probability, for any F that belongs to a certain class  of k-graphs, which includes, for example, all k-partite k-graphs, and the Fano plane. In particular, taking F to be a single edge, this settles a problem of Krivelevich, Kwan, and Sudakov. 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).

中文翻译：

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随机扰动超图的因素

我们确定，直到一个乘法常数 ， 对于任何 属于某一类 k -graphs，例如，包括所有k -partite k -graphs和 Fano 平面。特别是，以 F为单边，这解决了 Krivelevich、Kwan 和 Sudakov 的问题。我们还解决了主机图 H不密集的情况，表明从某些这样的 H本质上与从空图开始（即纯随机模型）相同。