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Factors in randomly perturbed hypergraphs
Random Structures and Algorithms ( IF 0.9 ) Pub Date : 2021-07-20 , DOI: 10.1002/rsa.21035 Yulin Chang 1 , Jie Han 2 , Yoshiharu Kohayakawa 3 , Patrick Morris 4 , Guilherme Oliveira Mota 3
Random Structures and Algorithms ( IF 0.9 ) Pub Date : 2021-07-20 , DOI: 10.1002/rsa.21035 Yulin Chang 1 , Jie Han 2 , Yoshiharu Kohayakawa 3 , Patrick Morris 4 , Guilherme Oliveira Mota 3
Affiliation
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:
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。
更新日期:2021-07-20
中文翻译:
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。