Let and be hypergraphs on vertices, and suppose has large enough minimum degree to necessarily contain a copy of as a subgraph. We give a general method to randomly embed into with good “spread”. More precisely, for a wide class of , we find a randomised embedding with the following property: for every , for any partial embedding of vertices of into , the probability that extends is at most . This is a common generalisation of several streams of research surrounding the classical Dirac-type problem.

中文翻译：

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狄拉克超图的跨越子图的最优分布


令 和 为顶点上的超图，并假设具有足够大的最小度以必然包含 的副本作为子图。我们给出了一种通用的方法来随机嵌入并具有良好的“传播”。更准确地说，对于 的广泛类别，我们找到具有以下属性的随机嵌入：对于每个 ，对于 的顶点的任何部分嵌入，扩展的概率至多为 。这是围绕经典狄拉克型问题的几个研究流派的共同概括。