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Compared to the classical binomial random (hyper)graph model, the study of random regular hypergraphs is made more challenging due to correlations between the occurrence of different edges. We develop an edge-switching technique for hypergraphs which allows us to show that these correlations are limited for a large range of densities. This extends some previous results of Kim, Sudakov, and Vu for graphs. From our results we deduce several corollaries on subgraph counts in random d-regular hypergraphs. We also prove a conjecture of Dudek, Frieze, Ruciński, and Šileikis on the threshold for the existence of an '-overlapping Hamilton cycle in a random d-regular r-graph. Moreover, we apply our results to prove bounds on the query complexity of testing subgraph-freeness. The problem of testing subgraph-freeness in the general graphs model was first studied by Alon, Kaufman, Krivelevich, and Ron, who obtained several bounds on the query complexity of testing triangle-freeness. We extend some of these previous results beyond the triangle setting and to the hypergraph setting. [ABSTRACT FROM AUTHOR]

A key feature of Simonovits' proof of the classic Erdőos--Pósa theorem is a simple subgraph of the host graph, a frame, that determines the outcome of the theorem. We transfer this frame technique to A-paths. With it we deduce a simple proof of Gallai's theorem, although with a worse bound, and we verify the Erdős--Pósa property for long and for even A-paths. We also show that even A-paths do not have the edge-Erdős--Pósa property. [ABSTRACT FROM AUTHOR]