On Turán numbers for disconnected hypergraphs
Raffaella Mulas and Jiaxi Nie
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Submission date: 21. Jul. 2022
Link to arXiv: See the arXiv entry of this preprint.
We introduce the following simpler variant of the Turán problem: Given integers n > k > r ≥ 2 and m ≥ 1, what is the smallest integer t for which there exists an r-uniform hypergraph with n vertices, t edges and m connected components such that any k-subset of the vertex set contains at least one edge? We prove some general estimates for this quantity and for its limit, normalized by , as n →∞. Moreover, we give a complete solution of the problem for the particular case when k = 5, r = 3 and m ≥ 2.