Geodesic
Extremal problems for convex geometric hypergraphs and ordered hypergraphs
Canadian journal of mathematics, Tome 73 (2021) no. 6, pp. 1648-1666

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DOI

An ordered hypergraph is a hypergraph whose vertex set is linearly ordered, and a convex geometric hypergraph is a hypergraph whose vertex set is cyclically ordered. Extremal problems for ordered and convex geometric graphs have a rich history with applications to a variety of problems in combinatorial geometry. In this paper, we consider analogous extremal problems for uniform hypergraphs, and determine the order of magnitude of the extremal function for various ordered and convex geometric paths and matchings. Our results generalize earlier works of Braß–Károlyi–Valtr, Capoyleas–Pach, and Aronov–Dujmovič–Morin–Ooms-da Silveira. We also provide a new variation of the Erdős-Ko-Rado theorem in the ordered setting.
DOI : 10.4153/S0008414X20000632
Mots-clés : Convex geometric hypergraph, extremal hypergraph 
Füredi, Zoltán; Jiang, Tao; Kostochka, Alexandr; Mubayi, Dhruv; Verstraëte, Jacques. Extremal problems for convex geometric hypergraphs and ordered hypergraphs. Canadian journal of mathematics, Tome 73 (2021) no. 6, pp. 1648-1666. doi: 10.4153/S0008414X20000632
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     title = {Extremal problems for convex geometric hypergraphs and ordered hypergraphs},
     journal = {Canadian journal of mathematics},
     pages = {1648--1666},
     year = {2021},
     volume = {73},
     number = {6},
     doi = {10.4153/S0008414X20000632},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X20000632/}
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