Extremal problems for convex geometric hypergraphs and ordered hypergraphs
Abstract
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 Bra{\ss}-K\'{a}rolyi-Valtr, Capoyleas-Pach and Aronov-Dujmovi\v{c}-Morin-Ooms-da Silveira. We also provide a new generalization of the Erd\H os-Ko-Rado theorem in the ordered setting.
Keywords
Cite
@article{arxiv.1906.04575,
title = {Extremal problems for convex geometric hypergraphs and ordered hypergraphs},
author = {Zoltán F\" uredi and Tao Jiang and Alexandr Kostochka and Dhruv Mubayi and Jacques Verstraëte},
journal= {arXiv preprint arXiv:1906.04575},
year = {2019}
}
Comments
19 pages 2 figures. arXiv admin note: substantial text overlap with arXiv:1807.05104