Füredi, Zoltán and Mubayi, Dhruv and O'Neill, Jason and Verstraete, Jacques (2022) Extremal problems for pairs of triangles. JOURNAL OF COMBINATORIAL THEORY SERIES B, 155. pp. 83-110. ISSN 0095-8956
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Abstract
A convex geometric hypergraph or cgh consists of a family of subsets of a strictly convex set of points in the plane. There are eight pairwise nonisomorphic cgh's consisting of two distinct triangles. These were studied at length by Brag [6] (2004) and by Aronov, Dujmovic, Morin, Ooms, and da Silveira [2] (2019). We determine the extremal functions exactly for seven of the eight configurations. The above results are about cyclically ordered hypergraphs. We extend some of them for triangle systems with vertices from a non-convex set. We also solve problems posed by P. Frankl, Holmsen and Kupavskii [15] (2020), in particular, we determine the exact maximum size of an intersecting family of triangles whose vertices come from a set of n points in the plane. (c) 2022 Elsevier Inc. All rights reserved.
| Item Type: | Article |
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| Additional Information: | Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, Budapest, H-1364, Hungary Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, United States Department of Mathematics, University of California, San Diego, United States Export Date: 19 January 2023 CODEN: JCBTB Funding details: National Science Foundation, NSF, DMS-1800332, DMS-1952767 Funding details: Directorate for Mathematical and Physical Sciences, MPS, 1800332 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, KH130371, NKFI–133819 Funding text 1: The research of the first author was supported in part by NKFIH grant KH130371 and NKFI–133819 . The second author was supported by NSF award DMS-1952767 and the last two authors were supported by NSF award DMS-1800332 . The authors are very grateful to both referees for carefully reading the paper and providing many valuable comments that improved the presentation. |
| Uncontrolled Keywords: | Extremal hypergraphs; Extremal hypergraphs; Intersecting planar triangle systems; Intersecting planar triangle systems; Ordered triple systems; Ordered triple systems; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 17 Mar 2023 08:05 |
| Last Modified: | 06 Apr 2023 14:24 |
| URI: | http://real.mtak.hu/id/eprint/162328 |
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