Tight paths in convex geometric hypergraphs
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2017
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| _version_ | 1866914916785455104 |
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| author | Füredi, Zoltán Jiang, Tao Kostochka, Alexandr Mubayi, Dhruv Verstraëte, Jacques |
| author_facet | Füredi, Zoltán Jiang, Tao Kostochka, Alexandr Mubayi, Dhruv Verstraëte, Jacques |
| contents | In this paper, we prove a theorem on tight paths in convex geometric hypergraphs, which is asymptotically sharp in infinitely many cases. Our geometric theorem is a common generalization of early results of Hopf and Pannwitz, Sutherland, Kupitz and Perles for convex geometric graphs, as well as the classical Erdős-Gallai Theorem for graphs. As a consequence, we obtain the first substantial improvement on the Turán problem for tight paths in uniform hypergraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1709_01173 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Tight paths in convex geometric hypergraphs Füredi, Zoltán Jiang, Tao Kostochka, Alexandr Mubayi, Dhruv Verstraëte, Jacques Combinatorics 05C In this paper, we prove a theorem on tight paths in convex geometric hypergraphs, which is asymptotically sharp in infinitely many cases. Our geometric theorem is a common generalization of early results of Hopf and Pannwitz, Sutherland, Kupitz and Perles for convex geometric graphs, as well as the classical Erdős-Gallai Theorem for graphs. As a consequence, we obtain the first substantial improvement on the Turán problem for tight paths in uniform hypergraphs. |
| title | Tight paths in convex geometric hypergraphs |
| topic | Combinatorics 05C |
| url | https://arxiv.org/abs/1709.01173 |