The number of cliques in hypergraphs with forbidden subgraphs
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909645397819392 |
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| author | Basu, Ayush Rodl, Vojtech Zhao, Yi |
| author_facet | Basu, Ayush Rodl, Vojtech Zhao, Yi |
| contents | We study the maximum number of $r$-vertex cliques in $(r-1)$-uniform hypergraphs not containing complete $r$-partite hypergraphs $K_r^{(r-1)}(a_1, \dots, a_r)$. By using the hypergraph removal lemma, we show that this maximum is $o( n^{r - 1/(a_1 \cdots a_{r-1})} )$. This immediately implies the corresponding results of Mubayi and Mukherjee and of Balogh, Jiang, and Luo for graphs. We also provide a lower bound by using hypergraph Turán numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The number of cliques in hypergraphs with forbidden subgraphs Basu, Ayush Rodl, Vojtech Zhao, Yi Combinatorics We study the maximum number of $r$-vertex cliques in $(r-1)$-uniform hypergraphs not containing complete $r$-partite hypergraphs $K_r^{(r-1)}(a_1, \dots, a_r)$. By using the hypergraph removal lemma, we show that this maximum is $o( n^{r - 1/(a_1 \cdots a_{r-1})} )$. This immediately implies the corresponding results of Mubayi and Mukherjee and of Balogh, Jiang, and Luo for graphs. We also provide a lower bound by using hypergraph Turán numbers. |
| title | The number of cliques in hypergraphs with forbidden subgraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.07763 |