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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.05601 |
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| _version_ | 1866913728995262464 |
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| author | Gerbner, Dániel Picollelli, Michael E. |
| author_facet | Gerbner, Dániel Picollelli, Michael E. |
| contents | We say that a hypergraph $\mathcal{H}$ contains a graph $H$ as a trace if there exists some set $S\subset V(\mathcal{H})$ such that $\mathcal{H}|_S=\{h\cap S: h\in E(\mathcal{H})\}$ contains a subhypergraph isomorphic to $H$. We study the largest number of hyperedges in 3-uniform hypergraphs avoiding some graph $F$ as trace. In particular, we improve a bound given by Luo and Spiro in the case $F=C_4$, and obtain exact bounds for large $n$ when $F$ is a book graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_05601 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On forbidding graphs as traces of hypergraphs Gerbner, Dániel Picollelli, Michael E. Combinatorics We say that a hypergraph $\mathcal{H}$ contains a graph $H$ as a trace if there exists some set $S\subset V(\mathcal{H})$ such that $\mathcal{H}|_S=\{h\cap S: h\in E(\mathcal{H})\}$ contains a subhypergraph isomorphic to $H$. We study the largest number of hyperedges in 3-uniform hypergraphs avoiding some graph $F$ as trace. In particular, we improve a bound given by Luo and Spiro in the case $F=C_4$, and obtain exact bounds for large $n$ when $F$ is a book graph. |
| title | On forbidding graphs as traces of hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2310.05601 |