Zarankiewicz numbers near the triple system threshold
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910523422932992 |
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| author | Chen, Guangzhou Horsley, Daniel Mammoliti, Adam |
| author_facet | Chen, Guangzhou Horsley, Daniel Mammoliti, Adam |
| contents | For positive integers $m$ and $n$, the Zarankiewicz number $Z_{2,2}(m,n)$ can be defined as the maximum total degree of a linear hypergraph with $m$ vertices and $n$ edges. Guy determined $Z_{2,2}(m,n)$ for all $n \geq \binom{m}{2}/3+O(m)$. Here, we extend this by determining $Z_{2,2}(m,n)$ for all $n \geq \binom{m}{2}/3$ and, when $m$ is large, for all $n \geq \binom{m}{2}/6+O(m)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_12685 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Zarankiewicz numbers near the triple system threshold Chen, Guangzhou Horsley, Daniel Mammoliti, Adam Combinatorics 05C35 (Primary) 05B40, 05B30 (Secondary) For positive integers $m$ and $n$, the Zarankiewicz number $Z_{2,2}(m,n)$ can be defined as the maximum total degree of a linear hypergraph with $m$ vertices and $n$ edges. Guy determined $Z_{2,2}(m,n)$ for all $n \geq \binom{m}{2}/3+O(m)$. Here, we extend this by determining $Z_{2,2}(m,n)$ for all $n \geq \binom{m}{2}/3$ and, when $m$ is large, for all $n \geq \binom{m}{2}/6+O(m)$. |
| title | Zarankiewicz numbers near the triple system threshold |
| topic | Combinatorics 05C35 (Primary) 05B40, 05B30 (Secondary) |
| url | https://arxiv.org/abs/2310.12685 |