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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2601.19068 |
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| _version_ | 1866912851674791936 |
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| author | Tang, Chaoliang Wu, Hehui Zhang, Junchi |
| author_facet | Tang, Chaoliang Wu, Hehui Zhang, Junchi |
| contents | We prove that for any linear 3-graph on $n$ vertices without a path of length 5, the number of edges is at most $\frac{15}{11}n$, and the equality holds if and only if the graph is the disjoint union of $G_0$, a graph with 11 vertices and 15 edges. Thus, $ex_L(n,P_5)\leq \frac{15}{11}n$, and the equality holds if and only if $11|n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19068 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The linear Turán number of the 3-graph $P_5$ Tang, Chaoliang Wu, Hehui Zhang, Junchi Combinatorics We prove that for any linear 3-graph on $n$ vertices without a path of length 5, the number of edges is at most $\frac{15}{11}n$, and the equality holds if and only if the graph is the disjoint union of $G_0$, a graph with 11 vertices and 15 edges. Thus, $ex_L(n,P_5)\leq \frac{15}{11}n$, and the equality holds if and only if $11|n$. |
| title | The linear Turán number of the 3-graph $P_5$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.19068 |