A short proof of Tuza's conjecture for weak saturation in hypergraphs
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916704875970560 |
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| author | Terekhov, Nikolai |
| author_facet | Terekhov, Nikolai |
| contents | Given an $r$-uniform hypergraph $H$ and a positive integer $n$, the weak saturation number $\mathrm{wsat}(n,H)$ is the minimum number of edges in an $r$-uniform hypergraph $F$ on $n$ vertices such that the missing edges in $F$ can be added, one at a time, so that each added edge creates a copy of $H$. Shapira and Tyomkyn (Proceedings of the American Mathematical Society, 2023) proved Tuza's conjecture on asymptotic behaviour of $\mathrm{wsat}(n, H)$. In this paper we provide a significantly shorter proof of the conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03816 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A short proof of Tuza's conjecture for weak saturation in hypergraphs Terekhov, Nikolai Combinatorics Given an $r$-uniform hypergraph $H$ and a positive integer $n$, the weak saturation number $\mathrm{wsat}(n,H)$ is the minimum number of edges in an $r$-uniform hypergraph $F$ on $n$ vertices such that the missing edges in $F$ can be added, one at a time, so that each added edge creates a copy of $H$. Shapira and Tyomkyn (Proceedings of the American Mathematical Society, 2023) proved Tuza's conjecture on asymptotic behaviour of $\mathrm{wsat}(n, H)$. In this paper we provide a significantly shorter proof of the conjecture. |
| title | A short proof of Tuza's conjecture for weak saturation in hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2504.03816 |