A complete $t$-intersection theorem for families of spanning trees
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912499137249280 |
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| author | Iarovikova, Elizaveta Kupavskii, Andrey |
| author_facet | Iarovikova, Elizaveta Kupavskii, Andrey |
| contents | Let $\mathcal T_n$ denote the set of all labelled spanning trees of $K_n$. A family $\mathcal F \subset \mathcal T_n$ is $t$-intersecting if for all $A, B \in \mathcal F$ the trees $A$ and $B$ share at least $t$ edges. In this paper, we determine for $n>n_0$ the size of the largest $t$-intersecting family $\mathcal F\subset \mathcal T_n$ for all meaningful values of $t$ ($t\le n-1$). This result is a rare instance when a complete $t$-intersection theorem for a given type of structures is known. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_17913 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A complete $t$-intersection theorem for families of spanning trees Iarovikova, Elizaveta Kupavskii, Andrey Combinatorics Discrete Mathematics Let $\mathcal T_n$ denote the set of all labelled spanning trees of $K_n$. A family $\mathcal F \subset \mathcal T_n$ is $t$-intersecting if for all $A, B \in \mathcal F$ the trees $A$ and $B$ share at least $t$ edges. In this paper, we determine for $n>n_0$ the size of the largest $t$-intersecting family $\mathcal F\subset \mathcal T_n$ for all meaningful values of $t$ ($t\le n-1$). This result is a rare instance when a complete $t$-intersection theorem for a given type of structures is known. |
| title | A complete $t$-intersection theorem for families of spanning trees |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2507.17913 |