On $t$-intersecting 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_ | 1866916861879255040 |
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| author | Saengrungkongka, Pitchayut |
| author_facet | Saengrungkongka, Pitchayut |
| contents | We prove that there exists a constant $c>0$ such that for all integers $2\leq t\leq cn$, if $\calA$ is a collection of spanning trees in $K_n$ such that any two intersect at at least $t$ edges, then $|\calA|\leq 2^tn^{n-t-2}$. This bound is tight; the equality is achieved when $\calA$ is a collection of spanning trees containing a fixed $t$ disjoint edges. This is an improvement of a result by Frankl, Hurlbert, Ihringer, Kupavskii, Lindzey, Meagher, and Pantagi, who proved such a result for $t=O\left(\frac n{\log n}\right)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_18629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On $t$-intersecting Families of Spanning Trees Saengrungkongka, Pitchayut Combinatorics We prove that there exists a constant $c>0$ such that for all integers $2\leq t\leq cn$, if $\calA$ is a collection of spanning trees in $K_n$ such that any two intersect at at least $t$ edges, then $|\calA|\leq 2^tn^{n-t-2}$. This bound is tight; the equality is achieved when $\calA$ is a collection of spanning trees containing a fixed $t$ disjoint edges. This is an improvement of a result by Frankl, Hurlbert, Ihringer, Kupavskii, Lindzey, Meagher, and Pantagi, who proved such a result for $t=O\left(\frac n{\log n}\right)$. |
| title | On $t$-intersecting Families of Spanning Trees |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.18629 |