A coarse Gallai theorem
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915756017451008 |
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| author | Distel, Marc Giocanti, Ugo Hodor, Jędrzej Legrand-Duchesne, Clément Micek, Piotr |
| author_facet | Distel, Marc Giocanti, Ugo Hodor, Jędrzej Legrand-Duchesne, Clément Micek, Piotr |
| contents | We prove that there exist functions $f$ and $g$ such that for all positive integers $k$ and $d$, for every graph $G$ and every subset $A$ of the vertices of $G$, either $G$ contains $k$ $A$-paths such that vertices of different $A$-paths are at distance at least $d$ in $G$, or there exists a set $X$ of the vertices of $G$ with $|X|\leq f(k)$ such that every $A$-path in $G$ contains a vertex of $B_G(X,g(k,d))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18439 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A coarse Gallai theorem Distel, Marc Giocanti, Ugo Hodor, Jędrzej Legrand-Duchesne, Clément Micek, Piotr Combinatorics We prove that there exist functions $f$ and $g$ such that for all positive integers $k$ and $d$, for every graph $G$ and every subset $A$ of the vertices of $G$, either $G$ contains $k$ $A$-paths such that vertices of different $A$-paths are at distance at least $d$ in $G$, or there exists a set $X$ of the vertices of $G$ with $|X|\leq f(k)$ such that every $A$-path in $G$ contains a vertex of $B_G(X,g(k,d))$. |
| title | A coarse Gallai theorem |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.18439 |