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arXiv · 2601.18439

A coarse Gallai theorem

Marc Distel·Ugo Giocanti·Jędrzej Hodor·Clément Legrand-Duchesne·Piotr Micek
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Abstract

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 $B_G(X,g(k,d))$.

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Marc Distel, Ugo Giocanti, Jędrzej Hodor, Clément Legrand-Duchesne, Piotr Micek. 2026-01-26. A coarse Gallai theorem. https://arxiv.org/abs/2601.18439

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