A coarse Gallai theorem

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Marc Distel, Ugo Giocanti, Jędrzej Hodor, Clément Legrand–Duchesne, Piotr Micek
DOI: 10.48550/arxiv.2601.18439
Cited by: 0

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

Fields of Study & Subjects

Advanced Graph Theory Research Limits and Structures in Graph Theory Complexity and Algorithms in Graphs

Publication details

Journal / source
arXiv (Cornell University)
Publication date
26 January 2026
Document type
Preprint