Tight bound for the Erd\Hos-P\'osa property of tree minors
<|reference_start|>Tight bound for the Erd\Hos-P\'osa property of tree minors: Let $T$ be a tree on $t$ vertices. We prove that for every positive integer $k$ and every graph $G$, either $G$ contains $k$ pairwise vertex-disjoint subgraphs each having a $T$ minor, or there exists a set $X$ of at most $t(k-1)$ vertices of $G$ such that $G-X$ has no $T$ minor. The bound on the size of $X$ is best possible and improves on an earlier $f(t)k$ bound proved by Fiorini, Joret, and Wood (2013) with some very fast growing function $f(t)$. Moreover, our proof is very short and simple.<|reference_end|>
@article{dujmović2024tight,
    title={Tight bound for the Erd\H{o}s-P\'osa property of tree minors},
    author={Vida Dujmovi'c and Gwena"el Joret and Piotr Micek and Pat Morin},
    journal={arXiv preprint arXiv:2403.06370},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.06370},
    primaryClass={math.CO cs.DM}
}