تقرير
Tight bound for the Erd\H{o}s-P\'osa property of tree minors
| العنوان: | Tight bound for the Erd\H{o}s-P\'osa property of tree minors |
|---|---|
| المؤلفون: | Dujmović, Vida, Joret, Gwenaël, Micek, Piotr, Morin, Pat |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, Computer Science - Discrete Mathematics |
| الوصف: | 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. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.06370 |
| رقم الأكسشن: | edsarx.2403.06370 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |