Erdős--Pósa property of cycles that are far apart
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917451550162944 |
|---|---|
| author | Dujmović, Vida Joret, Gwenaël Micek, Piotr Morin, Pat |
| author_facet | Dujmović, Vida Joret, Gwenaël Micek, Piotr Morin, Pat |
| contents | We prove that there exist functions $f,g:\mathbb{N}\to\mathbb{N}$ such that for all nonnegative integers $k$ and $d$, for every graph $G$, either $G$ contains $k$ cycles such that vertices of different cycles have distance greater than $d$ in $G$, or there exists a subset $X$ of vertices of $G$ with $|X|\leq f(k)$ such that $G-B_G(X,g(d))$ is a forest, where $B_G(X,r)$ denotes the set of vertices of $G$ having distance at most $r$ from a vertex of $X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13893 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Erdős--Pósa property of cycles that are far apart Dujmović, Vida Joret, Gwenaël Micek, Piotr Morin, Pat Combinatorics Discrete Mathematics We prove that there exist functions $f,g:\mathbb{N}\to\mathbb{N}$ such that for all nonnegative integers $k$ and $d$, for every graph $G$, either $G$ contains $k$ cycles such that vertices of different cycles have distance greater than $d$ in $G$, or there exists a subset $X$ of vertices of $G$ with $|X|\leq f(k)$ such that $G-B_G(X,g(d))$ is a forest, where $B_G(X,r)$ denotes the set of vertices of $G$ having distance at most $r$ from a vertex of $X$. |
| title | Erdős--Pósa property of cycles that are far apart |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2412.13893 |