Erd\H{o}s-P\'{o}sa property of cycles that are far apart
| Autor: | Dujmović, Vida, Joret, Gwenaël, Micek, Piotr, Morin, Pat |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $X$. Comment: 22 pages, lots of formulas |
| Databáze: | arXiv |
| Externí odkaz: |
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