Packing $A$-paths of length zero modulo a prime
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866914845383720960 |
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| author | Thomas, Robin Yoo, Youngho |
| author_facet | Thomas, Robin Yoo, Youngho |
| contents | It is known that $A$-paths of length $0$ mod $m$ satisfy the Erdős-Pósa property if $m=2$ or $m=4$, but not if $m > 4$ is composite. We show that if $p$ is prime, then $A$-paths of length $0$ mod $p$ satisfy the Erdős-Pósa property. More generally, in the framework of undirected group-labelled graphs, we characterize the abelian groups $Γ$ and elements $\ell \in Γ$ for which the Erdős-Pósa property holds for $A$-paths of weight $\ell$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_12230 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Packing $A$-paths of length zero modulo a prime Thomas, Robin Yoo, Youngho Combinatorics It is known that $A$-paths of length $0$ mod $m$ satisfy the Erdős-Pósa property if $m=2$ or $m=4$, but not if $m > 4$ is composite. We show that if $p$ is prime, then $A$-paths of length $0$ mod $p$ satisfy the Erdős-Pósa property. More generally, in the framework of undirected group-labelled graphs, we characterize the abelian groups $Γ$ and elements $\ell \in Γ$ for which the Erdős-Pósa property holds for $A$-paths of weight $\ell$. |
| title | Packing $A$-paths of length zero modulo a prime |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2009.12230 |