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arXiv · 2010.00663

Zero $A$-paths and the Erdős-Pósa property

Arthur Ulmer
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Abstract

Let $Γ$ be an Abelian group. In this paper I characterize the $A$-paths of weight $0\inΓ$ that have the Erdős-Pósa property. Using this in an auxiliary graph, one can also easily characterize the $A$-paths of weight $γ\inΓ$ that have the Erdős-Pósa property. These results also extend to long paths, that is paths of some minimum length. A structural result on zero walls with non-zero linkages will be proven as a means to prove the main result of this paper. This immediately implies that zero cycles with respect to an Abelian group $Γ$ have the Erdős-Pósa property.

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Arthur Ulmer. 2020-10-01. Zero $A$-paths and the Erdős-Pósa property. https://arxiv.org/abs/2010.00663

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