Zero $A$-paths and the Erd\H{o}s-P\'osa property

Arthur Ulmer

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arXiv · 2010.00663

Zero $A$-paths and the Erd\H{o}s-P\'osa property

Arthur Ulmer

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Abstract

Let $\Gamma$ be an Abelian group. In this paper I characterize the $A$-paths of weight $0\in\Gamma$ that have the Erd\H{o}s-P\'osa property. Using this in an auxiliary graph, one can also easily characterize the $A$-paths of weight $\gamma\in\Gamma$ that have the Erd\H{o}s-P\'osa 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 $\Gamma$ have the Erd\H{o}s-P\'osa property.

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Arthur Ulmer. 2020-10-01. Zero $A$-paths and the Erd\H{o}s-P\'osa property. https://arxiv.org/abs/2010.00663

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