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arXiv · 2009.12230

Packing $A$-paths of length zero modulo a prime

Robin Thomas·Youngho Yoo
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Abstract

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 $\ell$.

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Robin Thomas, Youngho Yoo. 2024-06-24. Packing $A$-paths of length zero modulo a prime. https://doi.org/10.1016/j.jctb.2022.12.007

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