Łukasz Bożyk ; Michał Pilipczuk - On the Erdős-Pósa property for immersions and topological minors in tournaments

dmtcs:7099 - Discrete Mathematics & Theoretical Computer Science, April 5, 2022, vol. 24, no. 1 - https://doi.org/10.46298/dmtcs.7099
On the Erdős-Pósa property for immersions and topological minors in tournaments

Authors: Łukasz Bożyk ; Michał Pilipczuk

We consider the Erdős-Pósa property for immersions and topological minors in tournaments. We prove that for every simple digraph $H$, $k\in \mathbb{N}$, and tournament $T$, the following statements hold: (i) If in $T$ one cannot find $k$ arc-disjoint immersion copies of $H$, then there exists a set of $\mathcal{O}_H(k^3)$ arcs that intersects all immersion copies of $H$ in $T$. (ii) If in $T$ one cannot find $k$ vertex-disjoint topological minor copies of $H$, then there exists a set of $\mathcal{O}_H(k\log k)$ vertices that intersects all topological minor copies of $H$ in $T$. This improves the results of Raymond [DMTCS '18], who proved similar statements under the assumption that $H$ is strongly connected.


Volume: vol. 24, no. 1
Section: Graph Theory
Published on: April 5, 2022
Accepted on: March 9, 2022
Submitted on: January 19, 2021
Keywords: Mathematics - Combinatorics,05C70,G.2.2


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