Erdős-Pósa property of tripods in directed graphs
Abstract
Let $D$ be a directed graphs with distinguished sets of sources $S\subseteq V(D)$ and sinks $T\subseteq V(D)$. A tripod in $D$ is a subgraph consisting of the union of two $S$-$T$-paths that have distinct start-vertices and the same end-vertex, and are disjoint apart from sharing a suffix. We prove that tripods in directed graphs exhibit the Erdős-Pósa property. More precisely, there is a function $f\colon \mathbb{N}\to \mathbb{N}$ such that for every digraph $D$ with sources $S$ and sinks $T$, if $D$ does not contain $k$ vertex-disjoint tripods, then there is a set of at most $f(k)$ vertices that meets all the tripods in $D$.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.16733
- arXiv:
- arXiv:2408.16733
- Bibcode:
- 2024arXiv240816733B
- Keywords:
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- Mathematics - Combinatorics;
- Computer Science - Discrete Mathematics
- E-Print:
- 12 pages, 4 figures