Erd\Hos-P\'osa property of tripods in directed graphs
<|reference_start|>Erd\Hos-P\'osa property of tripods in directed graphs: 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 Erd\H{o}s-P\'osa 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 $D$.<|reference_end|>
@article{briański2024erd\h{o}s-p\'osa,
    title={Erd\H{o}s-P\'osa property of tripods in directed graphs},
    author={Marcin Bria'nski and Meike Hatzel and Karolina Okrasa and Micha{l}
  Pilipczuk},
    journal={arXiv preprint arXiv:2408.16733},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.16733},
    primaryClass={math.CO cs.DM}
}