锦标赛中的击中子式、细分与浸入
Hitting minors, subdivisions, and immersions in tournaments
AI总结：
本文利用Chudnovsky等人结果，证明锦标赛中强子式、蝴蝶子式、拓扑子式及浸入的击中问题满足Erdős-Pósa性质。
摘要：
Erdős-Pósa性质关联了组合结构的覆盖与打包参数，并主要在无向图背景下被研究。在本注记中，我们利用Chudnovsky、Fradkin、Kim和Seymour的结果证明：对于每个有向图H（相应地，强连通有向图H），包含H作为强子式（相应地，蝴蝶子式、拓扑子式）的有向图类在锦标赛类中具有顶点Erdős-Pósa性质。我们还证明，若H是强连通有向图，则包含H作为浸入的有向图类在锦标赛类中具有边Erdős-Pósa性质。
英文摘要：
The Erdős-Pósa property relates parameters of covering and packing of combinatorial structures and has been mostly studied in the setting of undirected graphs. In this note, we use results of Chudnovsky, Fradkin, Kim, and Seymour to show that, for every directed graph $H$ (resp. strongly-connected directed graph $H$), the class of directed graphs that contain $H$ as a strong minor (resp. butterfly minor, topological minor) has the vertex-Erdős-Pósa property in the class of tournaments. We also prove that if $H$ is a strongly-connected directed graph, the class of directed graphs containing $H$ as an immersion has the edge-Erdős-Pósa property in the class of tournaments.
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