Hitting minors, subdivisions, and immersions in tournaments

Abstract

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.

arXiv commentAccepted to Discrete Mathematics & Theoretical Computer Science. Difference with the previous version: use of the DMTCS article class. For a version with hyperlinks see the previous version

References in corpus (1)

• On the pathwidth of almost semicomplete digraphs

Cited by in corpus (1)

• On the Erdős-Pósa property for immersions and topological minors in tournaments