Recent techniques and results on the Erd\H{o}s-P\'osa property

TL;DR

This paper reviews recent techniques related to the Erdős-Pósa property, emphasizing tree-like decompositions, and provides a unified overview of the current research landscape in this area.

Contribution

It offers a comprehensive synthesis of recent methods and results concerning the Erdős-Pósa property, highlighting advances and unifying diverse approaches.

Findings

Recent techniques leverage tree decompositions.

Unified presentation of Erdős-Pósa results.

Enhanced understanding of packing and covering relations.

Abstract

Several min-max relations in graph theory can be expressed in the framework of the Erd\H{o}s-P\'osa property. Typically, this property reveals a connection between packing and covering problems on graphs. We describe some recent techniques for proving this property that are related to tree-like decompositions. We also provide an unified presentation of the current state of the art on this topic.