### Tangles and approximate packing-covering duality

- Series
- Graph Theory Working Seminar
- Time
- Thursday, October 10, 2019 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Youngho Yoo – Georgia Tech

Tangles capture a notion of high-connectivity in graphs which differs from $k$-connectivity. Instead of requiring that a small vertex set $X$ does not disconnect the graph $G$, a tangle “points” to the connected component of $G-X$ that contains most of the “highly connected part”. Developed initially by Robertson and Seymour in the graph minors project, tangles have proven to be a fundamental tool in studying the general structure of graphs and matroids. Tangles are also useful in proving that certain families of graphs satisfy an approximate packing-covering duality, also known as the Erd\H{o}s-P\'osa property. In this talk I will give a gentle introduction to tangles and describe some basic applications related to the Erd\H{o}s-P\'osa property.