Seminar - Johannes Carmesin

Tree-structure vs. Tangles in Graphs and Matroids

Abstract: 

How do we decompose a k-connected graph into "its (k+1)-connected components"? One possible concept of highly connected components are tangles, as introduced by Robertson and Seymour. These can be separated in a tree-like way. But we can do much more...

Developed further for infinite graphs our methods, unexpectedly, solve
a 25-year-old problem of Diestel.

The infinite theorem can be further applied to show that the circles in any graph together with its topological ends give rise to a matroid. This had previously only been known for locally finite graphs, whose ends are all topological.