Tangles and Connectivity in Graphs

Abstract

This paper is a short introduction to the theory of tangles, both in graphs and general connectivity systems. An emphasis is put on the correspondence between tangles of order k and k-connected components. In particular, we prove that there is a one-to-one correspondence between the triconnected components of a graph and its tangles of order 3.

Preliminary version of a paper that will appear in Proceedings of the 10th International Conference on Language and Automata Theory and Applications, 2016