Tutte seminar - Geoff Whittle

Connectivity Functions

Abstract: 

For a finite set $E$ a function $\mu:2^E\rightarrow \mathbb Z$ is a {\em connectivity function} if it is symmetric and submodular. Matroid connectivity and vertex connectivity in graphs are captured by associated connectivity functions. Moreover, fundamental properties associated with branch width and tangles of matroids and graphs hold at the level of general connectivity functions. The fact that we can prove interesting things about them motivates the study of connectivity functions as objects of interest in their own right. In the talk I will discuss some initial findings of such a study. This is joint work with my MSc students Songbao Mo and Susan Jowett.