Ends and vertices of small degree in infinite minimally k-(edge)-connected graphs

TL;DR

This paper reviews known bounds on minimum degree and vertices in finite minimally k-connected graphs and extends these concepts to infinite graphs by including ends of small degree.

Contribution

It demonstrates that many finite graph results on minimal connectivity bounds also apply to infinite graphs when considering ends of small degree.

Findings

Finite graph bounds extend to infinite graphs with ends of small degree

Most finite minimally k-connected graph results carry over to infinite graphs

Inclusion of ends of small degree is crucial for infinite graph analysis

Abstract

Bounds on the minimum degree and on the number of vertices at- taining it have been much studied for finite edge-/vertex-minimally k- connected/k-edge-connected graphs. We give an overview of the results known for finite graphs, and show that most of these carry over to infinite graphs if we consider ends of small degree as well as vertices.