Ends and Vertices of Small Degree in Infinite Minimally $k$-(Edge)-Connected Graphs

Authors:
Maya Stein
Affiliations:
mstein@dim.uchile.cl
Venue:
SIAM Journal on Discrete Mathematics
Year:
2010

Citing 5
Cited 0

The number of vertices of degree k in a minimally k-edge-connected graph

Journal of Combinatorial Theory Series B
Connectivity and network flows

Handbook of combinatorics (vol. 1)
Forcing highly connected subgraphs

Journal of Graph Theory
On end degrees and infinite cycles in locally finite graphs

Combinatorica
Duality of ends

Combinatorics, Probability and Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Bounds on the minimum degree and on the number of vertices attaining 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.