Vertices of degree k in edge-minimal, k-edge-connected graphs
Combinatorics
2009-05-08 v1
Abstract
Halin showed that every edge minimal, k-vertex connected graph has a vertex of degree k. In this note, we prove the analogue to Halin's theorem for edge-minimal, k-edge-connected graphs. We show there are two vertices of degree k in every edge-minimal, k-edge-connected graph.
Cite
@article{arxiv.0905.1064,
title = {Vertices of degree k in edge-minimal, k-edge-connected graphs},
author = {Carl Kingsford and Guillaume Marçais},
journal= {arXiv preprint arXiv:0905.1064},
year = {2009}
}
Comments
3 pages