English

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.

Keywords

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