Vertices of degree k in edge-minimal, k-edge-connected graphs

Details Vertices of degree k in edge-minimal, k-edge-connected graphs Vertices of degree k in edge-minimal, k-edge-connected graphs

2009-05-07

arxiv.org/abs/0905.1064v1

Mathematics

Combinatorics

3 pages

Scientific paper

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.

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