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arXiv · 0905.1064

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

Carl Kingsford·Guillaume Marçais
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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.

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Carl Kingsford, Guillaume Marçais. 2009-05-07. Vertices of degree k in edge-minimal, k-edge-connected graphs. https://arxiv.org/abs/0905.1064

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