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

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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.
3 pages

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Combinatorics, 05C40

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http://salesiana.dossiersoluciones.com/handle/123456789/229654

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0905.1064
 http://arxiv.org/abs/0905.1064

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arXiv