Vertices of degree k in edge-minimal, k-edge-connected graphs
classification
🧮 math.CO
keywords
degreeedge-minimalk-edge-connectedeverygraphgraphshalinvertices
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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.
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