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Let every vertex of a graph $G$ have $\delta=3$ and let $G$ have no cut-edge. Then prove that $G$ has a perfect matching. A cut edge is an edge whose deletion increases the number of connected components.

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Is this homework? What have you learnt about in class? Could you say what you've tried? – Colin McQuillan Jul 7 '12 at 9:23
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This is the so called Petersen Theorem which can be proven using Tutte's theorem

Let me know if you need a more in depth proof.

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A more in-depth proof would be fantastic. – Xuan Huang Jul 7 '12 at 15:27

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