Let G be a connected graph, and let C be any circuit in G that does not contain every

Chapter 10, Problem 44

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Let G be a connected graph, and let C be any circuit in G that does not contain every vertex of C. Let \(G^{\prime}\) be the subgraph obtained by removing all the edges of C from G and also any vertices that become isolated when the edges of C are removed. Prove that there exists a vertex v such that v is in both C and \(G^{\prime}\).

Text Transcription:

G prime

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