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4. We need two quick definitions before the following question: Definition 0.3. Let G = (V, E) be an undirected graph, and let v EV.

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4. We need two quick definitions before the following question: Definition 0.3. Let G = (V, E) be an undirected graph, and let v EV. The degree of v is the number of edges in G involving v. Definition 0.4. A trail is called a maximal trail if it is not possible to insert vertices and edges into the trail to obtain a longer trail. Prove the following: Let G = (V, E) be an undirected graph. If every vertex of G has even degree, then every maximal trail of positive length in G has the same start and end vertex. hint: draw an actual graph where every vertex has even degree, and highlight a trail on it

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