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(a)Prove that the average degree of a tree is less than 2. (Hint: Induction on number of vertices in the tree.) (b) Suppose every vertex

(a)Prove that the average degree of a tree is less than 2. (Hint: Induction on number of vertices in the tree.)

(b) Suppose every vertex in a graph has degree at least k. Explain why the graph has a path of length k. (Hint: Consider a longest path.)

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