In this problem, you will develop a new proof that every tree with two or more vertices
Chapter 50, Problem 50.11(choose chapter or problem)
In this problem, you will develop a new proof that every tree with two or more vertices has a leaf. Here is an outline for your proof. a. First prove, using strong induction and the fact that every edge of a tree is a cut edge (Theorem 50.5), that a tree with n vertices has exactly n 1 edges. Please note that our previous proof of this fact (Theorem 50.9) used the fact that trees have leaves; that is why we need an alternative proof. b. Use (a) to prove that the average degree of a vertex in a tree is less than 2. c. Use (b) to prove that every tree (with at least two vertices) has a leaf.
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