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Unformatted text preview: T . By the induction hypothesis, T has one more leaf node than it has nodes of degree 2. Now, restore the leaf node that was removed to form T . There are two possible cases. (1) If this leaf node is the only child of its parent in T , then the number of nodes of degree 2 has not changed, nor has the number of leaf nodes. Thus, the theorem holds. (2) If this leaf node is the child of a node in T with degree 2, then that node has degree 1 in T . Thus, by restoring the leaf node we are adding one new leaf node and one new node of degree 2. Thus, the theorem holds. By mathematical induction, the theorem is correct. 32...
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- Fall '08