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  3. let a1 ? a2, . . . , an be a sequence of positive

Let a1 ? a2, . . . , an be a sequence of positive integers...

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Advance Math

Let a1 ? a2, . . . , an be a sequence of positive integers whosesum is 2n ? 2. Prove that there exists a tree T on n vertices whosevertices have degrees a1, a2, . . . , an.
Sketch of solution: Prove that there exist i and j such that ai = 1and aj ? 2. Remove ai, subtract 1 from aj and induct on n.

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