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

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

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Colby Messinger answered 1 year ago

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