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MacPhee","submitted_at":"2013-08-21T15:27:42Z","abstract_excerpt":"We study the asymptotic behavior of four statistics associated with subtrees of complete graphs: the uniform probability $p_n$ that a random subtree is a spanning tree of $K_n$, the weighted probability $q_n$ (where the probability a subtree is chosen is proportional to the number of edges in the subtree) that a random subtree spans and the two expectations associated with these two probabilities. 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