Abstract
The number of k-node subtrees of a tree is its kth Whitney number. This paper investigates the behavior of certain alternating sums of these Whitney numbers and shows how they are related to the structure of maximum matchings in the tree. It is shown that the alternating sum of the Whitney numbers gives the maximum cardinality of an independent set of nodes. Moreover, a weighted alternating sum yields the number of nodes left uncovered by at least one maximum matching.
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