Abstract
The number of k node subtrees of a tree is its kth Whitney number. This paper establishes quadratic bounds in the number of nodes on the alternating sum of the Whitney numbers weighted by k 2. The lower bound is achieved precisely for paths on an even number of nodes. The upper bound is achieved for Edmonds' alternating trees. A rooted alternating sum is shown to be related to the Gallai-Edmonds matching decomposition and the structure of maximum independent sets in the tree.
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