Graphs with treewidth ≤ k have spanning-tree polynomials T_G such that T_G^{-β} is completely monotone for every β > (k-1)/2.
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Bounded Treewidth and Complete Monotonicity for Scott-Sokal Spanning-Tree Polynomials
Graphs with treewidth ≤ k have spanning-tree polynomials T_G such that T_G^{-β} is completely monotone for every β > (k-1)/2.