This record contains the current manuscript for the project “Erdos Problem #993: Tree Independence Polynomial Unimodality. ” The paper proves that the mean independent-set size satisfies mu (T) < n/3 for every tree with dₗeaf <= 1, develops structural reductions that constrain any counterexample, and reports exhaustive verification of unimodality for all 8, 691, 747, 673 trees on n <= 29 vertices. It also includes asymptotic results for leaf attachment and a computer-assisted extremal analysis for spider families. This version is the minor-revision polish snapshot dated 2026-03-18. It tightens several arguments, clarifies the conditional framework and computational pipeline, and improves the presentation of formalization and artifact status. The conjecture that every tree independence polynomial is unimodal remains open.
Brett Reynolds (Thu,) studied this question.