Trees with non log-concave independent set sequences

David Galvin

Trees with non log-concave independent set sequences

Combinatorics 2026-01-27 v2

Authors: David Galvin

Abstract

We construct a family of trees with independence numbers going to infinity for which the log-concavity relation for the independent set sequence of a tree $T$ in the family fails at around $\alpha(T)\left(1-1/(16\log \alpha(T))\right)$ . Here $\alpha(T)$ is the independence number of $T$ . This resolves a conjecture of Kadrawi and Levit.

Cite

@article{arxiv.2502.10654,
  title  = {Trees with non log-concave independent set sequences},
  author = {David Galvin},
  journal= {arXiv preprint arXiv:2502.10654},
  year   = {2026}
}

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