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arXiv · 2502.10654

Trees with non log-concave independent set sequences

David Galvin
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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 $α(T)\left(1-1/(16\log α(T))\right)$. Here $α(T)$ is the independence number of $T$. This resolves a conjecture of Kadrawi and Levit.

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David Galvin. 2026-01-23. Trees with non log-concave independent set sequences. https://arxiv.org/abs/2502.10654

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