Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.03025 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In 1987, Alavi, Malde, Schwenk and Erdős conjectured that the independence polynomials of trees are unimodal. Subsequently, many researchers proposed strengthening this conjecture to log-concavity. In 2023, Kadrawi, Levit, Yosef, and Mizrachi discovered independence polynomials of trees of order 26 that are not log-concave, which led them to construct two infinite families of such polynomials, denoted by $T_{3,m,n}$ and $T_{3,m,n}^*$. In this paper, we show that these two infinite families also satisfy the unimodal conjecture raised by Alavi, Malde, Schwenk, and Erdős.