# Trees and Graphs with Non Log-concave Dominating Set Sequence via AI Tools

arXiv: https://arxiv.org/abs/2605.02193 · HTML: https://mlsanity.com/paper/2605.02193/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 19 references that are in the map.
- First posted on arXiv 4 May 2026.

## Builds on (most cited first, 2 of 2)

- [PatternBoost: Constructions in Mathematics with a Little Help from AI](https://mlsanity.com/paper/2411.00566/) (2024)
- [An AI enhanced approach to the tree unimodality conjecture](https://mlsanity.com/paper/2510.18826/) (2025)

## Abstract (arXiv)

We give new examples of graphs and trees with dominating set sequences that are not log-concave. These examples were generated by PatternBoost, a transformer-based reinforcement learning software developed by Charton-Ellenberg-Wagner-Williamson. We also show: for any positive integer m, there exists a tree whose dominating set sequence is not log-concave for at least m indices by modifying a similar construction of Bautista-Ramos for the independent set sequence. We show that a large class of caterpillar graphs has log-concave dominating set sequences. A continuous analogue of the sequence is also log-concave for all graphs.