Trees and Graphs with Non Log-concave Dominating Set Sequence via AI Tools
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915976778350592 |
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| author | Du, Alina Heilman, Steven Panova, Greta |
| author_facet | Du, Alina Heilman, Steven Panova, Greta |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02193 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Trees and Graphs with Non Log-concave Dominating Set Sequence via AI Tools Du, Alina Heilman, Steven Panova, Greta Combinatorics Artificial Intelligence Discrete Mathematics Machine Learning 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. |
| title | Trees and Graphs with Non Log-concave Dominating Set Sequence via AI Tools |
| topic | Combinatorics Artificial Intelligence Discrete Mathematics Machine Learning |
| url | https://arxiv.org/abs/2605.02193 |