mlsanityData to 14 Oct 2026

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

arXiv 2605.02193 ↗First posted 4 May 2026math.CO cs.AI cs.DMcited by 0

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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.

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.

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References · 2

  1. 2024PatternBoost: Constructions in Mathematics with a Little Help from AIcited by 34
  2. 2025An AI enhanced approach to the tree unimodality conjecturecited by 1

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