AI RESEARCH
Trees and Graphs with Non Log-concave Dominating Set Sequence via AI Tools
arXiv CS.LG
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ArXi:2605.02193v1 Announce Type: cross 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.